#sovietliterature — Public Fediverse posts
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Cecil Rhodes And His Time by Apolion Davidson
Cecil Rhodes…
He has been spoken and written about for a hundred years. Do we really need yet another book?
And does his time, the age when the world was divided up by the European countries using people like Rhodes, really need to be written about again? After all, the age of colonialism is past.
When undertaking this book, the author believed that only now that the political dominance of colonialism has ended can one truly grasp this phenomenon as a whole. And this must be done since the imprint of colonialism still remains on states, and even continents, and on the lives and characters of their inhabitants.
The figure of Rhodes helps one to understand a great deal about how colonialism functioned and about the psychology of people of that time. Why did Rhodes become a symbol of the largest empire in the history of mankind? Why was it Rhodes who became the idol of colonialism in the epoch of the division of the world? And what impression did his personality leave on the nature of colonialism?
These are some of the questions which the book tries to answer.
Translated from the Russian by Christopher English
Designed by Oleg Grebenyuk
Jacket: The battle of the Umguza (April 22, 1896). reproduced from Oliver Ransford’s book Bulawayo: Historic Battleground of Rhodesia, Cape Town, 1968.
Title page: A late nineteenth-century map of Southern Africa showing the countries conquered by Rhodes (from the book Rhodes by J. G. Lockhart and Hon. C. M. Woodhouse, London, 1963).
You can get the book here and here
This is a cleaned, optimised scan.
A 1988 Soviet work. Scanned by Ismail.Follow us on
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Contents
Page
6 Testament of a Young Man
The Gold and Diamond King
26 “How Cecil Rhodes Made His Fortune”
64 His Road to Politics
79 Battle of the Magnates
Hero of the Day
96 The Land of Ophir Between the Zambezi and the Limpopo
120 From the “White Queen” to Inkosi Lobengula
165 Setting Up His Own State
182 His First Military Campaign
214 And the First War
239 The Idol of His Day
Instigator of the Boer War
262 The Conspiracy Against the Afrikaners
286 Rhodesia Against Rhodes
314 Mere Setback or Utter Debacle?
338 “Terug na Die Ou Transvaal” (“Back to the Old Transvaal”)
370 Fading Away
393 Conclusion
400 Appendix
416 References
436 Name Index
#1988 #africanSubjugation #boerWars #britishColonialism #britishImperialism #deBeerCompany #history #southAfrica #southernAfrica #sovietLiterature -
Anthony Eden by V. Trukhanovsky
In his monograph, V. Trukhanovsky, Corresponding Member of the USSR Academy of Sciences and a specialist on contemporary British history, presents a political biography of the famous British diplomat, Foreign Minister and Prime Minister, Anthony Eden, who played an important role in British foreign policy from the 1930s to the 1950s.
This political portrait of Anthony Eden also serves to illustrate Anglo-Soviet, Anglo-American and Anglo-European relations, particularly in the immediate pre-war years.
The author devotes specific attention to Eden’s political activity during the creation of the anti-Hitler coalition and in the post-war period.
This book represents a notable contribution to the elaboration of the history of international relations, and will be of interest to the wide readership.
Translated from the Russian by Ruth English Designed by Inna BorisovaYou can get the book here and here
This is a cleaned optimised scan.
A 1984 Soviet work. Scanned by Ismail, sent to him by Crickwich.
Contents
From the Author 5
Chapter I The Beginning of the Road 7
Chapter II The First Stage in the Policy of “Appeasement” 41
Chapter III Foreign Secretary in a Government of “Appeasers” 96
Chapter IV The War Years 174
Chapter V Opposition: The First Post-War Decade 223
Chapter VI Failure of a Policy, Failure of a Career 285
Epilogue 345
#1984 #history #internationalRelations #sovietLiterature #sovietBritishRelations -
World War II Myth The Realities by Oleg Rheshevsky
The history of World War II continues, to fascinate scholars and writers, political leaders and statesmen, military specialists and laymen the world over. As before, it stirs people’s hearts and minds. That lasting impact is due to the organic link between present day developments and the realities of the past. This book gives the Soviet view of the causes, principal events and results of the war. The polemic against Western historians aims at a correct understanding of the lessons of the war and of the vital importance of the people’s endeavours in behalf of detente and international security for preventing another world holocaust that might spell the end of civilisation.
Translated from the Russian by Sergei Chulaki
Designed by Igor Saiko
You can get the book here and here
This is a cleaned, optimised scan.
A 1984 Soviet work. Scanned by Ismail, sent to him by Nathan O’Connor.
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Contents
Introduction 5
Chapter One
Could the Second World War Have Been Prevented? 11
The Causes of the War 11
Two Worlds Two Policies 29
A Stream of Lies and the Truth of History 57
The Policy of Appeasement Bears Its Fruit 79
Chapter Two
Aggression and Disaster 103
Moscow Stalingrad Kursk 104
The Liberation Mission of the Soviet Armed Forces 137
On the Soviet Contribution to the Victory over Japan 150
Why Is the Bourgeois Concept of “Decisive Battles” Unfounded? 157
Chapter Three
The Sources of Victory over the Aggressors 170
The Economic Factor 172
The Political Factor 193
The Art of War 209
The Vanguard of the People and the Army 221
Chapter Four
The Second World War and Our Time 227
The New Balance of Forces and the Myth of the Soviet Threat 228
Historians vs. History 245
Conclusion 269
Name Index 273
#1984 #history #naziGermany #sovietLiterature #sovietRedArmy #worldWar2 -
விலங்கியல் – வ. ஷாலாயேவ், நி. ரீக்கவ் (Zoology In Tamil by V. Shalayev, N. Rykov)
A comprehensive textbook on zoology.
Translated from the Russian.
விலங்கியல் தொடர்பான முழுமையான பாடநூல்.ரஷிய மொழியில் இருந்து மொழிபெயர்க்கப்பட்டது.
Original scan by Digital Tamil Studies project. This is a cleaned, optimised scan.
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#anatomy #animals #உடறகற #உடறபயல #சவயதஇலககயம #வலஙகயல #வலஙககள #physiology #sovietLiterature #zoology -
In The World Of Isotopes by V. Mezentsev
A little book describing basics of isotopes and their applications in various fields.
Translated from the Russian by George Yankovsky
You can get the book here and here
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Contents
1. On the Threshold of a New Era 5
#applicationsOfIsotopes #atomicEnergy #atomicNucleus #chemistry #electrons #irradiation #nuclearMedicine #nuclearTechnology #physics #popularScience #radioIsotopes #sovietLiterature #xRays
2. “Factories of Radioisotopes” 7
3. “Radioeyes” 12
4. Radioisotopes and Geological Prospecting 20
5. Tracer Atoms in Industry 22
6. Tracer Atoms in Chemistry 25
7. The Geological Clock 27
8. A Pocket Electric Station 32
9. The Atom in Agriculture 33
10. The Atom in Medicine 45 -
In The World Of Isotopes by V. Mezentsev
A little book describing basics of isotopes and their applications in various fields.
Translated from the Russian by George Yankovsky
You can get the book here and here
Credits to the original uploaders. This is a cleaned, optimised scan.
Follow us on
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Contents
1. On the Threshold of a New Era 5
#applicationsOfIsotopes #atomicEnergy #atomicNucleus #chemistry #electrons #irradiation #nuclearMedicine #nuclearTechnology #physics #popularScience #radioIsotopes #sovietLiterature #xRays
2. “Factories of Radioisotopes” 7
3. “Radioeyes” 12
4. Radioisotopes and Geological Prospecting 20
5. Tracer Atoms in Industry 22
6. Tracer Atoms in Chemistry 25
7. The Geological Clock 27
8. A Pocket Electric Station 32
9. The Atom in Agriculture 33
10. The Atom in Medicine 45 -
In The World Of Isotopes by V. Mezentsev
A little book describing basics of isotopes and their applications in various fields.
Translated from the Russian by George Yankovsky
You can get the book here and here
Credits to the original uploaders. This is a cleaned, optimised scan.
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
1. On the Threshold of a New Era 5
#applicationsOfIsotopes #atomicEnergy #atomicNucleus #chemistry #electrons #irradiation #nuclearMedicine #nuclearTechnology #physics #popularScience #radioIsotopes #sovietLiterature #xRays
2. “Factories of Radioisotopes” 7
3. “Radioeyes” 12
4. Radioisotopes and Geological Prospecting 20
5. Tracer Atoms in Industry 22
6. Tracer Atoms in Chemistry 25
7. The Geological Clock 27
8. A Pocket Electric Station 32
9. The Atom in Agriculture 33
10. The Atom in Medicine 45 -
In The World Of Isotopes by V. Mezentsev
A little book describing basics of isotopes and their applications in various fields.
Translated from the Russian by George Yankovsky
You can get the book here and here
Credits to the original uploaders. This is a cleaned, optimised scan.
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
1. On the Threshold of a New Era 5
#applicationsOfIsotopes #atomicEnergy #atomicNucleus #chemistry #electrons #irradiation #nuclearMedicine #nuclearTechnology #physics #popularScience #radioIsotopes #sovietLiterature #xRays
2. “Factories of Radioisotopes” 7
3. “Radioeyes” 12
4. Radioisotopes and Geological Prospecting 20
5. Tracer Atoms in Industry 22
6. Tracer Atoms in Chemistry 25
7. The Geological Clock 27
8. A Pocket Electric Station 32
9. The Atom in Agriculture 33
10. The Atom in Medicine 45 -
In The World Of Isotopes by V. Mezentsev
A little book describing basics of isotopes and their applications in various fields.
Translated from the Russian by George Yankovsky
You can get the book here and here
Credits to the original uploaders. This is a cleaned, optimised scan.
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
1. On the Threshold of a New Era 5
#applicationsOfIsotopes #atomicEnergy #atomicNucleus #chemistry #electrons #irradiation #nuclearMedicine #nuclearTechnology #physics #popularScience #radioIsotopes #sovietLiterature #xRays
2. “Factories of Radioisotopes” 7
3. “Radioeyes” 12
4. Radioisotopes and Geological Prospecting 20
5. Tracer Atoms in Industry 22
6. Tracer Atoms in Chemistry 25
7. The Geological Clock 27
8. A Pocket Electric Station 32
9. The Atom in Agriculture 33
10. The Atom in Medicine 45 -
A Brief Course Of Higher Mathematics by V.A. Kudryavtsev
The aim of this text is to set forth the essentials of higher mathematics and their applications in various fields. At present higher mathematics serves as the theoretical foundation for most branches of the natural, applied and engineering sciences. Therefore, every natural scientist must necessarily master its methods to be able to apply them for practical purposes.
Translated from the Russian by Leonid Levant
Many thanks to Guptaji for the scans and Balram Sharmaji of Kamgaar Prakashan for making this book available.
You can get the book here and here
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Contents
INTRODUCTION
Chapter 1. The Rectangular Coordinate System in the Plane and Its Application to Simple Problems
Sec. 1. Rectangular Coordinates of a Point in the Plane
Sec. 2. Transformation of Rectangular Coordinates
Sec. 3. The Distance Between Two Points in the Plane
Sec. 4. Dividing a Line Segment in a Given Ratio
Sec. 5. The Area of a Triangle
ExercisesChapter 2. The Equation of a Line
Sec. 6. Sets
Sec. 7. The Method of Coordinates in the Plane
Sec. 8. The Line as a Set of Points
Sec. 9. The Equation of a Line in the Plane
Sec. 10. Constructing a Line on the Basis of Its Equation
Sec. 11. Some Elementary Problems
Sec. 12. Two Basic Problems of Plane Analytical Geometry
Sec. 13. Algebraic Lines
ExercisesChapter 3. The Straight Line
Sec. 14. The Equation of a Straight Line
Sec. 15. The Angle Between Two Straight Lines
Sec. 16. The Equation of a Straight Line Passing Through a Given Point in a Given Direction
Sec. 17. The Equation of a Straight Line Passing Through Two Points (Two-Point Form)
Sec. 18. The Intercept Form of the Equation of a Straight Line
Sec. 19. The Point of Intersection of Two Straight Lines
Sec. 20. The Distance from a Point to a Straight Line
ExercisesChapter 4. Second-Order Lines
Sec. 21. The Circle
Sec. 22. Central Second-Order Curves (Conics)
Sec. 23. Focal Properties of Central Curves of the Second Order
Sec. 24. The Ellipse as a Uniformly Compressed Circle
Sec. 25. The Asymptotes of a Hyperbola
Sec. 26. The Graph of Inverse Proportionality
Sec. 27. Noncentral Quadric Curves
Sec. 28. The Focal Property of the Parabola
Sec. 29. The Graph of a Quadratic Trinomial
ExercisesChapter 5. Polar Coordinates. Parametric Equations of a Line
Sec. 30. Polar Coordinates
Sec. 31. Relationship Between Rectangular and Polar Coordinates
Sec. 32. Parametric Equations of a Line
Sec. 33. Parametric Equations of the Cycloid
ExercisesChapter 6. Functions
Sec. 34. Constants and Variables
Sec. 35. The Concept of Function
Sec. 36. Simplest Functional Relations
1. Direct Proportional Relation
2. Linear Relation
3. Inverse Proportional Relation
4. Quadratic Relation
5. Sinusoidal Relation
Sec. 37. Methods of Representing Functions
1. The Analytical Method
2. The Tabular Method
3. The Graphical Method
Sec. 38. The Concept of Function of Several Variables
Sec. 39. Implicit Function
Sec. 40. Inverse Function
Sec. 41. Classification of Functions of One Argument
Sec. 42. The Graphs of the Basic Elementary Functions
Sec. 43. Interpolation of Functions
ExercisesChapter 7. The Theory of Limits
Sec. 44. Real Numbers
Sec. 45. Errors of Approximate Numbers
Sec. 46. Limit of a Function
Sec. 47. One-Sided Limits of a Function
Sec. 48. Limit of a Sequence
Sec. 49. Infinitesimals
Sec. 50. Infinitely Large Quantities
Sec. 51. Basic Properties of Infinitesimals
Sec. 52. Basic Limit Theorems
Sec. 53. Some Tests for the Existence of the Limit of a Function
Sec. 54. The Limit of X
Sec. 55. The Number e
Sec. 56. Natural Logarithms
Sec. 57. Asymptotic Formulas
ExercisesChapter 8. Continuity of Functions
Sec. 58. Increments of an Argument and a Function. Continuity of a Function
Sec. 59. Another Definition of the Continuity of a Function
Sec. 60. Continuity of Basic Elementary Functions
Sec. 61. Basic Theorems on Continuous Functions
Sec. 62. Evaluation of Indeterminacies
Sec. 63. Classification of the Points of Discontinuity of a Function
ExercisesChapter 9. The Derivative of a Function
Sec. 64. A Tangent to a Curve – 159
Sec. 65. Velocity of a Moving Point – 161
Sec. 66. The Derivative Defined Generally – 163
Sec. 67. Other Applications of the Derivative – 166
Sec. 68. Relation Between the Continuity and Differentiability of a Function – 167
Sec. 69. The Notion of an Infinite Derivative – 169
Exercises – 169Chapter 10. Basic Derivative Theorems
Sec. 70. Introductory Notes – 170
Sec. 71. The Derivatives of Certain Simple Functions – 170
Sec. 72. Basic Differentiation Rules – 174
Sec. 73. The Derivative of a Composite Function – 179
Sec. 74. The Derivative of an Inverse Function – 182
Sec. 75. The Derivative of an Implicit Function – 184
Sec. 76. The Derivative of a Logarithmic Function – 185
Sec. 77. A Logarithmic Derivative – 188
Sec. 78. The Derivative of an Exponential Function – 188
Sec. 79. The Derivative of a Power Function – 190
Sec. 80. The Derivatives of Inverse Trigonometric Functions – 191
Sec. 81. The Derivative of a Function Represented Parametrically – 193
Sec. 82. The Table of Differentiation Formulas – 194
Sec. 83. Derivatives of Higher Orders – 195
Sec. 84. Physical Meaning of the Second Derivative – 195
Exercises – 196Chapter 11. Applications of Derivatives
Sec. 85. The Theorem About Finite Increments of a Function and Its Corollaries – 199
Sec. 86. Increase and Decrease of a Function of One Argument – 201
Sec. 87. L’Hospital’s Rule – 204
Sec. 88. Taylor’s Formula for a Polynomial – 208
Sec. 89. Binomial Formula – 210
Sec. 90. Taylor’s Formula for a Function – 211
Sec. 91. Maxima and Minima of a Function of One Variable – 213
Sec. 92. Concavity and Convexity of the Graph of a Function. Points of Inflection – 220
Sec. 93. Approximate Solution of Equations – 223
Sec. 94. Construction of Graphs of Functions – 227
Exercises – 230Chapter 12. Differentials
Sec. 95. The Differential of a Function – 232
Sec. 96. Relation Between the Differential of a Function and Its Derivative. The Differential of the Independent Variable – 235
Sec. 97. The Geometrical Meaning of the Differential – 237
Sec. 98. The Physical Meaning of the Differential – 237
Sec. 99. Approximate Calculation of Small Increments of a Function – 238
Sec. 100. Equivalence of the Increment and Differential of a Function – 239
Sec. 101. Properties of the Differential – 242
Sec. 102. Differentials of Higher Orders – 245
Exercises – 247Chapter 13. Indefinite Integral
Sec. 103. Antiderivative. Indefinite Integral – 248
Sec. 104. Basic Properties of the Indefinite Integral – 251
Sec. 105. Table of Simplest Indefinite Integrals – 253
Sec. 106. Independence of the Form of an Indefinite Integral of the Argument Chosen – 254
Sec. 107. Basic Integration Methods – 258
Sec. 108. Techniques for Integrating Rational Fractions with a Quadratic Denominator – 263
Sec. 109. Integration of Simplest Irrational Expressions – 267
Sec. 110. Integration of Trigonometric Functions – 269
Sec. 111. Integration of Certain Transcendental Functions – 271
Sec. 112. Cauchy’s Theorem. Some Important Integrals Inexpressible in Terms of Elementary Functions – 271
Exercises – 272Chapter 14. The Definite Integral
Sec. 113. The Concept of the Definite Integral – 275
Sec. 114. A Definite Integral with a Variable Upper Limit – 277
Sec. 115. Geometrical Meaning of the Definite Integral – 279
Sec. 116. Physical Meaning of the Definite Integral – 281
Sec. 117. Basic Properties of the Definite Integral – 282
Sec. 118. The Mean Value Theorem – 286
Sec. 119. Integration by Parts in the Definite Integral – 288
Sec. 120. Change of Variable in the Definite Integral (Integration by Substitution) – 289
Sec. 121. The Definite Integral as the Limit of an Integral Sum – 291
Sec. 122. Approximate Evaluation of Definite Integrals – 293
Sec. 123. Simpson’s Formula – 296
Sec. 124. Improper Integrals – 297
Exercises – 299Chapter 15. Applications of the Definite Integral
Sec. 125. Areas in Rectangular Coordinates – 301
Sec. 126. Areas in Polar Coordinates – 305
Sec. 127. The Arc Length in Rectangular Coordinates – 307
Sec. 128. The Arc Length in Polar Coordinates – 313
Sec. 129. Computing the Volume of a Solid by Known Cross Sections – 314
Sec. 130. The Volume of a Solid of Revolution – 316
Sec. 131. The Work of a Variable Force – 319
Sec. 132. Other Applications of the Definite Integral in Physics – 320
Exercises – 322Chapter 16. Complex Numbers
Sec. 133. Arithmetic Operations on Complex Numbers – 325
Sec. 134. The Complex Plane – 326
Sec. 135. Theorems on the Modulus and Argument – 328
Sec. 136. Taking the Root from a Complex Number – 329
Sec. 137. The Concept of a Function of a Complex Variable – 331
Exercises – 332Chapter 17. Determinants of Second and Third Order
Sec. 138. Second-Order Determinants – 335
Sec. 139. A System of Two Homogeneous Equations in Three Unknowns – 335
Sec. 140. Third-Order Determinants – 337
Sec. 141. Basic Properties of Determinants – 339
Sec. 142. A System of Three Linear Equations – 342
Sec. 143. A Homogeneous System of Three Linear Equations – 344
Sec. 144. A System of Linear Equations in Many Unknowns. Gauss’ Method – 346
Exercises – 349Chapter 18. Fundamentals of Vector Algebra
Sec. 145. Scalars and Vectors – 351
Sec. 146. The Sum of Several Vectors – 352
Sec. 147. The Difference of Vectors – 353
Sec. 148. Multiplication of a Vector by a Scalar – 353
Sec. 149. Collinear Vectors – 354
Sec. 150. Coplanar Vectors – 355
Sec. 151. The Projection of a Vector on an Axis – 356
Sec. 152. The Rectangular Cartesian Coordinates in Space – 359
Sec. 153. The Length and Direction of a Vector – 360
Sec. 154. The Distance Between Two Points in Space – 361
Sec. 155. Operations on Vectors Represented in the Coordinate Form – 362
Sec. 156. Scalar Product of Two Vectors – 364
Sec. 157. Scalar Product of Vectors in the Coordinate Form – 366
Sec. 158. Vector Product of Vectors – 367
Sec. 159. Vector Product in the Coordinate Form – 369
Sec. 160. Triple Scalar Product – 371
Exercises – 373Chapter 19. Fundamentals of Solid Analytic Geometry
Sec. 161. The Equations of a Surface and a Line in Space – 374
Sec. 162. The General Equation of a Plane – 380
Sec. 163. Angle Between Two Planes – 382
Sec. 164. Equations of a Straight Line in Space – 383
Sec. 165. The Derivative of a Vector Function – 387
Sec. 166. The Equation of a Sphere – 389
Sec. 167. The Equation of an Ellipsoid – 391
Sec. 168. The Equation of a Paraboloid of Revolution – 392
Exercises – 393Chapter 20. Functions of Several Variables
Sec. 169. The Concept of a Function of Several Variables – 395
Sec. 170. Continuity – 398
Sec. 171. Partial Derivatives of the First Order – 401
Sec. 172. The Total Differential of a Function – 403
Sec. 173. Application of the Differential of a Function to Approximate Computations – 409
Sec. 174. Directional Derivatives – 410
Sec. 175. The Gradient – 413
Sec. 176. Partial Derivatives of Higher Orders – 417
Sec. 177. Test for the Total Differential – 418
Sec. 178. The Extremum (Maximum or Minimum) of a Function of Several Variables – 420
Sec. 179. An Absolute Extremum of a Function – 422
Sec. 180. Constructing Empirical Formulas by the Method of Least Squares – 424
Exercises – 428Chapter 21. Series
Sec. 181. Examples of Infinite Series – 430
Sec. 182. Convergence of a Series – 431
Sec. 183. A Necessary Condition for Convergence of a Series – 435
Sec. 184. Comparison Tests – 437
Sec. 185. D’Alembert’s Test for Convergence – 440
Sec. 186. Absolute Convergence – 444
Sec. 187. Alternating Series. Leibniz’ Test – 446
Sec. 188. Power Series – 447
Sec. 189. Differentiation and Integration of Power Series – 450
Sec. 190. Expanding a Given Function into a Power Series – 450
Sec. 191. Maclaurin’s Series – 452
Sec. 192. Applying Maclaurin’s Series to Expanding Some Functions into Power Series – 453
Sec. 193. Applying Power Series to Approximate Calculations – 456
Sec. 194. Taylor’s Series – 459
Sec. 195. Series in a Complex Domain – 462
Sec. 196. Euler’s Formulas – 463
Sec. 197. Fourier Trigonometric Series – 464
Sec. 198. The Fourier Series of Even and Odd Functions – 473
Sec. 199. The Fourier Series of Nonperiodic Functions – 475
Exercises – 479Chapter 22. Differential Equations
Sec. 200. Basic Concepts – 481
Sec. 201. Differential Equations of the First Order – 484
Sec. 202. First-Order Equations with Variables Separable – 486
Sec. 203. Homogeneous Differential Equations of the First Order – 492
Sec. 204. Linear Differential Equations of the First Order – 495
Sec. 205. Euler’s Method – 500
Sec. 206. Differential Equations of the Second Order – 502
Sec. 207. Integrable Types of Second-Order Differential Equations – 504
Sec. 208. Reducing the Order of a Differential Equation – 510
Sec. 209. Integrating Differential Equations with the Aid of Power Series – 513
Sec. 210. Common Properties of the Solutions of Second-Order Linear Homogeneous Differential Equations – 514
Sec. 211. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients – 517
Sec. 212. Second-Order Linear Nonhomogeneous Differential Equations with Constant Coefficients – 523
Sec. 213. Differential Equations Containing Partial Derivatives – 533
Sec. 214. Linear Differential Equations with Partial Derivatives – 536
Sec. 215. Deriving the Heat Conduction Equation – 538
Sec. 216. The Problem on Temperature Distribution in a Limited Rod – 540
Exercises – 543
Chapter 23. Line Integrals
Sec. 217. The Line Integral of the First Kind – 546
Sec. 218. The Line Integral of the Second Kind – 548
Sec. 219. The Physical Meaning of the Line Integral of the Second Kind – 552
Sec. 220. Condition Under Which the Line Integral of the Second Kind is Independent of Path – 554
Sec. 221. The Work Performed by a Potential Force – 556
Exercises – 557Chapter 24. Double and Triple Integrals
Sec. 222. Double Integrals – 561
Sec. 223. The Double Integral in Rectangular Cartesian Coordinates – 564
Sec. 224. Expressing a Double Integral in Polar Coordinates – 571
Sec. 225. The Euler-Poisson Integral – 575
Sec. 226. Mean-Value Theorem – 576
Sec. 227. Geometrical Applications of the Double Integral – 578
Sec. 228. Physical Applications of the Double Integral – 579
Sec. 229. Triple Integrals – 584
Exercises – 588Chapter 25. Fundamentals of the Theory of Probability
A. Basic Definitions and Theorems
Sec. 230. Random Events – 591
Sec. 231. Algebra of Events – 593
Sec. 232. The Classical Definition of Probability – 594
Sec. 233. The Statistical Definition of Probability – 597
Sec. 234. The Theorem on Addition of Probabilities – 598
Sec. 235. A Complete Group of Events – 599
Sec. 236. The Theorem on Multiplication of Probabilities – 600
Sec. 237. Bayes’ Formula – 603B. Repeated Independent Trials
Sec. 238. Elements of Combinatorial Analysis – 604
Sec. 239. The Formula of Total Probability – 605
Sec. 240. The Binomial Law of Distribution of Probabilities – 607
Sec. 241. The Laplace Local Theorem – 608
Sec. 242. The Laplace Integral Theorem – 610
Sec. 243. Poisson’s Theorem – 614C. Random Variables and Their Numerical Characteristics
Sec. 244. A Random Discrete Variable and Its Distribution Law – 615
Sec. 245. Mathematical Expectation – 617
Sec. 246. Basic Properties of Mathematical Expectation – 618
Sec. 247. Variance – 621
Sec. 248. Continuous Random Variables. Distribution Functions – 626
Sec. 249. Numerical Characteristics of a Continuous Random Variable – 630
Sec. 250. Uniform Distribution – 631
Sec. 251. Normal Distribution – 633
Exercises – 636Chapter 26. The Concept of Linear Programming
Sec. 252. An n-Dimensional Vector Space – 639
Sec. 253. Sets in n-Dimensional Space – 641
Sec. 254. The Problem of Linear Programming – 645APPENDICES
A. Most Important Constants – 650
B. List of Formulas (Classified and Explained) – 650
I. Plane Analytic Geometry – 650
II. Differential Calculus—Functions of One Variable – 652
III. Integral Calculus – 654
IV. Complex Numbers, Determinants, and Systems of Simultaneous Equations – 658
V. Elements of Vector Algebra – 660
VI. Solid Analytic Geometry – 661
VII. Differential Calculus—Functions of Several Variables – 662
VIII. Series – 663
IX. Differential Equations – 666
X. Line Integrals – 668
XI. Double and Triple Integrals – 669
XII. Probability Theory – 671ANSWERS – 674
#1981 #complexNumbers #Derivatives #differentialEquations #functions #intergration #lineIntegrals #linearProgramming #mathematics #series #solidAnalyticGeometry #sovietLiterature #theoryOfLimits #vectorAlgebra
SUBJECT INDEX – 684 -
A Brief Course Of Higher Mathematics by V.A. Kudryavtsev
The aim of this text is to set forth the essentials of higher mathematics and their applications in various fields. At present higher mathematics serves as the theoretical foundation for most branches of the natural, applied and engineering sciences. Therefore, every natural scientist must necessarily master its methods to be able to apply them for practical purposes.
Translated from the Russian by Leonid Levant
Many thanks to Guptaji for the scans and Balram Sharmaji of Kamgaar Prakashan for making this book available.
You can get the book here and here
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
INTRODUCTION
Chapter 1. The Rectangular Coordinate System in the Plane and Its Application to Simple Problems
Sec. 1. Rectangular Coordinates of a Point in the Plane
Sec. 2. Transformation of Rectangular Coordinates
Sec. 3. The Distance Between Two Points in the Plane
Sec. 4. Dividing a Line Segment in a Given Ratio
Sec. 5. The Area of a Triangle
ExercisesChapter 2. The Equation of a Line
Sec. 6. Sets
Sec. 7. The Method of Coordinates in the Plane
Sec. 8. The Line as a Set of Points
Sec. 9. The Equation of a Line in the Plane
Sec. 10. Constructing a Line on the Basis of Its Equation
Sec. 11. Some Elementary Problems
Sec. 12. Two Basic Problems of Plane Analytical Geometry
Sec. 13. Algebraic Lines
ExercisesChapter 3. The Straight Line
Sec. 14. The Equation of a Straight Line
Sec. 15. The Angle Between Two Straight Lines
Sec. 16. The Equation of a Straight Line Passing Through a Given Point in a Given Direction
Sec. 17. The Equation of a Straight Line Passing Through Two Points (Two-Point Form)
Sec. 18. The Intercept Form of the Equation of a Straight Line
Sec. 19. The Point of Intersection of Two Straight Lines
Sec. 20. The Distance from a Point to a Straight Line
ExercisesChapter 4. Second-Order Lines
Sec. 21. The Circle
Sec. 22. Central Second-Order Curves (Conics)
Sec. 23. Focal Properties of Central Curves of the Second Order
Sec. 24. The Ellipse as a Uniformly Compressed Circle
Sec. 25. The Asymptotes of a Hyperbola
Sec. 26. The Graph of Inverse Proportionality
Sec. 27. Noncentral Quadric Curves
Sec. 28. The Focal Property of the Parabola
Sec. 29. The Graph of a Quadratic Trinomial
ExercisesChapter 5. Polar Coordinates. Parametric Equations of a Line
Sec. 30. Polar Coordinates
Sec. 31. Relationship Between Rectangular and Polar Coordinates
Sec. 32. Parametric Equations of a Line
Sec. 33. Parametric Equations of the Cycloid
ExercisesChapter 6. Functions
Sec. 34. Constants and Variables
Sec. 35. The Concept of Function
Sec. 36. Simplest Functional Relations
1. Direct Proportional Relation
2. Linear Relation
3. Inverse Proportional Relation
4. Quadratic Relation
5. Sinusoidal Relation
Sec. 37. Methods of Representing Functions
1. The Analytical Method
2. The Tabular Method
3. The Graphical Method
Sec. 38. The Concept of Function of Several Variables
Sec. 39. Implicit Function
Sec. 40. Inverse Function
Sec. 41. Classification of Functions of One Argument
Sec. 42. The Graphs of the Basic Elementary Functions
Sec. 43. Interpolation of Functions
ExercisesChapter 7. The Theory of Limits
Sec. 44. Real Numbers
Sec. 45. Errors of Approximate Numbers
Sec. 46. Limit of a Function
Sec. 47. One-Sided Limits of a Function
Sec. 48. Limit of a Sequence
Sec. 49. Infinitesimals
Sec. 50. Infinitely Large Quantities
Sec. 51. Basic Properties of Infinitesimals
Sec. 52. Basic Limit Theorems
Sec. 53. Some Tests for the Existence of the Limit of a Function
Sec. 54. The Limit of X
Sec. 55. The Number e
Sec. 56. Natural Logarithms
Sec. 57. Asymptotic Formulas
ExercisesChapter 8. Continuity of Functions
Sec. 58. Increments of an Argument and a Function. Continuity of a Function
Sec. 59. Another Definition of the Continuity of a Function
Sec. 60. Continuity of Basic Elementary Functions
Sec. 61. Basic Theorems on Continuous Functions
Sec. 62. Evaluation of Indeterminacies
Sec. 63. Classification of the Points of Discontinuity of a Function
ExercisesChapter 9. The Derivative of a Function
Sec. 64. A Tangent to a Curve – 159
Sec. 65. Velocity of a Moving Point – 161
Sec. 66. The Derivative Defined Generally – 163
Sec. 67. Other Applications of the Derivative – 166
Sec. 68. Relation Between the Continuity and Differentiability of a Function – 167
Sec. 69. The Notion of an Infinite Derivative – 169
Exercises – 169Chapter 10. Basic Derivative Theorems
Sec. 70. Introductory Notes – 170
Sec. 71. The Derivatives of Certain Simple Functions – 170
Sec. 72. Basic Differentiation Rules – 174
Sec. 73. The Derivative of a Composite Function – 179
Sec. 74. The Derivative of an Inverse Function – 182
Sec. 75. The Derivative of an Implicit Function – 184
Sec. 76. The Derivative of a Logarithmic Function – 185
Sec. 77. A Logarithmic Derivative – 188
Sec. 78. The Derivative of an Exponential Function – 188
Sec. 79. The Derivative of a Power Function – 190
Sec. 80. The Derivatives of Inverse Trigonometric Functions – 191
Sec. 81. The Derivative of a Function Represented Parametrically – 193
Sec. 82. The Table of Differentiation Formulas – 194
Sec. 83. Derivatives of Higher Orders – 195
Sec. 84. Physical Meaning of the Second Derivative – 195
Exercises – 196Chapter 11. Applications of Derivatives
Sec. 85. The Theorem About Finite Increments of a Function and Its Corollaries – 199
Sec. 86. Increase and Decrease of a Function of One Argument – 201
Sec. 87. L’Hospital’s Rule – 204
Sec. 88. Taylor’s Formula for a Polynomial – 208
Sec. 89. Binomial Formula – 210
Sec. 90. Taylor’s Formula for a Function – 211
Sec. 91. Maxima and Minima of a Function of One Variable – 213
Sec. 92. Concavity and Convexity of the Graph of a Function. Points of Inflection – 220
Sec. 93. Approximate Solution of Equations – 223
Sec. 94. Construction of Graphs of Functions – 227
Exercises – 230Chapter 12. Differentials
Sec. 95. The Differential of a Function – 232
Sec. 96. Relation Between the Differential of a Function and Its Derivative. The Differential of the Independent Variable – 235
Sec. 97. The Geometrical Meaning of the Differential – 237
Sec. 98. The Physical Meaning of the Differential – 237
Sec. 99. Approximate Calculation of Small Increments of a Function – 238
Sec. 100. Equivalence of the Increment and Differential of a Function – 239
Sec. 101. Properties of the Differential – 242
Sec. 102. Differentials of Higher Orders – 245
Exercises – 247Chapter 13. Indefinite Integral
Sec. 103. Antiderivative. Indefinite Integral – 248
Sec. 104. Basic Properties of the Indefinite Integral – 251
Sec. 105. Table of Simplest Indefinite Integrals – 253
Sec. 106. Independence of the Form of an Indefinite Integral of the Argument Chosen – 254
Sec. 107. Basic Integration Methods – 258
Sec. 108. Techniques for Integrating Rational Fractions with a Quadratic Denominator – 263
Sec. 109. Integration of Simplest Irrational Expressions – 267
Sec. 110. Integration of Trigonometric Functions – 269
Sec. 111. Integration of Certain Transcendental Functions – 271
Sec. 112. Cauchy’s Theorem. Some Important Integrals Inexpressible in Terms of Elementary Functions – 271
Exercises – 272Chapter 14. The Definite Integral
Sec. 113. The Concept of the Definite Integral – 275
Sec. 114. A Definite Integral with a Variable Upper Limit – 277
Sec. 115. Geometrical Meaning of the Definite Integral – 279
Sec. 116. Physical Meaning of the Definite Integral – 281
Sec. 117. Basic Properties of the Definite Integral – 282
Sec. 118. The Mean Value Theorem – 286
Sec. 119. Integration by Parts in the Definite Integral – 288
Sec. 120. Change of Variable in the Definite Integral (Integration by Substitution) – 289
Sec. 121. The Definite Integral as the Limit of an Integral Sum – 291
Sec. 122. Approximate Evaluation of Definite Integrals – 293
Sec. 123. Simpson’s Formula – 296
Sec. 124. Improper Integrals – 297
Exercises – 299Chapter 15. Applications of the Definite Integral
Sec. 125. Areas in Rectangular Coordinates – 301
Sec. 126. Areas in Polar Coordinates – 305
Sec. 127. The Arc Length in Rectangular Coordinates – 307
Sec. 128. The Arc Length in Polar Coordinates – 313
Sec. 129. Computing the Volume of a Solid by Known Cross Sections – 314
Sec. 130. The Volume of a Solid of Revolution – 316
Sec. 131. The Work of a Variable Force – 319
Sec. 132. Other Applications of the Definite Integral in Physics – 320
Exercises – 322Chapter 16. Complex Numbers
Sec. 133. Arithmetic Operations on Complex Numbers – 325
Sec. 134. The Complex Plane – 326
Sec. 135. Theorems on the Modulus and Argument – 328
Sec. 136. Taking the Root from a Complex Number – 329
Sec. 137. The Concept of a Function of a Complex Variable – 331
Exercises – 332Chapter 17. Determinants of Second and Third Order
Sec. 138. Second-Order Determinants – 335
Sec. 139. A System of Two Homogeneous Equations in Three Unknowns – 335
Sec. 140. Third-Order Determinants – 337
Sec. 141. Basic Properties of Determinants – 339
Sec. 142. A System of Three Linear Equations – 342
Sec. 143. A Homogeneous System of Three Linear Equations – 344
Sec. 144. A System of Linear Equations in Many Unknowns. Gauss’ Method – 346
Exercises – 349Chapter 18. Fundamentals of Vector Algebra
Sec. 145. Scalars and Vectors – 351
Sec. 146. The Sum of Several Vectors – 352
Sec. 147. The Difference of Vectors – 353
Sec. 148. Multiplication of a Vector by a Scalar – 353
Sec. 149. Collinear Vectors – 354
Sec. 150. Coplanar Vectors – 355
Sec. 151. The Projection of a Vector on an Axis – 356
Sec. 152. The Rectangular Cartesian Coordinates in Space – 359
Sec. 153. The Length and Direction of a Vector – 360
Sec. 154. The Distance Between Two Points in Space – 361
Sec. 155. Operations on Vectors Represented in the Coordinate Form – 362
Sec. 156. Scalar Product of Two Vectors – 364
Sec. 157. Scalar Product of Vectors in the Coordinate Form – 366
Sec. 158. Vector Product of Vectors – 367
Sec. 159. Vector Product in the Coordinate Form – 369
Sec. 160. Triple Scalar Product – 371
Exercises – 373Chapter 19. Fundamentals of Solid Analytic Geometry
Sec. 161. The Equations of a Surface and a Line in Space – 374
Sec. 162. The General Equation of a Plane – 380
Sec. 163. Angle Between Two Planes – 382
Sec. 164. Equations of a Straight Line in Space – 383
Sec. 165. The Derivative of a Vector Function – 387
Sec. 166. The Equation of a Sphere – 389
Sec. 167. The Equation of an Ellipsoid – 391
Sec. 168. The Equation of a Paraboloid of Revolution – 392
Exercises – 393Chapter 20. Functions of Several Variables
Sec. 169. The Concept of a Function of Several Variables – 395
Sec. 170. Continuity – 398
Sec. 171. Partial Derivatives of the First Order – 401
Sec. 172. The Total Differential of a Function – 403
Sec. 173. Application of the Differential of a Function to Approximate Computations – 409
Sec. 174. Directional Derivatives – 410
Sec. 175. The Gradient – 413
Sec. 176. Partial Derivatives of Higher Orders – 417
Sec. 177. Test for the Total Differential – 418
Sec. 178. The Extremum (Maximum or Minimum) of a Function of Several Variables – 420
Sec. 179. An Absolute Extremum of a Function – 422
Sec. 180. Constructing Empirical Formulas by the Method of Least Squares – 424
Exercises – 428Chapter 21. Series
Sec. 181. Examples of Infinite Series – 430
Sec. 182. Convergence of a Series – 431
Sec. 183. A Necessary Condition for Convergence of a Series – 435
Sec. 184. Comparison Tests – 437
Sec. 185. D’Alembert’s Test for Convergence – 440
Sec. 186. Absolute Convergence – 444
Sec. 187. Alternating Series. Leibniz’ Test – 446
Sec. 188. Power Series – 447
Sec. 189. Differentiation and Integration of Power Series – 450
Sec. 190. Expanding a Given Function into a Power Series – 450
Sec. 191. Maclaurin’s Series – 452
Sec. 192. Applying Maclaurin’s Series to Expanding Some Functions into Power Series – 453
Sec. 193. Applying Power Series to Approximate Calculations – 456
Sec. 194. Taylor’s Series – 459
Sec. 195. Series in a Complex Domain – 462
Sec. 196. Euler’s Formulas – 463
Sec. 197. Fourier Trigonometric Series – 464
Sec. 198. The Fourier Series of Even and Odd Functions – 473
Sec. 199. The Fourier Series of Nonperiodic Functions – 475
Exercises – 479Chapter 22. Differential Equations
Sec. 200. Basic Concepts – 481
Sec. 201. Differential Equations of the First Order – 484
Sec. 202. First-Order Equations with Variables Separable – 486
Sec. 203. Homogeneous Differential Equations of the First Order – 492
Sec. 204. Linear Differential Equations of the First Order – 495
Sec. 205. Euler’s Method – 500
Sec. 206. Differential Equations of the Second Order – 502
Sec. 207. Integrable Types of Second-Order Differential Equations – 504
Sec. 208. Reducing the Order of a Differential Equation – 510
Sec. 209. Integrating Differential Equations with the Aid of Power Series – 513
Sec. 210. Common Properties of the Solutions of Second-Order Linear Homogeneous Differential Equations – 514
Sec. 211. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients – 517
Sec. 212. Second-Order Linear Nonhomogeneous Differential Equations with Constant Coefficients – 523
Sec. 213. Differential Equations Containing Partial Derivatives – 533
Sec. 214. Linear Differential Equations with Partial Derivatives – 536
Sec. 215. Deriving the Heat Conduction Equation – 538
Sec. 216. The Problem on Temperature Distribution in a Limited Rod – 540
Exercises – 543
Chapter 23. Line Integrals
Sec. 217. The Line Integral of the First Kind – 546
Sec. 218. The Line Integral of the Second Kind – 548
Sec. 219. The Physical Meaning of the Line Integral of the Second Kind – 552
Sec. 220. Condition Under Which the Line Integral of the Second Kind is Independent of Path – 554
Sec. 221. The Work Performed by a Potential Force – 556
Exercises – 557Chapter 24. Double and Triple Integrals
Sec. 222. Double Integrals – 561
Sec. 223. The Double Integral in Rectangular Cartesian Coordinates – 564
Sec. 224. Expressing a Double Integral in Polar Coordinates – 571
Sec. 225. The Euler-Poisson Integral – 575
Sec. 226. Mean-Value Theorem – 576
Sec. 227. Geometrical Applications of the Double Integral – 578
Sec. 228. Physical Applications of the Double Integral – 579
Sec. 229. Triple Integrals – 584
Exercises – 588Chapter 25. Fundamentals of the Theory of Probability
A. Basic Definitions and Theorems
Sec. 230. Random Events – 591
Sec. 231. Algebra of Events – 593
Sec. 232. The Classical Definition of Probability – 594
Sec. 233. The Statistical Definition of Probability – 597
Sec. 234. The Theorem on Addition of Probabilities – 598
Sec. 235. A Complete Group of Events – 599
Sec. 236. The Theorem on Multiplication of Probabilities – 600
Sec. 237. Bayes’ Formula – 603B. Repeated Independent Trials
Sec. 238. Elements of Combinatorial Analysis – 604
Sec. 239. The Formula of Total Probability – 605
Sec. 240. The Binomial Law of Distribution of Probabilities – 607
Sec. 241. The Laplace Local Theorem – 608
Sec. 242. The Laplace Integral Theorem – 610
Sec. 243. Poisson’s Theorem – 614C. Random Variables and Their Numerical Characteristics
Sec. 244. A Random Discrete Variable and Its Distribution Law – 615
Sec. 245. Mathematical Expectation – 617
Sec. 246. Basic Properties of Mathematical Expectation – 618
Sec. 247. Variance – 621
Sec. 248. Continuous Random Variables. Distribution Functions – 626
Sec. 249. Numerical Characteristics of a Continuous Random Variable – 630
Sec. 250. Uniform Distribution – 631
Sec. 251. Normal Distribution – 633
Exercises – 636Chapter 26. The Concept of Linear Programming
Sec. 252. An n-Dimensional Vector Space – 639
Sec. 253. Sets in n-Dimensional Space – 641
Sec. 254. The Problem of Linear Programming – 645APPENDICES
A. Most Important Constants – 650
B. List of Formulas (Classified and Explained) – 650
I. Plane Analytic Geometry – 650
II. Differential Calculus—Functions of One Variable – 652
III. Integral Calculus – 654
IV. Complex Numbers, Determinants, and Systems of Simultaneous Equations – 658
V. Elements of Vector Algebra – 660
VI. Solid Analytic Geometry – 661
VII. Differential Calculus—Functions of Several Variables – 662
VIII. Series – 663
IX. Differential Equations – 666
X. Line Integrals – 668
XI. Double and Triple Integrals – 669
XII. Probability Theory – 671ANSWERS – 674
#1981 #complexNumbers #Derivatives #differentialEquations #functions #intergration #lineIntegrals #linearProgramming #mathematics #series #solidAnalyticGeometry #sovietLiterature #theoryOfLimits #vectorAlgebra
SUBJECT INDEX – 684 -
A Brief Course Of Higher Mathematics by V.A. Kudryavtsev
The aim of this text is to set forth the essentials of higher mathematics and their applications in various fields. At present higher mathematics serves as the theoretical foundation for most branches of the natural, applied and engineering sciences. Therefore, every natural scientist must necessarily master its methods to be able to apply them for practical purposes.
Translated from the Russian by Leonid Levant
Many thanks to Guptaji for the scans and Balram Sharmaji of Kamgaar Prakashan for making this book available.
You can get the book here and here
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
INTRODUCTION
Chapter 1. The Rectangular Coordinate System in the Plane and Its Application to Simple Problems
Sec. 1. Rectangular Coordinates of a Point in the Plane
Sec. 2. Transformation of Rectangular Coordinates
Sec. 3. The Distance Between Two Points in the Plane
Sec. 4. Dividing a Line Segment in a Given Ratio
Sec. 5. The Area of a Triangle
ExercisesChapter 2. The Equation of a Line
Sec. 6. Sets
Sec. 7. The Method of Coordinates in the Plane
Sec. 8. The Line as a Set of Points
Sec. 9. The Equation of a Line in the Plane
Sec. 10. Constructing a Line on the Basis of Its Equation
Sec. 11. Some Elementary Problems
Sec. 12. Two Basic Problems of Plane Analytical Geometry
Sec. 13. Algebraic Lines
ExercisesChapter 3. The Straight Line
Sec. 14. The Equation of a Straight Line
Sec. 15. The Angle Between Two Straight Lines
Sec. 16. The Equation of a Straight Line Passing Through a Given Point in a Given Direction
Sec. 17. The Equation of a Straight Line Passing Through Two Points (Two-Point Form)
Sec. 18. The Intercept Form of the Equation of a Straight Line
Sec. 19. The Point of Intersection of Two Straight Lines
Sec. 20. The Distance from a Point to a Straight Line
ExercisesChapter 4. Second-Order Lines
Sec. 21. The Circle
Sec. 22. Central Second-Order Curves (Conics)
Sec. 23. Focal Properties of Central Curves of the Second Order
Sec. 24. The Ellipse as a Uniformly Compressed Circle
Sec. 25. The Asymptotes of a Hyperbola
Sec. 26. The Graph of Inverse Proportionality
Sec. 27. Noncentral Quadric Curves
Sec. 28. The Focal Property of the Parabola
Sec. 29. The Graph of a Quadratic Trinomial
ExercisesChapter 5. Polar Coordinates. Parametric Equations of a Line
Sec. 30. Polar Coordinates
Sec. 31. Relationship Between Rectangular and Polar Coordinates
Sec. 32. Parametric Equations of a Line
Sec. 33. Parametric Equations of the Cycloid
ExercisesChapter 6. Functions
Sec. 34. Constants and Variables
Sec. 35. The Concept of Function
Sec. 36. Simplest Functional Relations
1. Direct Proportional Relation
2. Linear Relation
3. Inverse Proportional Relation
4. Quadratic Relation
5. Sinusoidal Relation
Sec. 37. Methods of Representing Functions
1. The Analytical Method
2. The Tabular Method
3. The Graphical Method
Sec. 38. The Concept of Function of Several Variables
Sec. 39. Implicit Function
Sec. 40. Inverse Function
Sec. 41. Classification of Functions of One Argument
Sec. 42. The Graphs of the Basic Elementary Functions
Sec. 43. Interpolation of Functions
ExercisesChapter 7. The Theory of Limits
Sec. 44. Real Numbers
Sec. 45. Errors of Approximate Numbers
Sec. 46. Limit of a Function
Sec. 47. One-Sided Limits of a Function
Sec. 48. Limit of a Sequence
Sec. 49. Infinitesimals
Sec. 50. Infinitely Large Quantities
Sec. 51. Basic Properties of Infinitesimals
Sec. 52. Basic Limit Theorems
Sec. 53. Some Tests for the Existence of the Limit of a Function
Sec. 54. The Limit of X
Sec. 55. The Number e
Sec. 56. Natural Logarithms
Sec. 57. Asymptotic Formulas
ExercisesChapter 8. Continuity of Functions
Sec. 58. Increments of an Argument and a Function. Continuity of a Function
Sec. 59. Another Definition of the Continuity of a Function
Sec. 60. Continuity of Basic Elementary Functions
Sec. 61. Basic Theorems on Continuous Functions
Sec. 62. Evaluation of Indeterminacies
Sec. 63. Classification of the Points of Discontinuity of a Function
ExercisesChapter 9. The Derivative of a Function
Sec. 64. A Tangent to a Curve – 159
Sec. 65. Velocity of a Moving Point – 161
Sec. 66. The Derivative Defined Generally – 163
Sec. 67. Other Applications of the Derivative – 166
Sec. 68. Relation Between the Continuity and Differentiability of a Function – 167
Sec. 69. The Notion of an Infinite Derivative – 169
Exercises – 169Chapter 10. Basic Derivative Theorems
Sec. 70. Introductory Notes – 170
Sec. 71. The Derivatives of Certain Simple Functions – 170
Sec. 72. Basic Differentiation Rules – 174
Sec. 73. The Derivative of a Composite Function – 179
Sec. 74. The Derivative of an Inverse Function – 182
Sec. 75. The Derivative of an Implicit Function – 184
Sec. 76. The Derivative of a Logarithmic Function – 185
Sec. 77. A Logarithmic Derivative – 188
Sec. 78. The Derivative of an Exponential Function – 188
Sec. 79. The Derivative of a Power Function – 190
Sec. 80. The Derivatives of Inverse Trigonometric Functions – 191
Sec. 81. The Derivative of a Function Represented Parametrically – 193
Sec. 82. The Table of Differentiation Formulas – 194
Sec. 83. Derivatives of Higher Orders – 195
Sec. 84. Physical Meaning of the Second Derivative – 195
Exercises – 196Chapter 11. Applications of Derivatives
Sec. 85. The Theorem About Finite Increments of a Function and Its Corollaries – 199
Sec. 86. Increase and Decrease of a Function of One Argument – 201
Sec. 87. L’Hospital’s Rule – 204
Sec. 88. Taylor’s Formula for a Polynomial – 208
Sec. 89. Binomial Formula – 210
Sec. 90. Taylor’s Formula for a Function – 211
Sec. 91. Maxima and Minima of a Function of One Variable – 213
Sec. 92. Concavity and Convexity of the Graph of a Function. Points of Inflection – 220
Sec. 93. Approximate Solution of Equations – 223
Sec. 94. Construction of Graphs of Functions – 227
Exercises – 230Chapter 12. Differentials
Sec. 95. The Differential of a Function – 232
Sec. 96. Relation Between the Differential of a Function and Its Derivative. The Differential of the Independent Variable – 235
Sec. 97. The Geometrical Meaning of the Differential – 237
Sec. 98. The Physical Meaning of the Differential – 237
Sec. 99. Approximate Calculation of Small Increments of a Function – 238
Sec. 100. Equivalence of the Increment and Differential of a Function – 239
Sec. 101. Properties of the Differential – 242
Sec. 102. Differentials of Higher Orders – 245
Exercises – 247Chapter 13. Indefinite Integral
Sec. 103. Antiderivative. Indefinite Integral – 248
Sec. 104. Basic Properties of the Indefinite Integral – 251
Sec. 105. Table of Simplest Indefinite Integrals – 253
Sec. 106. Independence of the Form of an Indefinite Integral of the Argument Chosen – 254
Sec. 107. Basic Integration Methods – 258
Sec. 108. Techniques for Integrating Rational Fractions with a Quadratic Denominator – 263
Sec. 109. Integration of Simplest Irrational Expressions – 267
Sec. 110. Integration of Trigonometric Functions – 269
Sec. 111. Integration of Certain Transcendental Functions – 271
Sec. 112. Cauchy’s Theorem. Some Important Integrals Inexpressible in Terms of Elementary Functions – 271
Exercises – 272Chapter 14. The Definite Integral
Sec. 113. The Concept of the Definite Integral – 275
Sec. 114. A Definite Integral with a Variable Upper Limit – 277
Sec. 115. Geometrical Meaning of the Definite Integral – 279
Sec. 116. Physical Meaning of the Definite Integral – 281
Sec. 117. Basic Properties of the Definite Integral – 282
Sec. 118. The Mean Value Theorem – 286
Sec. 119. Integration by Parts in the Definite Integral – 288
Sec. 120. Change of Variable in the Definite Integral (Integration by Substitution) – 289
Sec. 121. The Definite Integral as the Limit of an Integral Sum – 291
Sec. 122. Approximate Evaluation of Definite Integrals – 293
Sec. 123. Simpson’s Formula – 296
Sec. 124. Improper Integrals – 297
Exercises – 299Chapter 15. Applications of the Definite Integral
Sec. 125. Areas in Rectangular Coordinates – 301
Sec. 126. Areas in Polar Coordinates – 305
Sec. 127. The Arc Length in Rectangular Coordinates – 307
Sec. 128. The Arc Length in Polar Coordinates – 313
Sec. 129. Computing the Volume of a Solid by Known Cross Sections – 314
Sec. 130. The Volume of a Solid of Revolution – 316
Sec. 131. The Work of a Variable Force – 319
Sec. 132. Other Applications of the Definite Integral in Physics – 320
Exercises – 322Chapter 16. Complex Numbers
Sec. 133. Arithmetic Operations on Complex Numbers – 325
Sec. 134. The Complex Plane – 326
Sec. 135. Theorems on the Modulus and Argument – 328
Sec. 136. Taking the Root from a Complex Number – 329
Sec. 137. The Concept of a Function of a Complex Variable – 331
Exercises – 332Chapter 17. Determinants of Second and Third Order
Sec. 138. Second-Order Determinants – 335
Sec. 139. A System of Two Homogeneous Equations in Three Unknowns – 335
Sec. 140. Third-Order Determinants – 337
Sec. 141. Basic Properties of Determinants – 339
Sec. 142. A System of Three Linear Equations – 342
Sec. 143. A Homogeneous System of Three Linear Equations – 344
Sec. 144. A System of Linear Equations in Many Unknowns. Gauss’ Method – 346
Exercises – 349Chapter 18. Fundamentals of Vector Algebra
Sec. 145. Scalars and Vectors – 351
Sec. 146. The Sum of Several Vectors – 352
Sec. 147. The Difference of Vectors – 353
Sec. 148. Multiplication of a Vector by a Scalar – 353
Sec. 149. Collinear Vectors – 354
Sec. 150. Coplanar Vectors – 355
Sec. 151. The Projection of a Vector on an Axis – 356
Sec. 152. The Rectangular Cartesian Coordinates in Space – 359
Sec. 153. The Length and Direction of a Vector – 360
Sec. 154. The Distance Between Two Points in Space – 361
Sec. 155. Operations on Vectors Represented in the Coordinate Form – 362
Sec. 156. Scalar Product of Two Vectors – 364
Sec. 157. Scalar Product of Vectors in the Coordinate Form – 366
Sec. 158. Vector Product of Vectors – 367
Sec. 159. Vector Product in the Coordinate Form – 369
Sec. 160. Triple Scalar Product – 371
Exercises – 373Chapter 19. Fundamentals of Solid Analytic Geometry
Sec. 161. The Equations of a Surface and a Line in Space – 374
Sec. 162. The General Equation of a Plane – 380
Sec. 163. Angle Between Two Planes – 382
Sec. 164. Equations of a Straight Line in Space – 383
Sec. 165. The Derivative of a Vector Function – 387
Sec. 166. The Equation of a Sphere – 389
Sec. 167. The Equation of an Ellipsoid – 391
Sec. 168. The Equation of a Paraboloid of Revolution – 392
Exercises – 393Chapter 20. Functions of Several Variables
Sec. 169. The Concept of a Function of Several Variables – 395
Sec. 170. Continuity – 398
Sec. 171. Partial Derivatives of the First Order – 401
Sec. 172. The Total Differential of a Function – 403
Sec. 173. Application of the Differential of a Function to Approximate Computations – 409
Sec. 174. Directional Derivatives – 410
Sec. 175. The Gradient – 413
Sec. 176. Partial Derivatives of Higher Orders – 417
Sec. 177. Test for the Total Differential – 418
Sec. 178. The Extremum (Maximum or Minimum) of a Function of Several Variables – 420
Sec. 179. An Absolute Extremum of a Function – 422
Sec. 180. Constructing Empirical Formulas by the Method of Least Squares – 424
Exercises – 428Chapter 21. Series
Sec. 181. Examples of Infinite Series – 430
Sec. 182. Convergence of a Series – 431
Sec. 183. A Necessary Condition for Convergence of a Series – 435
Sec. 184. Comparison Tests – 437
Sec. 185. D’Alembert’s Test for Convergence – 440
Sec. 186. Absolute Convergence – 444
Sec. 187. Alternating Series. Leibniz’ Test – 446
Sec. 188. Power Series – 447
Sec. 189. Differentiation and Integration of Power Series – 450
Sec. 190. Expanding a Given Function into a Power Series – 450
Sec. 191. Maclaurin’s Series – 452
Sec. 192. Applying Maclaurin’s Series to Expanding Some Functions into Power Series – 453
Sec. 193. Applying Power Series to Approximate Calculations – 456
Sec. 194. Taylor’s Series – 459
Sec. 195. Series in a Complex Domain – 462
Sec. 196. Euler’s Formulas – 463
Sec. 197. Fourier Trigonometric Series – 464
Sec. 198. The Fourier Series of Even and Odd Functions – 473
Sec. 199. The Fourier Series of Nonperiodic Functions – 475
Exercises – 479Chapter 22. Differential Equations
Sec. 200. Basic Concepts – 481
Sec. 201. Differential Equations of the First Order – 484
Sec. 202. First-Order Equations with Variables Separable – 486
Sec. 203. Homogeneous Differential Equations of the First Order – 492
Sec. 204. Linear Differential Equations of the First Order – 495
Sec. 205. Euler’s Method – 500
Sec. 206. Differential Equations of the Second Order – 502
Sec. 207. Integrable Types of Second-Order Differential Equations – 504
Sec. 208. Reducing the Order of a Differential Equation – 510
Sec. 209. Integrating Differential Equations with the Aid of Power Series – 513
Sec. 210. Common Properties of the Solutions of Second-Order Linear Homogeneous Differential Equations – 514
Sec. 211. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients – 517
Sec. 212. Second-Order Linear Nonhomogeneous Differential Equations with Constant Coefficients – 523
Sec. 213. Differential Equations Containing Partial Derivatives – 533
Sec. 214. Linear Differential Equations with Partial Derivatives – 536
Sec. 215. Deriving the Heat Conduction Equation – 538
Sec. 216. The Problem on Temperature Distribution in a Limited Rod – 540
Exercises – 543
Chapter 23. Line Integrals
Sec. 217. The Line Integral of the First Kind – 546
Sec. 218. The Line Integral of the Second Kind – 548
Sec. 219. The Physical Meaning of the Line Integral of the Second Kind – 552
Sec. 220. Condition Under Which the Line Integral of the Second Kind is Independent of Path – 554
Sec. 221. The Work Performed by a Potential Force – 556
Exercises – 557Chapter 24. Double and Triple Integrals
Sec. 222. Double Integrals – 561
Sec. 223. The Double Integral in Rectangular Cartesian Coordinates – 564
Sec. 224. Expressing a Double Integral in Polar Coordinates – 571
Sec. 225. The Euler-Poisson Integral – 575
Sec. 226. Mean-Value Theorem – 576
Sec. 227. Geometrical Applications of the Double Integral – 578
Sec. 228. Physical Applications of the Double Integral – 579
Sec. 229. Triple Integrals – 584
Exercises – 588Chapter 25. Fundamentals of the Theory of Probability
A. Basic Definitions and Theorems
Sec. 230. Random Events – 591
Sec. 231. Algebra of Events – 593
Sec. 232. The Classical Definition of Probability – 594
Sec. 233. The Statistical Definition of Probability – 597
Sec. 234. The Theorem on Addition of Probabilities – 598
Sec. 235. A Complete Group of Events – 599
Sec. 236. The Theorem on Multiplication of Probabilities – 600
Sec. 237. Bayes’ Formula – 603B. Repeated Independent Trials
Sec. 238. Elements of Combinatorial Analysis – 604
Sec. 239. The Formula of Total Probability – 605
Sec. 240. The Binomial Law of Distribution of Probabilities – 607
Sec. 241. The Laplace Local Theorem – 608
Sec. 242. The Laplace Integral Theorem – 610
Sec. 243. Poisson’s Theorem – 614C. Random Variables and Their Numerical Characteristics
Sec. 244. A Random Discrete Variable and Its Distribution Law – 615
Sec. 245. Mathematical Expectation – 617
Sec. 246. Basic Properties of Mathematical Expectation – 618
Sec. 247. Variance – 621
Sec. 248. Continuous Random Variables. Distribution Functions – 626
Sec. 249. Numerical Characteristics of a Continuous Random Variable – 630
Sec. 250. Uniform Distribution – 631
Sec. 251. Normal Distribution – 633
Exercises – 636Chapter 26. The Concept of Linear Programming
Sec. 252. An n-Dimensional Vector Space – 639
Sec. 253. Sets in n-Dimensional Space – 641
Sec. 254. The Problem of Linear Programming – 645APPENDICES
A. Most Important Constants – 650
B. List of Formulas (Classified and Explained) – 650
I. Plane Analytic Geometry – 650
II. Differential Calculus—Functions of One Variable – 652
III. Integral Calculus – 654
IV. Complex Numbers, Determinants, and Systems of Simultaneous Equations – 658
V. Elements of Vector Algebra – 660
VI. Solid Analytic Geometry – 661
VII. Differential Calculus—Functions of Several Variables – 662
VIII. Series – 663
IX. Differential Equations – 666
X. Line Integrals – 668
XI. Double and Triple Integrals – 669
XII. Probability Theory – 671ANSWERS – 674
#1981 #complexNumbers #Derivatives #differentialEquations #functions #intergration #lineIntegrals #linearProgramming #mathematics #series #solidAnalyticGeometry #sovietLiterature #theoryOfLimits #vectorAlgebra
SUBJECT INDEX – 684 -
A Brief Course Of Higher Mathematics by V.A. Kudryavtsev
The aim of this text is to set forth the essentials of higher mathematics and their applications in various fields. At present higher mathematics serves as the theoretical foundation for most branches of the natural, applied and engineering sciences. Therefore, every natural scientist must necessarily master its methods to be able to apply them for practical purposes.
Translated from the Russian by Leonid Levant
Many thanks to Guptaji for the scans and Balram Sharmaji of Kamgaar Prakashan for making this book available.
You can get the book here and here
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
INTRODUCTION
Chapter 1. The Rectangular Coordinate System in the Plane and Its Application to Simple Problems
Sec. 1. Rectangular Coordinates of a Point in the Plane
Sec. 2. Transformation of Rectangular Coordinates
Sec. 3. The Distance Between Two Points in the Plane
Sec. 4. Dividing a Line Segment in a Given Ratio
Sec. 5. The Area of a Triangle
ExercisesChapter 2. The Equation of a Line
Sec. 6. Sets
Sec. 7. The Method of Coordinates in the Plane
Sec. 8. The Line as a Set of Points
Sec. 9. The Equation of a Line in the Plane
Sec. 10. Constructing a Line on the Basis of Its Equation
Sec. 11. Some Elementary Problems
Sec. 12. Two Basic Problems of Plane Analytical Geometry
Sec. 13. Algebraic Lines
ExercisesChapter 3. The Straight Line
Sec. 14. The Equation of a Straight Line
Sec. 15. The Angle Between Two Straight Lines
Sec. 16. The Equation of a Straight Line Passing Through a Given Point in a Given Direction
Sec. 17. The Equation of a Straight Line Passing Through Two Points (Two-Point Form)
Sec. 18. The Intercept Form of the Equation of a Straight Line
Sec. 19. The Point of Intersection of Two Straight Lines
Sec. 20. The Distance from a Point to a Straight Line
ExercisesChapter 4. Second-Order Lines
Sec. 21. The Circle
Sec. 22. Central Second-Order Curves (Conics)
Sec. 23. Focal Properties of Central Curves of the Second Order
Sec. 24. The Ellipse as a Uniformly Compressed Circle
Sec. 25. The Asymptotes of a Hyperbola
Sec. 26. The Graph of Inverse Proportionality
Sec. 27. Noncentral Quadric Curves
Sec. 28. The Focal Property of the Parabola
Sec. 29. The Graph of a Quadratic Trinomial
ExercisesChapter 5. Polar Coordinates. Parametric Equations of a Line
Sec. 30. Polar Coordinates
Sec. 31. Relationship Between Rectangular and Polar Coordinates
Sec. 32. Parametric Equations of a Line
Sec. 33. Parametric Equations of the Cycloid
ExercisesChapter 6. Functions
Sec. 34. Constants and Variables
Sec. 35. The Concept of Function
Sec. 36. Simplest Functional Relations
1. Direct Proportional Relation
2. Linear Relation
3. Inverse Proportional Relation
4. Quadratic Relation
5. Sinusoidal Relation
Sec. 37. Methods of Representing Functions
1. The Analytical Method
2. The Tabular Method
3. The Graphical Method
Sec. 38. The Concept of Function of Several Variables
Sec. 39. Implicit Function
Sec. 40. Inverse Function
Sec. 41. Classification of Functions of One Argument
Sec. 42. The Graphs of the Basic Elementary Functions
Sec. 43. Interpolation of Functions
ExercisesChapter 7. The Theory of Limits
Sec. 44. Real Numbers
Sec. 45. Errors of Approximate Numbers
Sec. 46. Limit of a Function
Sec. 47. One-Sided Limits of a Function
Sec. 48. Limit of a Sequence
Sec. 49. Infinitesimals
Sec. 50. Infinitely Large Quantities
Sec. 51. Basic Properties of Infinitesimals
Sec. 52. Basic Limit Theorems
Sec. 53. Some Tests for the Existence of the Limit of a Function
Sec. 54. The Limit of X
Sec. 55. The Number e
Sec. 56. Natural Logarithms
Sec. 57. Asymptotic Formulas
ExercisesChapter 8. Continuity of Functions
Sec. 58. Increments of an Argument and a Function. Continuity of a Function
Sec. 59. Another Definition of the Continuity of a Function
Sec. 60. Continuity of Basic Elementary Functions
Sec. 61. Basic Theorems on Continuous Functions
Sec. 62. Evaluation of Indeterminacies
Sec. 63. Classification of the Points of Discontinuity of a Function
ExercisesChapter 9. The Derivative of a Function
Sec. 64. A Tangent to a Curve – 159
Sec. 65. Velocity of a Moving Point – 161
Sec. 66. The Derivative Defined Generally – 163
Sec. 67. Other Applications of the Derivative – 166
Sec. 68. Relation Between the Continuity and Differentiability of a Function – 167
Sec. 69. The Notion of an Infinite Derivative – 169
Exercises – 169Chapter 10. Basic Derivative Theorems
Sec. 70. Introductory Notes – 170
Sec. 71. The Derivatives of Certain Simple Functions – 170
Sec. 72. Basic Differentiation Rules – 174
Sec. 73. The Derivative of a Composite Function – 179
Sec. 74. The Derivative of an Inverse Function – 182
Sec. 75. The Derivative of an Implicit Function – 184
Sec. 76. The Derivative of a Logarithmic Function – 185
Sec. 77. A Logarithmic Derivative – 188
Sec. 78. The Derivative of an Exponential Function – 188
Sec. 79. The Derivative of a Power Function – 190
Sec. 80. The Derivatives of Inverse Trigonometric Functions – 191
Sec. 81. The Derivative of a Function Represented Parametrically – 193
Sec. 82. The Table of Differentiation Formulas – 194
Sec. 83. Derivatives of Higher Orders – 195
Sec. 84. Physical Meaning of the Second Derivative – 195
Exercises – 196Chapter 11. Applications of Derivatives
Sec. 85. The Theorem About Finite Increments of a Function and Its Corollaries – 199
Sec. 86. Increase and Decrease of a Function of One Argument – 201
Sec. 87. L’Hospital’s Rule – 204
Sec. 88. Taylor’s Formula for a Polynomial – 208
Sec. 89. Binomial Formula – 210
Sec. 90. Taylor’s Formula for a Function – 211
Sec. 91. Maxima and Minima of a Function of One Variable – 213
Sec. 92. Concavity and Convexity of the Graph of a Function. Points of Inflection – 220
Sec. 93. Approximate Solution of Equations – 223
Sec. 94. Construction of Graphs of Functions – 227
Exercises – 230Chapter 12. Differentials
Sec. 95. The Differential of a Function – 232
Sec. 96. Relation Between the Differential of a Function and Its Derivative. The Differential of the Independent Variable – 235
Sec. 97. The Geometrical Meaning of the Differential – 237
Sec. 98. The Physical Meaning of the Differential – 237
Sec. 99. Approximate Calculation of Small Increments of a Function – 238
Sec. 100. Equivalence of the Increment and Differential of a Function – 239
Sec. 101. Properties of the Differential – 242
Sec. 102. Differentials of Higher Orders – 245
Exercises – 247Chapter 13. Indefinite Integral
Sec. 103. Antiderivative. Indefinite Integral – 248
Sec. 104. Basic Properties of the Indefinite Integral – 251
Sec. 105. Table of Simplest Indefinite Integrals – 253
Sec. 106. Independence of the Form of an Indefinite Integral of the Argument Chosen – 254
Sec. 107. Basic Integration Methods – 258
Sec. 108. Techniques for Integrating Rational Fractions with a Quadratic Denominator – 263
Sec. 109. Integration of Simplest Irrational Expressions – 267
Sec. 110. Integration of Trigonometric Functions – 269
Sec. 111. Integration of Certain Transcendental Functions – 271
Sec. 112. Cauchy’s Theorem. Some Important Integrals Inexpressible in Terms of Elementary Functions – 271
Exercises – 272Chapter 14. The Definite Integral
Sec. 113. The Concept of the Definite Integral – 275
Sec. 114. A Definite Integral with a Variable Upper Limit – 277
Sec. 115. Geometrical Meaning of the Definite Integral – 279
Sec. 116. Physical Meaning of the Definite Integral – 281
Sec. 117. Basic Properties of the Definite Integral – 282
Sec. 118. The Mean Value Theorem – 286
Sec. 119. Integration by Parts in the Definite Integral – 288
Sec. 120. Change of Variable in the Definite Integral (Integration by Substitution) – 289
Sec. 121. The Definite Integral as the Limit of an Integral Sum – 291
Sec. 122. Approximate Evaluation of Definite Integrals – 293
Sec. 123. Simpson’s Formula – 296
Sec. 124. Improper Integrals – 297
Exercises – 299Chapter 15. Applications of the Definite Integral
Sec. 125. Areas in Rectangular Coordinates – 301
Sec. 126. Areas in Polar Coordinates – 305
Sec. 127. The Arc Length in Rectangular Coordinates – 307
Sec. 128. The Arc Length in Polar Coordinates – 313
Sec. 129. Computing the Volume of a Solid by Known Cross Sections – 314
Sec. 130. The Volume of a Solid of Revolution – 316
Sec. 131. The Work of a Variable Force – 319
Sec. 132. Other Applications of the Definite Integral in Physics – 320
Exercises – 322Chapter 16. Complex Numbers
Sec. 133. Arithmetic Operations on Complex Numbers – 325
Sec. 134. The Complex Plane – 326
Sec. 135. Theorems on the Modulus and Argument – 328
Sec. 136. Taking the Root from a Complex Number – 329
Sec. 137. The Concept of a Function of a Complex Variable – 331
Exercises – 332Chapter 17. Determinants of Second and Third Order
Sec. 138. Second-Order Determinants – 335
Sec. 139. A System of Two Homogeneous Equations in Three Unknowns – 335
Sec. 140. Third-Order Determinants – 337
Sec. 141. Basic Properties of Determinants – 339
Sec. 142. A System of Three Linear Equations – 342
Sec. 143. A Homogeneous System of Three Linear Equations – 344
Sec. 144. A System of Linear Equations in Many Unknowns. Gauss’ Method – 346
Exercises – 349Chapter 18. Fundamentals of Vector Algebra
Sec. 145. Scalars and Vectors – 351
Sec. 146. The Sum of Several Vectors – 352
Sec. 147. The Difference of Vectors – 353
Sec. 148. Multiplication of a Vector by a Scalar – 353
Sec. 149. Collinear Vectors – 354
Sec. 150. Coplanar Vectors – 355
Sec. 151. The Projection of a Vector on an Axis – 356
Sec. 152. The Rectangular Cartesian Coordinates in Space – 359
Sec. 153. The Length and Direction of a Vector – 360
Sec. 154. The Distance Between Two Points in Space – 361
Sec. 155. Operations on Vectors Represented in the Coordinate Form – 362
Sec. 156. Scalar Product of Two Vectors – 364
Sec. 157. Scalar Product of Vectors in the Coordinate Form – 366
Sec. 158. Vector Product of Vectors – 367
Sec. 159. Vector Product in the Coordinate Form – 369
Sec. 160. Triple Scalar Product – 371
Exercises – 373Chapter 19. Fundamentals of Solid Analytic Geometry
Sec. 161. The Equations of a Surface and a Line in Space – 374
Sec. 162. The General Equation of a Plane – 380
Sec. 163. Angle Between Two Planes – 382
Sec. 164. Equations of a Straight Line in Space – 383
Sec. 165. The Derivative of a Vector Function – 387
Sec. 166. The Equation of a Sphere – 389
Sec. 167. The Equation of an Ellipsoid – 391
Sec. 168. The Equation of a Paraboloid of Revolution – 392
Exercises – 393Chapter 20. Functions of Several Variables
Sec. 169. The Concept of a Function of Several Variables – 395
Sec. 170. Continuity – 398
Sec. 171. Partial Derivatives of the First Order – 401
Sec. 172. The Total Differential of a Function – 403
Sec. 173. Application of the Differential of a Function to Approximate Computations – 409
Sec. 174. Directional Derivatives – 410
Sec. 175. The Gradient – 413
Sec. 176. Partial Derivatives of Higher Orders – 417
Sec. 177. Test for the Total Differential – 418
Sec. 178. The Extremum (Maximum or Minimum) of a Function of Several Variables – 420
Sec. 179. An Absolute Extremum of a Function – 422
Sec. 180. Constructing Empirical Formulas by the Method of Least Squares – 424
Exercises – 428Chapter 21. Series
Sec. 181. Examples of Infinite Series – 430
Sec. 182. Convergence of a Series – 431
Sec. 183. A Necessary Condition for Convergence of a Series – 435
Sec. 184. Comparison Tests – 437
Sec. 185. D’Alembert’s Test for Convergence – 440
Sec. 186. Absolute Convergence – 444
Sec. 187. Alternating Series. Leibniz’ Test – 446
Sec. 188. Power Series – 447
Sec. 189. Differentiation and Integration of Power Series – 450
Sec. 190. Expanding a Given Function into a Power Series – 450
Sec. 191. Maclaurin’s Series – 452
Sec. 192. Applying Maclaurin’s Series to Expanding Some Functions into Power Series – 453
Sec. 193. Applying Power Series to Approximate Calculations – 456
Sec. 194. Taylor’s Series – 459
Sec. 195. Series in a Complex Domain – 462
Sec. 196. Euler’s Formulas – 463
Sec. 197. Fourier Trigonometric Series – 464
Sec. 198. The Fourier Series of Even and Odd Functions – 473
Sec. 199. The Fourier Series of Nonperiodic Functions – 475
Exercises – 479Chapter 22. Differential Equations
Sec. 200. Basic Concepts – 481
Sec. 201. Differential Equations of the First Order – 484
Sec. 202. First-Order Equations with Variables Separable – 486
Sec. 203. Homogeneous Differential Equations of the First Order – 492
Sec. 204. Linear Differential Equations of the First Order – 495
Sec. 205. Euler’s Method – 500
Sec. 206. Differential Equations of the Second Order – 502
Sec. 207. Integrable Types of Second-Order Differential Equations – 504
Sec. 208. Reducing the Order of a Differential Equation – 510
Sec. 209. Integrating Differential Equations with the Aid of Power Series – 513
Sec. 210. Common Properties of the Solutions of Second-Order Linear Homogeneous Differential Equations – 514
Sec. 211. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients – 517
Sec. 212. Second-Order Linear Nonhomogeneous Differential Equations with Constant Coefficients – 523
Sec. 213. Differential Equations Containing Partial Derivatives – 533
Sec. 214. Linear Differential Equations with Partial Derivatives – 536
Sec. 215. Deriving the Heat Conduction Equation – 538
Sec. 216. The Problem on Temperature Distribution in a Limited Rod – 540
Exercises – 543
Chapter 23. Line Integrals
Sec. 217. The Line Integral of the First Kind – 546
Sec. 218. The Line Integral of the Second Kind – 548
Sec. 219. The Physical Meaning of the Line Integral of the Second Kind – 552
Sec. 220. Condition Under Which the Line Integral of the Second Kind is Independent of Path – 554
Sec. 221. The Work Performed by a Potential Force – 556
Exercises – 557Chapter 24. Double and Triple Integrals
Sec. 222. Double Integrals – 561
Sec. 223. The Double Integral in Rectangular Cartesian Coordinates – 564
Sec. 224. Expressing a Double Integral in Polar Coordinates – 571
Sec. 225. The Euler-Poisson Integral – 575
Sec. 226. Mean-Value Theorem – 576
Sec. 227. Geometrical Applications of the Double Integral – 578
Sec. 228. Physical Applications of the Double Integral – 579
Sec. 229. Triple Integrals – 584
Exercises – 588Chapter 25. Fundamentals of the Theory of Probability
A. Basic Definitions and Theorems
Sec. 230. Random Events – 591
Sec. 231. Algebra of Events – 593
Sec. 232. The Classical Definition of Probability – 594
Sec. 233. The Statistical Definition of Probability – 597
Sec. 234. The Theorem on Addition of Probabilities – 598
Sec. 235. A Complete Group of Events – 599
Sec. 236. The Theorem on Multiplication of Probabilities – 600
Sec. 237. Bayes’ Formula – 603B. Repeated Independent Trials
Sec. 238. Elements of Combinatorial Analysis – 604
Sec. 239. The Formula of Total Probability – 605
Sec. 240. The Binomial Law of Distribution of Probabilities – 607
Sec. 241. The Laplace Local Theorem – 608
Sec. 242. The Laplace Integral Theorem – 610
Sec. 243. Poisson’s Theorem – 614C. Random Variables and Their Numerical Characteristics
Sec. 244. A Random Discrete Variable and Its Distribution Law – 615
Sec. 245. Mathematical Expectation – 617
Sec. 246. Basic Properties of Mathematical Expectation – 618
Sec. 247. Variance – 621
Sec. 248. Continuous Random Variables. Distribution Functions – 626
Sec. 249. Numerical Characteristics of a Continuous Random Variable – 630
Sec. 250. Uniform Distribution – 631
Sec. 251. Normal Distribution – 633
Exercises – 636Chapter 26. The Concept of Linear Programming
Sec. 252. An n-Dimensional Vector Space – 639
Sec. 253. Sets in n-Dimensional Space – 641
Sec. 254. The Problem of Linear Programming – 645APPENDICES
A. Most Important Constants – 650
B. List of Formulas (Classified and Explained) – 650
I. Plane Analytic Geometry – 650
II. Differential Calculus—Functions of One Variable – 652
III. Integral Calculus – 654
IV. Complex Numbers, Determinants, and Systems of Simultaneous Equations – 658
V. Elements of Vector Algebra – 660
VI. Solid Analytic Geometry – 661
VII. Differential Calculus—Functions of Several Variables – 662
VIII. Series – 663
IX. Differential Equations – 666
X. Line Integrals – 668
XI. Double and Triple Integrals – 669
XII. Probability Theory – 671ANSWERS – 674
#1981 #complexNumbers #Derivatives #differentialEquations #functions #intergration #lineIntegrals #linearProgramming #mathematics #series #solidAnalyticGeometry #sovietLiterature #theoryOfLimits #vectorAlgebra
SUBJECT INDEX – 684 -
A Brief Course Of Higher Mathematics by V.A. Kudryavtsev
The aim of this text is to set forth the essentials of higher mathematics and their applications in various fields. At present higher mathematics serves as the theoretical foundation for most branches of the natural, applied and engineering sciences. Therefore, every natural scientist must necessarily master its methods to be able to apply them for practical purposes.
Translated from the Russian by Leonid Levant
Many thanks to Guptaji for the scans and Balram Sharmaji of Kamgaar Prakashan for making this book available.
You can get the book here and here
Follow us on
Twitter https://x.com/MirTitles
Mastadon https://mastodon.social/@mirtitles
Bluesky https://bsky.app/profile/mirtitles.bsky.social
Tumblr https://www.tumblr.com/mirtitles
Internet Archive https://archive.org/details/mir-titles
Fork us on gitlab https://gitlab.com/mirtitles
Contents
INTRODUCTION
Chapter 1. The Rectangular Coordinate System in the Plane and Its Application to Simple Problems
Sec. 1. Rectangular Coordinates of a Point in the Plane
Sec. 2. Transformation of Rectangular Coordinates
Sec. 3. The Distance Between Two Points in the Plane
Sec. 4. Dividing a Line Segment in a Given Ratio
Sec. 5. The Area of a Triangle
ExercisesChapter 2. The Equation of a Line
Sec. 6. Sets
Sec. 7. The Method of Coordinates in the Plane
Sec. 8. The Line as a Set of Points
Sec. 9. The Equation of a Line in the Plane
Sec. 10. Constructing a Line on the Basis of Its Equation
Sec. 11. Some Elementary Problems
Sec. 12. Two Basic Problems of Plane Analytical Geometry
Sec. 13. Algebraic Lines
ExercisesChapter 3. The Straight Line
Sec. 14. The Equation of a Straight Line
Sec. 15. The Angle Between Two Straight Lines
Sec. 16. The Equation of a Straight Line Passing Through a Given Point in a Given Direction
Sec. 17. The Equation of a Straight Line Passing Through Two Points (Two-Point Form)
Sec. 18. The Intercept Form of the Equation of a Straight Line
Sec. 19. The Point of Intersection of Two Straight Lines
Sec. 20. The Distance from a Point to a Straight Line
ExercisesChapter 4. Second-Order Lines
Sec. 21. The Circle
Sec. 22. Central Second-Order Curves (Conics)
Sec. 23. Focal Properties of Central Curves of the Second Order
Sec. 24. The Ellipse as a Uniformly Compressed Circle
Sec. 25. The Asymptotes of a Hyperbola
Sec. 26. The Graph of Inverse Proportionality
Sec. 27. Noncentral Quadric Curves
Sec. 28. The Focal Property of the Parabola
Sec. 29. The Graph of a Quadratic Trinomial
ExercisesChapter 5. Polar Coordinates. Parametric Equations of a Line
Sec. 30. Polar Coordinates
Sec. 31. Relationship Between Rectangular and Polar Coordinates
Sec. 32. Parametric Equations of a Line
Sec. 33. Parametric Equations of the Cycloid
ExercisesChapter 6. Functions
Sec. 34. Constants and Variables
Sec. 35. The Concept of Function
Sec. 36. Simplest Functional Relations
1. Direct Proportional Relation
2. Linear Relation
3. Inverse Proportional Relation
4. Quadratic Relation
5. Sinusoidal Relation
Sec. 37. Methods of Representing Functions
1. The Analytical Method
2. The Tabular Method
3. The Graphical Method
Sec. 38. The Concept of Function of Several Variables
Sec. 39. Implicit Function
Sec. 40. Inverse Function
Sec. 41. Classification of Functions of One Argument
Sec. 42. The Graphs of the Basic Elementary Functions
Sec. 43. Interpolation of Functions
ExercisesChapter 7. The Theory of Limits
Sec. 44. Real Numbers
Sec. 45. Errors of Approximate Numbers
Sec. 46. Limit of a Function
Sec. 47. One-Sided Limits of a Function
Sec. 48. Limit of a Sequence
Sec. 49. Infinitesimals
Sec. 50. Infinitely Large Quantities
Sec. 51. Basic Properties of Infinitesimals
Sec. 52. Basic Limit Theorems
Sec. 53. Some Tests for the Existence of the Limit of a Function
Sec. 54. The Limit of X
Sec. 55. The Number e
Sec. 56. Natural Logarithms
Sec. 57. Asymptotic Formulas
ExercisesChapter 8. Continuity of Functions
Sec. 58. Increments of an Argument and a Function. Continuity of a Function
Sec. 59. Another Definition of the Continuity of a Function
Sec. 60. Continuity of Basic Elementary Functions
Sec. 61. Basic Theorems on Continuous Functions
Sec. 62. Evaluation of Indeterminacies
Sec. 63. Classification of the Points of Discontinuity of a Function
ExercisesChapter 9. The Derivative of a Function
Sec. 64. A Tangent to a Curve – 159
Sec. 65. Velocity of a Moving Point – 161
Sec. 66. The Derivative Defined Generally – 163
Sec. 67. Other Applications of the Derivative – 166
Sec. 68. Relation Between the Continuity and Differentiability of a Function – 167
Sec. 69. The Notion of an Infinite Derivative – 169
Exercises – 169Chapter 10. Basic Derivative Theorems
Sec. 70. Introductory Notes – 170
Sec. 71. The Derivatives of Certain Simple Functions – 170
Sec. 72. Basic Differentiation Rules – 174
Sec. 73. The Derivative of a Composite Function – 179
Sec. 74. The Derivative of an Inverse Function – 182
Sec. 75. The Derivative of an Implicit Function – 184
Sec. 76. The Derivative of a Logarithmic Function – 185
Sec. 77. A Logarithmic Derivative – 188
Sec. 78. The Derivative of an Exponential Function – 188
Sec. 79. The Derivative of a Power Function – 190
Sec. 80. The Derivatives of Inverse Trigonometric Functions – 191
Sec. 81. The Derivative of a Function Represented Parametrically – 193
Sec. 82. The Table of Differentiation Formulas – 194
Sec. 83. Derivatives of Higher Orders – 195
Sec. 84. Physical Meaning of the Second Derivative – 195
Exercises – 196Chapter 11. Applications of Derivatives
Sec. 85. The Theorem About Finite Increments of a Function and Its Corollaries – 199
Sec. 86. Increase and Decrease of a Function of One Argument – 201
Sec. 87. L’Hospital’s Rule – 204
Sec. 88. Taylor’s Formula for a Polynomial – 208
Sec. 89. Binomial Formula – 210
Sec. 90. Taylor’s Formula for a Function – 211
Sec. 91. Maxima and Minima of a Function of One Variable – 213
Sec. 92. Concavity and Convexity of the Graph of a Function. Points of Inflection – 220
Sec. 93. Approximate Solution of Equations – 223
Sec. 94. Construction of Graphs of Functions – 227
Exercises – 230Chapter 12. Differentials
Sec. 95. The Differential of a Function – 232
Sec. 96. Relation Between the Differential of a Function and Its Derivative. The Differential of the Independent Variable – 235
Sec. 97. The Geometrical Meaning of the Differential – 237
Sec. 98. The Physical Meaning of the Differential – 237
Sec. 99. Approximate Calculation of Small Increments of a Function – 238
Sec. 100. Equivalence of the Increment and Differential of a Function – 239
Sec. 101. Properties of the Differential – 242
Sec. 102. Differentials of Higher Orders – 245
Exercises – 247Chapter 13. Indefinite Integral
Sec. 103. Antiderivative. Indefinite Integral – 248
Sec. 104. Basic Properties of the Indefinite Integral – 251
Sec. 105. Table of Simplest Indefinite Integrals – 253
Sec. 106. Independence of the Form of an Indefinite Integral of the Argument Chosen – 254
Sec. 107. Basic Integration Methods – 258
Sec. 108. Techniques for Integrating Rational Fractions with a Quadratic Denominator – 263
Sec. 109. Integration of Simplest Irrational Expressions – 267
Sec. 110. Integration of Trigonometric Functions – 269
Sec. 111. Integration of Certain Transcendental Functions – 271
Sec. 112. Cauchy’s Theorem. Some Important Integrals Inexpressible in Terms of Elementary Functions – 271
Exercises – 272Chapter 14. The Definite Integral
Sec. 113. The Concept of the Definite Integral – 275
Sec. 114. A Definite Integral with a Variable Upper Limit – 277
Sec. 115. Geometrical Meaning of the Definite Integral – 279
Sec. 116. Physical Meaning of the Definite Integral – 281
Sec. 117. Basic Properties of the Definite Integral – 282
Sec. 118. The Mean Value Theorem – 286
Sec. 119. Integration by Parts in the Definite Integral – 288
Sec. 120. Change of Variable in the Definite Integral (Integration by Substitution) – 289
Sec. 121. The Definite Integral as the Limit of an Integral Sum – 291
Sec. 122. Approximate Evaluation of Definite Integrals – 293
Sec. 123. Simpson’s Formula – 296
Sec. 124. Improper Integrals – 297
Exercises – 299Chapter 15. Applications of the Definite Integral
Sec. 125. Areas in Rectangular Coordinates – 301
Sec. 126. Areas in Polar Coordinates – 305
Sec. 127. The Arc Length in Rectangular Coordinates – 307
Sec. 128. The Arc Length in Polar Coordinates – 313
Sec. 129. Computing the Volume of a Solid by Known Cross Sections – 314
Sec. 130. The Volume of a Solid of Revolution – 316
Sec. 131. The Work of a Variable Force – 319
Sec. 132. Other Applications of the Definite Integral in Physics – 320
Exercises – 322Chapter 16. Complex Numbers
Sec. 133. Arithmetic Operations on Complex Numbers – 325
Sec. 134. The Complex Plane – 326
Sec. 135. Theorems on the Modulus and Argument – 328
Sec. 136. Taking the Root from a Complex Number – 329
Sec. 137. The Concept of a Function of a Complex Variable – 331
Exercises – 332Chapter 17. Determinants of Second and Third Order
Sec. 138. Second-Order Determinants – 335
Sec. 139. A System of Two Homogeneous Equations in Three Unknowns – 335
Sec. 140. Third-Order Determinants – 337
Sec. 141. Basic Properties of Determinants – 339
Sec. 142. A System of Three Linear Equations – 342
Sec. 143. A Homogeneous System of Three Linear Equations – 344
Sec. 144. A System of Linear Equations in Many Unknowns. Gauss’ Method – 346
Exercises – 349Chapter 18. Fundamentals of Vector Algebra
Sec. 145. Scalars and Vectors – 351
Sec. 146. The Sum of Several Vectors – 352
Sec. 147. The Difference of Vectors – 353
Sec. 148. Multiplication of a Vector by a Scalar – 353
Sec. 149. Collinear Vectors – 354
Sec. 150. Coplanar Vectors – 355
Sec. 151. The Projection of a Vector on an Axis – 356
Sec. 152. The Rectangular Cartesian Coordinates in Space – 359
Sec. 153. The Length and Direction of a Vector – 360
Sec. 154. The Distance Between Two Points in Space – 361
Sec. 155. Operations on Vectors Represented in the Coordinate Form – 362
Sec. 156. Scalar Product of Two Vectors – 364
Sec. 157. Scalar Product of Vectors in the Coordinate Form – 366
Sec. 158. Vector Product of Vectors – 367
Sec. 159. Vector Product in the Coordinate Form – 369
Sec. 160. Triple Scalar Product – 371
Exercises – 373Chapter 19. Fundamentals of Solid Analytic Geometry
Sec. 161. The Equations of a Surface and a Line in Space – 374
Sec. 162. The General Equation of a Plane – 380
Sec. 163. Angle Between Two Planes – 382
Sec. 164. Equations of a Straight Line in Space – 383
Sec. 165. The Derivative of a Vector Function – 387
Sec. 166. The Equation of a Sphere – 389
Sec. 167. The Equation of an Ellipsoid – 391
Sec. 168. The Equation of a Paraboloid of Revolution – 392
Exercises – 393Chapter 20. Functions of Several Variables
Sec. 169. The Concept of a Function of Several Variables – 395
Sec. 170. Continuity – 398
Sec. 171. Partial Derivatives of the First Order – 401
Sec. 172. The Total Differential of a Function – 403
Sec. 173. Application of the Differential of a Function to Approximate Computations – 409
Sec. 174. Directional Derivatives – 410
Sec. 175. The Gradient – 413
Sec. 176. Partial Derivatives of Higher Orders – 417
Sec. 177. Test for the Total Differential – 418
Sec. 178. The Extremum (Maximum or Minimum) of a Function of Several Variables – 420
Sec. 179. An Absolute Extremum of a Function – 422
Sec. 180. Constructing Empirical Formulas by the Method of Least Squares – 424
Exercises – 428Chapter 21. Series
Sec. 181. Examples of Infinite Series – 430
Sec. 182. Convergence of a Series – 431
Sec. 183. A Necessary Condition for Convergence of a Series – 435
Sec. 184. Comparison Tests – 437
Sec. 185. D’Alembert’s Test for Convergence – 440
Sec. 186. Absolute Convergence – 444
Sec. 187. Alternating Series. Leibniz’ Test – 446
Sec. 188. Power Series – 447
Sec. 189. Differentiation and Integration of Power Series – 450
Sec. 190. Expanding a Given Function into a Power Series – 450
Sec. 191. Maclaurin’s Series – 452
Sec. 192. Applying Maclaurin’s Series to Expanding Some Functions into Power Series – 453
Sec. 193. Applying Power Series to Approximate Calculations – 456
Sec. 194. Taylor’s Series – 459
Sec. 195. Series in a Complex Domain – 462
Sec. 196. Euler’s Formulas – 463
Sec. 197. Fourier Trigonometric Series – 464
Sec. 198. The Fourier Series of Even and Odd Functions – 473
Sec. 199. The Fourier Series of Nonperiodic Functions – 475
Exercises – 479Chapter 22. Differential Equations
Sec. 200. Basic Concepts – 481
Sec. 201. Differential Equations of the First Order – 484
Sec. 202. First-Order Equations with Variables Separable – 486
Sec. 203. Homogeneous Differential Equations of the First Order – 492
Sec. 204. Linear Differential Equations of the First Order – 495
Sec. 205. Euler’s Method – 500
Sec. 206. Differential Equations of the Second Order – 502
Sec. 207. Integrable Types of Second-Order Differential Equations – 504
Sec. 208. Reducing the Order of a Differential Equation – 510
Sec. 209. Integrating Differential Equations with the Aid of Power Series – 513
Sec. 210. Common Properties of the Solutions of Second-Order Linear Homogeneous Differential Equations – 514
Sec. 211. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients – 517
Sec. 212. Second-Order Linear Nonhomogeneous Differential Equations with Constant Coefficients – 523
Sec. 213. Differential Equations Containing Partial Derivatives – 533
Sec. 214. Linear Differential Equations with Partial Derivatives – 536
Sec. 215. Deriving the Heat Conduction Equation – 538
Sec. 216. The Problem on Temperature Distribution in a Limited Rod – 540
Exercises – 543
Chapter 23. Line Integrals
Sec. 217. The Line Integral of the First Kind – 546
Sec. 218. The Line Integral of the Second Kind – 548
Sec. 219. The Physical Meaning of the Line Integral of the Second Kind – 552
Sec. 220. Condition Under Which the Line Integral of the Second Kind is Independent of Path – 554
Sec. 221. The Work Performed by a Potential Force – 556
Exercises – 557Chapter 24. Double and Triple Integrals
Sec. 222. Double Integrals – 561
Sec. 223. The Double Integral in Rectangular Cartesian Coordinates – 564
Sec. 224. Expressing a Double Integral in Polar Coordinates – 571
Sec. 225. The Euler-Poisson Integral – 575
Sec. 226. Mean-Value Theorem – 576
Sec. 227. Geometrical Applications of the Double Integral – 578
Sec. 228. Physical Applications of the Double Integral – 579
Sec. 229. Triple Integrals – 584
Exercises – 588Chapter 25. Fundamentals of the Theory of Probability
A. Basic Definitions and Theorems
Sec. 230. Random Events – 591
Sec. 231. Algebra of Events – 593
Sec. 232. The Classical Definition of Probability – 594
Sec. 233. The Statistical Definition of Probability – 597
Sec. 234. The Theorem on Addition of Probabilities – 598
Sec. 235. A Complete Group of Events – 599
Sec. 236. The Theorem on Multiplication of Probabilities – 600
Sec. 237. Bayes’ Formula – 603B. Repeated Independent Trials
Sec. 238. Elements of Combinatorial Analysis – 604
Sec. 239. The Formula of Total Probability – 605
Sec. 240. The Binomial Law of Distribution of Probabilities – 607
Sec. 241. The Laplace Local Theorem – 608
Sec. 242. The Laplace Integral Theorem – 610
Sec. 243. Poisson’s Theorem – 614C. Random Variables and Their Numerical Characteristics
Sec. 244. A Random Discrete Variable and Its Distribution Law – 615
Sec. 245. Mathematical Expectation – 617
Sec. 246. Basic Properties of Mathematical Expectation – 618
Sec. 247. Variance – 621
Sec. 248. Continuous Random Variables. Distribution Functions – 626
Sec. 249. Numerical Characteristics of a Continuous Random Variable – 630
Sec. 250. Uniform Distribution – 631
Sec. 251. Normal Distribution – 633
Exercises – 636Chapter 26. The Concept of Linear Programming
Sec. 252. An n-Dimensional Vector Space – 639
Sec. 253. Sets in n-Dimensional Space – 641
Sec. 254. The Problem of Linear Programming – 645APPENDICES
A. Most Important Constants – 650
B. List of Formulas (Classified and Explained) – 650
I. Plane Analytic Geometry – 650
II. Differential Calculus—Functions of One Variable – 652
III. Integral Calculus – 654
IV. Complex Numbers, Determinants, and Systems of Simultaneous Equations – 658
V. Elements of Vector Algebra – 660
VI. Solid Analytic Geometry – 661
VII. Differential Calculus—Functions of Several Variables – 662
VIII. Series – 663
IX. Differential Equations – 666
X. Line Integrals – 668
XI. Double and Triple Integrals – 669
XII. Probability Theory – 671ANSWERS – 674
#1981 #complexNumbers #Derivatives #differentialEquations #functions #intergration #lineIntegrals #linearProgramming #mathematics #series #solidAnalyticGeometry #sovietLiterature #theoryOfLimits #vectorAlgebra
SUBJECT INDEX – 684 -
Hilbert’s Fourth Problem by A. V. Pogorelov
Hilbert’s fourth problem, which involves finding all geometries where “ordinary lines” are “geodesics,” is both accessible and profound. While the problem can be appreciated by beginning graduate students, its solution requires tools from various branches of mathematics, including geometry, analysis, and the calculus of variations.
A partial solution was provided by Georg Hamel in 1901. Later, A. V. Pogorelov, inspired by Herbert Busemann’s idea presented at the 1966 International Congress of Mathematicians in Moscow, offered an elegant and comprehensive solution. Pogorelov’s approach, which slightly reformulates Hilbert’s problem, is celebrated for its clarity and mathematical depth.
The book is well-written, introducing necessary mathematical concepts as needed, making it accessible to readers with a foundation in advanced calculus. The English translation, reviewed by Eugene Zaustinsky, includes helpful notes guiding readers to further literature.
Pogorelov’s work is a valuable contribution to the mathematical literature, particularly for those interested in geometry and its foundations.
You can get the book here and here.
INTRODUCTION 5
SECTIONS
1. Projective Space 9
2. Projective Transformations 13
3. Desarguesian Metrizations of Projective Space 19
4. Regular Desarguesian Metrics in the Two-Dimensional Case 24
5. Averaging Desarguesian Metrics 31
6. The Regular Approximation of Desarguesian Metrics 38
7. General Desarguesian Metrics in the Two-Dimensional Case 46
8. Funk’s Problem 54
9. Desarguesian Metrics in the Three-Dimensional Case 61
10. Axioms for the Classical Geometries 68
11. Statement of Hilbert’s Problem 75
12. Solution of Hilbert’s Problem 82
NOTES 88
BIBLIOGRAPHY 93
INDEX 95
#classicalGeometry #foundationsOfGeometry #geometry #mathematics #solutionToHilbertSProblem #sovietLiterature
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Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich
This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.Revised English Edition
Translated and Edited by Richard A. SilvermanYou can get the book here and here.
#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral
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Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich
This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.Revised English Edition
Translated and Edited by Richard A. SilvermanYou can get the book here and here.
#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral
-
Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich
This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.Revised English Edition
Translated and Edited by Richard A. SilvermanYou can get the book here and here.
#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral
-
Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich
This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.Revised English Edition
Translated and Edited by Richard A. SilvermanYou can get the book here and here.
#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral
-
Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich
This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.Revised English Edition
Translated and Edited by Richard A. SilvermanYou can get the book here and here.
#1966 #derivative #higherMathematics #integral #lebesgueIntegral #LeviSTheorem #mathematics #measureTheory #physics #RiemannIntegral #sovietLiterature #StieltjesIntegral #theoryOfIntegral
-
Gaseous Composition Of The Atmosphere And Its Analysis by B. A. Mirtov
The problem of the gaseous composition of the atmosphere is one of the central questions of modern atmospheric physics. We need not consider in detail the fact that the gaseous composition, which varies considerably with height, has a vital influence on most phenomena occurring in the Earth’s atmosphere. In the upper layers of the atmosphere, there is no single problem (with the possible exception of the wind conditions) that can be solved accurately without a knowledge of the chemical nature of these layers.
As far as I know, this is the first book to appear in either Russian or foreign literature which attempts to collect and systematize the large amount of work devoted to the investigation of the composition of the Earth’s air cover. Hundreds of papers, not connected by any unifying idea—some of them old and undeservedly forgotten, others scattered throughout various journals—cannot give a complete impression of the gaseous composition of the atmosphere. The scattered nature of the material makes it necessary to spend a large amount of time and trouble just to become acquainted with the work that has been done.
The absence of a critical appraisal of the often somewhat contradictory results of various experiments has led to the inclusion of incorrect information in modern courses on atmospheric physics and in most reference books. This has happened even when dealing with the lower atmosphere, which has been most thoroughly investigated.
The recent use of rockets and artificial satellites has led to rapid progress in our exploration of the upper atmosphere. The large amount of very interesting material, which has accumulated within the short space of the last decade, needs analysis and detailed commentary. All these considerations have led me to write this monograph, in which I have tried to collect and critically discuss the existing experimental material on the chemical composition of the atmosphere.
This book deals with a series of problems connected with the investigation of the composition of the atmosphere, but it is by no means my intention to try to describe all sides of this subject. In order to avoid giving the reader a false impression of the volume of work discussed, I shall now clearly define the range covered.
You can get the book here and here.
PREFACE 1
CHAPTER I. INVESTIGATIONS OF THE LOWER ATMOSPHERE
IntroductionEarly geophysical investigations 9
The discovery of new gases in air the present state of knowledge of the gaseous composition of the lower atmosphere 18
Conclusion 26
CHAPTER II. INVESTIGATIONS OF THE COMPOSITION OF THE MIDDLE ATMOSPHERE (up to a height of 30 km)
Introduction 27Balloon ascents 28
Discovery of the stratosphere and the problem of the gravitational separation of gases 30
Early investigations of the composition of the atmosphere at high altitudes by indirect methods 32
Direct investigations in the stratosphere 33
Balloon ascents into the stratosphere 36
Sounding-balloon investigations with automatic equipment 41
Conclusion 49
CHAPTER III. INVESTIGATIONS OF THE COMPOSITION OF THE UPPER ATMOSPHERE USING ROCKETS (sampling method)
Introduction 51Gaseous composition one of the central problems of the physics of the upper atmosphere 56
Sounding rockets 57
Characteristics of rocket investigations 63
Methods and results of investigations of gaseous composition 64
Conclusion 78
CHAPTER IV. SOVIET INVESTIGATIONS OF THE UPPER ATMOSPHERE USING ROCKETS (sampling method)
Introduction 80Sampling 81
Storing the samples 91
Analysis of the samples 93
Spectroscopic microanalysis of gases 95
The vacuum apparatus 101
Experimental results 106
CHAPTER V. INVESTIGATIONS OF THE COMPOSITION OF THE UPPER ATMOSPHERE USING ROCKET-BORNE RADIO-FREQUENCY MASS SPECTROMETERS
Introduction 110Characteristics of the composition of the upper atmosphere 110
The use of the radio-frequency mass spectrometer for investigating the upper atmosphere 113
American investigations on the neutral composition of the atmosphere 117
Investigations of the neutral composition of the atmosphere carried out in the Soviet Union 128
Discussion of results 133
Investigations of the ionic composition of the atmosphere carried out in the USA 136
Investigations of the ionic composition of the atmosphere carried out in the USSR 142
Conclusion 144
CHAPTER VI. INVESTIGATIONS OF THE IONIC COMPOSITION OF THE UPPER ATMOSPHERE USING RADIO-FREQUENCY MASS SPECTROMETERS MOUNTED IN ARTIFICIAL SATELLITES (SPUTNIKS)The use of artificial satellites for the investigation of the Earth’s upper and outer atmosphere 146
Characteristics of the method of investigation 147
Investigations of the ionic composition of the upper atmosphere 157
Discussion of the results 163
Conclusion 165
BIBLIOGRAPHY 172APPENDIX THE CONCENTRATION OF OZONE IN THE ATMOSPHERE
Introduction 179
The variation of the overall ozone content and the study of ozone in the lower atmosphere 180
Investigations on the vertical distribution of ozone at high altitudes 187
Photochemical theory 193
Conclusion 196
Bibliography 198LIST OF ABBREVIATIONS 209
#1964 #atmosphere #atmosphericComposition #meteorology #nasaTechnicalTranslations #physicsOfAir #sovietLiterature
-
Gaseous Composition Of The Atmosphere And Its Analysis by B. A. Mirtov
The problem of the gaseous composition of the atmosphere is one of the central questions of modern atmospheric physics. We need not consider in detail the fact that the gaseous composition, which varies considerably with height, has a vital influence on most phenomena occurring in the Earth’s atmosphere. In the upper layers of the atmosphere, there is no single problem (with the possible exception of the wind conditions) that can be solved accurately without a knowledge of the chemical nature of these layers.
As far as I know, this is the first book to appear in either Russian or foreign literature which attempts to collect and systematize the large amount of work devoted to the investigation of the composition of the Earth’s air cover. Hundreds of papers, not connected by any unifying idea—some of them old and undeservedly forgotten, others scattered throughout various journals—cannot give a complete impression of the gaseous composition of the atmosphere. The scattered nature of the material makes it necessary to spend a large amount of time and trouble just to become acquainted with the work that has been done.
The absence of a critical appraisal of the often somewhat contradictory results of various experiments has led to the inclusion of incorrect information in modern courses on atmospheric physics and in most reference books. This has happened even when dealing with the lower atmosphere, which has been most thoroughly investigated.
The recent use of rockets and artificial satellites has led to rapid progress in our exploration of the upper atmosphere. The large amount of very interesting material, which has accumulated within the short space of the last decade, needs analysis and detailed commentary. All these considerations have led me to write this monograph, in which I have tried to collect and critically discuss the existing experimental material on the chemical composition of the atmosphere.
This book deals with a series of problems connected with the investigation of the composition of the atmosphere, but it is by no means my intention to try to describe all sides of this subject. In order to avoid giving the reader a false impression of the volume of work discussed, I shall now clearly define the range covered.
You can get the book here and here.
PREFACE 1
CHAPTER I. INVESTIGATIONS OF THE LOWER ATMOSPHERE
IntroductionEarly geophysical investigations 9
The discovery of new gases in air the present state of knowledge of the gaseous composition of the lower atmosphere 18
Conclusion 26
CHAPTER II. INVESTIGATIONS OF THE COMPOSITION OF THE MIDDLE ATMOSPHERE (up to a height of 30 km)
Introduction 27Balloon ascents 28
Discovery of the stratosphere and the problem of the gravitational separation of gases 30
Early investigations of the composition of the atmosphere at high altitudes by indirect methods 32
Direct investigations in the stratosphere 33
Balloon ascents into the stratosphere 36
Sounding-balloon investigations with automatic equipment 41
Conclusion 49
CHAPTER III. INVESTIGATIONS OF THE COMPOSITION OF THE UPPER ATMOSPHERE USING ROCKETS (sampling method)
Introduction 51Gaseous composition one of the central problems of the physics of the upper atmosphere 56
Sounding rockets 57
Characteristics of rocket investigations 63
Methods and results of investigations of gaseous composition 64
Conclusion 78
CHAPTER IV. SOVIET INVESTIGATIONS OF THE UPPER ATMOSPHERE USING ROCKETS (sampling method)
Introduction 80Sampling 81
Storing the samples 91
Analysis of the samples 93
Spectroscopic microanalysis of gases 95
The vacuum apparatus 101
Experimental results 106
CHAPTER V. INVESTIGATIONS OF THE COMPOSITION OF THE UPPER ATMOSPHERE USING ROCKET-BORNE RADIO-FREQUENCY MASS SPECTROMETERS
Introduction 110Characteristics of the composition of the upper atmosphere 110
The use of the radio-frequency mass spectrometer for investigating the upper atmosphere 113
American investigations on the neutral composition of the atmosphere 117
Investigations of the neutral composition of the atmosphere carried out in the Soviet Union 128
Discussion of results 133
Investigations of the ionic composition of the atmosphere carried out in the USA 136
Investigations of the ionic composition of the atmosphere carried out in the USSR 142
Conclusion 144
CHAPTER VI. INVESTIGATIONS OF THE IONIC COMPOSITION OF THE UPPER ATMOSPHERE USING RADIO-FREQUENCY MASS SPECTROMETERS MOUNTED IN ARTIFICIAL SATELLITES (SPUTNIKS)The use of artificial satellites for the investigation of the Earth’s upper and outer atmosphere 146
Characteristics of the method of investigation 147
Investigations of the ionic composition of the upper atmosphere 157
Discussion of the results 163
Conclusion 165
BIBLIOGRAPHY 172APPENDIX THE CONCENTRATION OF OZONE IN THE ATMOSPHERE
Introduction 179
The variation of the overall ozone content and the study of ozone in the lower atmosphere 180
Investigations on the vertical distribution of ozone at high altitudes 187
Photochemical theory 193
Conclusion 196
Bibliography 198LIST OF ABBREVIATIONS 209
#1964 #atmosphere #atmosphericComposition #meteorology #nasaTechnicalTranslations #physicsOfAir #sovietLiterature
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Equations Of The Mixed Type by A.V. Bitsadze
The theory of equations of mixed type originated in the fundamental researches of the Italian mathematician Francesco Tricomi, which were published in the twenties of this century. Owing to the importance of its applications, the discussion of problems concerned with equations of mixed type has become, in the last ten years, one of the central problems in the theory of partial differential equations.
The present work is not meant to be a summary of all results in this field, especially since the number of results increases with great speed; nevertheless, the reader of this monograph will obtain an idea of the present state of the theory of equations of mixed type.
This book was developed from a series of lectures dealing with certain fundamental questions in the theory of equations of mixed type, which the Author delivered in scientific establishments in the Chinese People’s Republic at the end of 1957 and the beginning of 1958.
Translated by P. Zador
Translation edited by I. N. Sneddon
You can get the book here and here.
CONTENTS
Foreword ix
Introduction xi
1. General remarks on linear partial differential equations of mixed type 1
1. Equation of the second order with two independent variables 1
2. The theory of Cibrario 3
3. Systems of two first order equations 12
4. Linear systems of partial differential equations of the second order with two independent variables 17
2. The study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parabolicity 20
1. The Riemann function for a second order hyperbolic linear equation 20
2. A class of hyperbolic systems of second order linear equations 27
3. The Cauchy problem for hyperbolic equations with given initial conditions on the line of parabolic degeneracy 32
4. Generalizations 41
3. The study of the solutions of second order elliptic equations for a domain, the boundary of which includes a segment of the curve of parabolic degeneracy 44
1. The linear elliptic partial differential equation of the second order 44
2. Elliptic systems of second order 49
3. The Dirichlet problem for second order elliptic equations in a domain, the boundary of which includes a segment of the curve of parabolic degeneracy 58
4. Some other problems and generalizations 66
4. The problem of Tricomi 71
1. The statement of the problem of Tricomi 72
2. The extremal principle and the uniqueness of the solution of problem T 74
3. Solution of problem T by means of the method of integral equations 78
4. Continuation. The proof for the existence of a solution of the integral equations obtained in the preceding paragraph 90
5. Other methods for solving problem T 94
6. Examples and generalizations 103
5. Other mixed problems 112
1. The mixed problem M 112
2. The proof of the uniqueness of solution for problem M 113
3. Concerning the existence of the solution of problem M 117
4. The general mixed problem 124
5. The problem of Frankl 135
6. Short indication of some important generalizations and applications 141
References 151
Index 157
#1964 #differentialEquations #mathematics #solutionsToDifferentialEquations #sovietLiterature #tricomiProblem
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Eternal Wind by Sergei Zhemaitis
The Eternal Wind is a science-fiction story about people of the not-too-distant future. The setting is an island float in the Indian Ocean, a biostation and a scientific centre for the biological research of ocean life. The main characters are students spending the summer on field practice. They unriddle the secrets of the ocean and help in utilizing its countless riches. The book also tells of the dolphin, man’s closest friend, of killer whales and many strange denizens of the deeps. The book is full of thrills for the young reader—romance, adventure and danger accompanies the two student-heroes of this tale of the sea.
Translated from the Russian by Gladys Evans
You can get the book here and here.
#1975 #creaturesOfTheDeep #mirPublishers #oceans #scienceFiction #sovietLiterature #sovietScienceFiction
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Problems In Mathematics With Hints And Solutions by V. Govorov; P. Dybov; N. Miroshin; S. Smirnova
The book contains more than three thousand mathematics problems and covers each topic taught at school. The problems were contributed by 120 of the higher schools of the USSR and all the universities.
The book is divided into, four parts: algebra and trigonometry, fundamentals of analysis, geometry and vector algebra, and the problems and questions set during oral examinations. The authors considered it necessary to include some material relating to complex numbers, combinatorics, the binomial theorem, elementary trigonometric inequalities, and set theory and the method of coordinates. The authors believe that this material will help the readers systematize their knowledge in the principal divisions of mathematics.
In writing the book, the authors have used their experience of examining students in mathematics at higher schools and the preparation of television courses designed to help students revise their knowledge for the entrance examinations to higher educational establishments.
To make it easier for readers to grasp the material, some of the sections have been supplemented with explanatory text. The problems are all answered and some have additional hints or complete solutions.
The more difficult problems are marked with asterisks. Part 4 is entitled “Oral Examination Problems and Questions” and includes samples suggested by the higher schools.
The authors hope that this book will help those who want to enter the various types of higher school, aid the teachers, and be of use to all those who want to deepen and systematize their knowledge of mathematics.
EDITED BY PROF. A.I. PRILEPKO, D.Sc.
Translated from the Russian by Irene Aleksanova
You can get the book here and here.
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Preface 5
Part 1 Algebra Trigonometry and Elementary Functions 9
1.1 Problems on Integers Criteria for Divisibility 9
1.2 Real Numbers Transformation of Algebraic Expressions 13
1.3 Mathematical Induction Elements of Combinatorics Binomial Theorem
1.4 Equations and Inequalities of the First and the Second Degree
1.5 Equations of Higher Degrees Rational Inequalities
1.6 Irrational Equations and Inequalities
1.7 Systems of Equations and Inequalities
1.8 The Domain of Definition and the Range of a Function
1.9 Exponential and Logarithmic Equations and Inequalities
1.10 Transformations of Trigonometric Expressions Inverse Trigonometric Functions
1.11 Solution of Trigonometric Equations Inequalities and Systems of Equations
1.12 Progressions
1.13 Solution of Problems on Derivation of Equations
1.14 Complex Numbers
Part 2 Fundamentals of Mathematical Analysis
2.1 Sequences and Their Limits An Infinitely Decreasing Geometric Progression Limits of Functions
2.2 The Derivative Investigating the Behaviour of Functions with the Aid of the Derivative
2.3 Graphs of Functions
2.4 The Antiderivative The Integral The Area of a Curvilinear Trapezoid
Part 3 Geometry and Vector Algebra
3.1 Vector Algebra
3.2 Plane Geometry Problems on Proof
3.3 Plane Geometry Construction Problems
3.4 Plane Geometry Calculation Problems
3.5 Solid Geometry Problems on Proof
3.6 Solid Geometry Calculation Problems
Part 4 Oral Examination Problems and Questions 241
4.1 Sample Examination Papers 241
4.2 Problems Set at an Oral Examination 244
Hints and Answers 265
Appendix 386#algebra #geometry #mathematics #problemBooks #problemsAndSolutions #sovietLiterature #trigonometry
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A Collection Of Problems On A Course Of Mathematical Analysis by G. N. Berman
THE present Collection of Problems is intended for students studying mathematical analysis within the framework of a technical college course. In the arrangement of the material, the style of the exposition and basic pedagogical tendencies the Collection is most suited to the widely used Course of Mathematical Analysis of A. F. Bermant. At the same time, since the book contains systematically selected problems and exercises on the main branches of a Technical College course of mathematical analysis, it forms a useful adjunct independently of the text-book on which the course is based.
Translated by D. E. Brown
Translation edited by Ian N. SneddonYou can get the book here and here.
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Show Yourselves Martians! – Pavel Klushantsev
ANNOTATION
This book provides an overview of the mysteries and explorations of Mars. The Red Planet has fascinated humanity since antiquity. The invention of the telescope only deepened its enigmas, particularly with the discovery of the so-called ‘canals.’ This led to the idea of Martians living on the planet in science fiction. But is there really life on Mars? Do Martians exist? What are the canals? To answer questions like these space probes from the USSR and USA started the exploration of Mars in the 1960s. Going to Mars is not straightforward and reaching Mars is an engineering and technological feat. Ever since then we have continued our explorations of the Red Planet. We now have sophisticated rovers on the surface of Mars and orbiters in orbit around Mars. In the last few decades our knowledge of Mars has improved in leaps and bounds with new discoveries shedding more and more light on the mysterious planets past and future. This volume presents an outline of these explorations, a journey that continues to advance the bounds of human knowledge with hopes that one day humans will inhabit Mars.
Drawings by V. Korolkov
Translated from the Spanish and Typset in Scribus by Damitr MazanavReleased on the web by The Mir Titles Project in 2025
This work is an Open Educational Resource (OER)
Creative Commons BY Share Alike 4.0 License
You can get the book here and here
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Internet Archive: https://archive.org/details/mir-titlesTranslators Note
One of the first books that I remember reading was All About the Telescope by Pavel Klushantsev translated to Marathi. The book got me fascinated about science in general and astronomy in particular.
So, when I saw this book by Klushantsev on Mars only available in Spanish, I could not resist from translating it. Though I started the work on this some years back, it was never completed for various reasons. One of them being the complex nature of typsetting in the book. So for this book I have used Scribus for typsetting and the results have been pleasing.
Since the book was written, our knowledge about Mars has increased by leaps and bounds. I have added an additional chapter in the book that summarises the various spacecraft since the 1990s that have taken our knowledge of Mars to the next level. The Martian surface has been revelead unprecendented detail with numerous rovers and orbiters around it. The attribution of images in the last section is provided with the images.
We now have active rovers on the surface of Mars and orbiters around it sending us vital information about the Red Planet. All this with hopes that humans would one day land there. It is to those future astronauts this translation and additional sections are dedicated.
Some screenshots
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TABLE OF CONTENTS
TRANSLATOR’S NOTE
THAT LITTLE STAR IS MARS! 1
THE MYSTERIES OF MARS 14
WHERE CAN YOU LIVE 22
UNEXPLAINED PHENOMENA OF MARS 32
WE MUST SOLVE THE MYSTERY OF “CANALS” 41
DO MARTIANS EXIST? 46
TRACES OF MARTIANS 56
ARE THE MARTIANS OUR ENEMIES 67
ARE MARTIANS OUR FRIENDS? 77
WE MUST FLY TO MARS 87
IS IT DIFFICULT TO REACH MARS 97
WHAT DID THE SPACE PROBES SEE FROM THEIR ORBIT 117
WATER! 129
THE SEARCH FOR LIFE ON MARS 136
IN THE FUTURE 152
FROM UNCERTAINTY TO DISCOVERY: MARS SINCE THE 1990s – Damitr Mazanav 163#Ccbysa #Oer #ingenuity #ISRO #mangalyaan #marsExploration #marsExplorer #marsExpress #marsMission #marsProbes #martianProbes #mirTitlesProject #NASA #perseverance #sovietLiterature #spaceExploration #spaceTravel #ussr #viking
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The Origin Of Continents And Ocean Basins by M. V. Muratov
Professor Mikhail Muratov, P.Sc., Corr. Mem. USSR Acad. Sci., is Head of the Chair of Regional Geology and Paleontology, Moscow Institute of Geological Prospecting. He is the winner of State and Lenin Prizes.
This book deals with the origin, structure, and tectonic behavior of the earth’s crust beneath continents and oceans and describes principal stages of the earth’s geologic history. The author attaches much importance to geosynclinal cycles and their role in continental crust build-up and discusses intriguing hypotheses explaining the present day face of our planet.
Translated from the Russian by V. Agranat
You can get the book here and here.
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Bluesky: mirtitles.bsky.socialPreface
Chapter I. Structure and Age of the Earth’s Crust
Face of the Earth (9)
Continental and Oceanic Crust of the Earth (12)
Age of the Earth’s Crust (17)Chapter II. Continental Crust
Inhomogeneity of the Structure (24)
Unconformities and Their Significance (30)
Evolution of Fold Areas and Formation of Platform Basement (33)Chapter III. The Basic Component Parts of the Continents: Ancient Platforms and Fold Belts
The Importance of Ancient and Young Platforms in the Structure of Continents (36)
A Brief Outline of the Structure of Continents (36)
Constituent Elements of Ancient Platforms (40)
Fold Belts (41)Chapter IV. The Structure and History of Geosynclinal Fold Areas
The Study of Geosynclines (48)
The Structure of Geosynclinal Fold Areas (50)
An Outline History of Geosynclinal Areas (52)
Main Stage (52)
Orogenic Stage (59)
Formations of Sedimentary and Volcanic Series of Geosynclinal Areas (61)
Differences in Ages of Geosynclinal Areas and in Formations of Troughs (69)
The Role of Intrusive Complexes in the Geosynclinal Cycle (73)
Geosynclinal Areas: Proliferous Sources of Valuable Minerals (79)
Two Principal Types of Geosynclinal Areas and Their Role in the Build-up of the Granitic-Metamorphic Layer of the Earth’s Crust (85)Chapter V. Structure and History of the Basement of Ancient Platforms
Major Structural Units (87)
The Structure of Archean Massifs (88)
Proterozoic Fold Areas (90)
The Protosedimentary Cover of Ancient Platforms (94)
Outline History of the Basement of Ancient Platforms (95)
The Basement of Ancient Platforms: Mineral Resources (98)Chapter VI. History of Fold Belts and Formation of the Basement of Young Platforms
Generation of the Riphean Basement of Major and Minor Belts (100)
Formation of the Paleozoic Basement of the Ural-Mongolia, Atlantic, and Arctic Belts (103)
History of the Mediterranean Fold Belt (106)
Inland Sea Basins and the Indonesia Area (108)
History of the Circum-Pacific Belt (112)
Formation of Granitic and Metamorphic Rocks of the Basement Within Fold Belts (124)Chapter VII. Evolution of Ancient and Young Platforms
Basic Stages (127)
The Origin of Platform-Type Depressions (130)
Principal Valuable Minerals of the Sedimentary Cover of Platforms (132)
Volcanic Belts and Epiplatform Orogenesis (132)
Valuable Minerals in the Activated Areas of Platforms (134)Chapter VIII. The Topography and Tectonics of the Ocean Floor
Principal Topographic Features and the Physiography (136)
Principal Tectonic Features of the Ocean Floor (140)
Pacific Ocean (140)
Indian Ocean (143)
Atlantic Ocean (144)
Arctic Ocean (147)Chapter IX. The Origin of Ocean Basins in the Light of Geologic Evidence
The Physiography of the Pacific Bed and Its Probable Origin (149)
The Physiography of the Atlantic, Indian, and Arctic Beds and Their Origin (154)
Hypotheses Explaining the Conversion of Crustal Material Beneath the Ocean Floor (157)
Mobilistic Hypotheses Involving Continental Displacement (158)
Expanding Earth Hypothesis (165)
The Probable Age and the Mode of Formation of Ocean Basins (167)Chapter X. Major Historical Events and the Stages of Formation of the Earth’s Crust
The Early Existence of the Earth Before Crust Formation (170)
The Basaltic Crust Before Hydrosphere Formation (170)
The Formation of the Granitic-Metamorphic Crust of Ancient Platforms (173)
The Consolidation of the Basement of Young Platforms (175)
The Latest Stage in the Development of the Earth’s Crust (177)
The General Trend in the Development of the Earth’s Crust (179)Bibliography
Name Index
Subject Index#1977 #geography #geologicalCycles #mirPublishers #oceanFloors #oceans #plateTectonics #sovietLiterature
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Macroscopic Theories Of Matter And Fields A Thermodynamic Approach ( Advances in Science and Technology in the USSR)
Advances in Science and Technology in the USSR
Mathematics and Mechanics SeriesThis is a collection of articles by Soviet scientists on current issues of building macroscopic models of matter and fields. Based on thermodynamics concepts the papers develop general variational techniques of modeling material continuous media and fields allowing for their interactions in reversible and irreversible processes. The book is intended for researchers, engineers, graduate and postgraduate students interested in the mechanics of continuous media.
Translated from the Russian by Eugene Yankovsky
You can get the book here and here.
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Preface, L. I. Sedov 7
A Thermodynamic Approach to the Basic Variational Equation for Building Models of Continuous Media, L. I. Sedov 19
Applying the Basic Variational Equation for Building Models of Matter and Fields, L. I. Sedov 43Introduction 43
Definitions 43
Variations of Tensors for Which Scalar Invariants Retain Their Form 46
Special Types of Tensor Components Qlj 48
Defining Variations and Their Interrelationship in the Comoving and the Observer’s Reference Frame 50
Auxiliary Formulas for Variations 55
Given Scalar and Tensor Parameters Characterizing Models of Material Media and Fields 56
The Determining Parameters in the Characteristics of a Continuous Medium as a Whole and the Characteristics of Individual World Lines 60
The Basic Variational Equation and Identities Following from the Scalar Nature of the Lagrangian Density 62
The Euler Equations for the Basic Variational Equation (2.8.1) 66
The Conditions at Strong Discontinuities 71
On Models of Fluids 74
An Elastic-Body Model 79
Constructing Models of Fields 81
A Model of Interacting Material Medium and Electromagnetic Field 83
Examples 90
Transition from Relativistic to Newtonian Mechanics in the Presence of Irreversible Processes, L. T. Chernyi 98
The Basic Vibrational Equation 98
The Euler Equations and Conditions on Discontinuities 102
Transition to Newtonian Mechanics 106
Irreversible Processes 108
Conclusion 114
Models of Ferromagnetic Continuous Media with Magnetic Hysteresis, L. T. Chernyi 116Introduction 116
The Determining Parameters 118
The Variational Principle and the Main Equations 121
A Phenomenological Theory of Irreversible Processes 126
Some Corollaries of the General Theory 130
Examples of Models of Magnetizable Media 137
Magnetizable and Polarizable Media with Microstructure, V. A. Zhelnorovich 141The Determining Parameters of Magnetizable and Polarizable Media with Microstructure 141
Relaxation Models of Magnetizable and Polarizable Media Without Microstructure 150
Models of Magnetizable Liquids with Intrinsic Moment of Momentum 156
Couette Flow of an Incompressible Viscous Magnetizable Liquid 156
Poiseuille Flow in Cylindrical Channel 157
Magnetoacoustic Waves in Magnetizable Liquids 160
On Exact Solutions for Interacting Gravitational and Electromagnetic Fields, G. A. Alekseev 168Introduction 168
The Einstein-Maxwell Equations in Matrix Form 169
Building the Associated Linear System and the Reduction Conditions 172
Soliton Solutions of the Einstein-Maxwell Equations 176
One-Soliton Solutions with Minkowski’s Space-Time as Background 180
Interaction of Solitons with a Uniform Electromagnetic Field 184
Neutrino Fields in General Relativity, N. R. Sibgatullin 187Introduction 187
Canonical Equations of Neutrino Fields and Waves 188
On the Infinite Dimensional Algebra and the Lie Group of Neutrino Vacuum Equations 199
Exact Solutions of Neutrino Vacuum Equations 208
Rotation of the Polarization Vector of Gravitational Waves in a Burst of Neutrino Radiation 220
Tensor Representation of Spinor Fields, V. A. Zhelnorovich 224Introduction 224
Dirac Matrices 224
The Spinor Representation of the Lorentz Group 226
Spinors in Four-Dimensional Pseudo-Euclidean Vector Space 231
Conjugate Spinors 233
The Relation Between Even-Rank Spinors and Tensors 234
The Relation Between First-Rank Spinors and Systems of Complex Tensors 234
Real-Valued Tensors Determined by a Spinor 238
Rotations in Four-Dimensional Space and Spinors 240
Invariant Spinor Subspaces 243
Spinors in Three-Dimensional Euclidean Space 244
Tensor Representation of Spinors in Three-Dimensional Euclidean Space 246
Rotations in Three-Dimensional Space and Spinors 248
Tensor Representation of Differential Spinor Equations in the Minkowski Space 250
Some Solutions of Differential Equations for Relativistic Models of Magnetizable Fluids with Intrinsic Angular Momentum in an Electromagnetic Field 254
Index 26#elementaryParticles #generalRelativity #mirPublishers #physics #quantumMechanics #sovietLiterature #variationalPrinciples
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Terrestrial Oceans And Lunar Maria by G.F. Makarenko
About the Book
Both the Earth and the Moon have been repeatedly involved in episodes of volcanic activity induced by the heating of the interior of the two planets. Before the onset of each epoch of outpourings of lava that filled volcanic seas, arcuate and ring-shaped mountain chains encircled these seas in different regions of the planets.The Moon is a “simplified model” of the Earth. Reviewing the structures of the Earth and the Moon simultaneously, we shall better understand the origins and compositions of the mountain ranges of the Pacific coast and see why the Atlantic-type oceans are not surrounded by mountains, and what is common in the structure of the volcanic floor of terrestrial oceans and lunar maria.
The book is intended for a wide circle of geologists, geographers, and astronomers and will also be of interest to those who are specializing in the geology of the Earth and the Moon.
About the Author
Galina Makarenko graduated from the Moscow Geological Exploration Institute named after Sergo Ordzhonikidse as an engineer-geologist. She is currently a member of the geological faculty at Moscow State University, where she conducts scientific research in the areas of geotectonics and volcanism. In addition to her research, she teaches general geology and trains both students and post-graduate students.
For many years, Makarenko participated in scientific expeditions in regions of ancient volcanism, with her candidate thesis dedicated to the geology of these areas. Her expeditions to Kamchatka and the Kuril Islands focused on comparing ancient volcanoes with active ones. Her doctoral thesis is centered on the extensive sheets of volcanic rocks found on the Earth’s continents and oceans.She has published three monographs and numerous articles. Today, the author is actively engaged in collecting new data in the field of comparative planetology.
Translated from the Russian by
V.F. AGRANAT and V.F. POMINOV
You can get the book here and here.
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Bluesky: mirtitles.bsky.socialIntroduction 7
Earth: A Planet in a Basaltic Shell 11
A View of the Earth from Space 11
Mountains and Plains of Terrestrial Continents and Oceans 14
Volcanic Seas of Terrestrial Continents 22
Magma Melts Solidified at Depth 35
Basaltic Seas on Terrestrial Ocean Floors 40
Volcanic Rises on the Basaltic Ocean Floor 49
What Is Concealed by Lavas Lying on the Ocean Floor? 52The Age of Terrestrial Basalts and Their Relationships with Different Structures 58
The Age of Trap Seas on the Continents 58
The Age of Volcanic Seas on the Ocean Floor 63
Volcanic Seas of Continents and Geosynclines 70
Volcanic Seas on the Ocean Floors and Island Arcs 81
Are Continental Basalts Similar to Oceanic Basalts on Earth? 88Lava Maria on the Waterless Moon 93
The Distribution of Volcanic Maria 93
The Age of Lunar Basaltic Maria 102
Ridges and Grooves on the Floor of Lunar Maria 115
How Lunar Maria Were Formed? 120Volcanic Maria of Planets Behind Arcuate Mountains 123
Volcanic Seas of the Earth and the Moon Have Similar Constitution 123
The Structures of the Earth and the Moon Are Symmetrical Relative to Their Axes of Rotation 131
Arcs and Rings of the Earth’s Oldest Mountains 135
The Centrifugal Wave in the Development of Mountain Arcs 147
The Moon Is a Simplified Model of the Earth 154#earth #geology #lava #lavaFlow #moon #mountains #oceanFloors #plateTectonics #rocks #seas #sovietLiterature #valleys #volcanicSeas
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यह सभी कुत्तें है – ईगर अकीमुश्किन(The Dog Family Stories In Hindi by Igor Akimushkin)
A little book describing various members of the dog family
कुत्ते के परिवार के विभिन्न सदस्यों का वर्णन करने वाली एक छोटी सी किताबचित्रकारः अ० केलेइनिकोव
अनुवादकः संगमलाल मालवीयYou can get the book here and here
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The Year Of Victory by I. Konev
The author Marshal of the Soviet Union I. Konev, was army and Front commander. The book covers the short concluding phase of the war against Nazi Germany, a period exceptionally rich in events. At the time, I. Konev commanded the 1st Ukrainian Front of the Soviet Army. He tells a vivid and fascinating story of the great Soviet offensive, analyses the military and strategic situation at the time, makes apt and revealing comments on many renowned military leaders, and shows the stamina of the Russian soldier and the magnitude of his feat in the past war.
Marshal of the Soviet Union Ivan Konev occupies an eminent place among the distinguished military leaders of the past world war. Troops under his command defeated the Nazis in battles fought at Smolensk, near Moscow and at Kursk and in the Korsun-Shevchenkovskaya, Vistula- Oder and Berlin operations, and liberated Prague, the Czechoslovak capital.
In reply to the questions of Western journalists as to whether he was a career officer in the old Russian Army and how big his family estate was, Konev said:
“I’m afraid I will disappoint you, gentlemen. I’m the son of a poor peasant and belong to that generation of Russian people who met the October Revolution in their youth and identified themselves with it. My military training is Soviet, and therefore good. The successes of the Fronts, which I have been fortunate enough to command, are inseparable from the general successes of the Red Army. We, Soviet workers in soldiers greatcoats, are in all our thoughts bound to our people; we live their lives and fight for our common ideas. This is the source of our strength. For his distinguished service. Marshal Konev was awarded the Order of Victory, the highest Soviet military order.”Translated from the Russian by David Mishne
Edited by Robert Daglish
Designed by Victor KorolkovYou can get the book here and here
Cleaned, optimised version of original scan
A 1969 (second printing 1984) Soviet work. Scanned by Ismail, sent to him by Christian Kellum.
From Thomas Mrett’s archive collectionTwitter: @MirTitles
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FROM THK VISTULA TO THE ODER 5
FROM THE ODER TO THE NEISSE 50
THE SO-CALLED LULL 67
THE BERLIN OPERATION 79
THE PRAGUE OPERATION 193
INSTEAD OF A CONCLUSION 239#battles #berlinCampaign #history #hitler #naziGermaany #sovietLiterature #sovietRedArmy #stalin #ussr #worldWar2
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𝗥𝗲𝘃𝗶𝗲𝘄: "𝗪𝗲" 𝗯𝘆 𝗬𝗲𝘃𝗴𝗲𝗻𝘆 𝗭𝗮𝗺𝘆𝗮𝘁𝗶𝗻 -
Early Soviet dystopia, the terror at the loss of humanity, the glorification of service to State, and a protagonist who may not want to be saved.
https://waywordsstudio.com/general/reviews/we-by-yevgeny-zamyatin/
#bookreviews #literature #books #bookworm #read #book #readreadread #yevgenyzamyatin #we #dystopia #sovietliterature #russianliterature #sciencefiction #sf #scifi