Live and recent posts from across the Fediverse tagged #mirpublishers, aggregated by home.social.
Mir Publishers’ books from the Soviet era were really good & very cheap in India – I miss them sorely 😢:
“Mir Books” (https://mirtitles.org/).
On HN: https://news.ycombinator.com/item?id=48739018
#Books #USSR #Russia #SovietUnion #Mir #MirBooks #SoftDiplomacy #India #MirPublishers
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
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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Preface
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
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 Series
This 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.
Twitter: @MirTitles
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Contents
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 43
Introduction 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 116
Introduction 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 141
The 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 168
Introduction 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 187
Introduction 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 224
Introduction 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
Tropical Meteorology by G.G. Tarakanov
This text is written in accordance with the course in tropical meteorology as read at the Leningrad Hydrometeorologic Institute. It discusses the processes of the tropical atmosphere, basic weather elements, and general principles of weather analysis and forecasting in the tropics.
Translated from Russian by Michael C. Edelev
Note: Scan quality is not great.
You can get the book here and here.
Twitter: @MirTitles
Mastodon: @[email protected]
Mastodon: @[email protected]
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CONTENTS
Preface 5
Chapter 1. Introduction 9
1.1. Tropical Meteorology Defined. An Outline of the Tropical Atmosphere 10
1.2. Weather Observing System in the Tropics
Chapter 2. Variation of the Main Weather Elements
2.1. Temperature
2.2. Pressure
2.3. Wind
2.4. Pressure and Wind Fields
2.5. Cloudiness
2.6. Rainfall
Chapter 3. Types of Convection and the Initiating Conditions
3.1. Types of Convection and the Initiating Conditions
3.2. An Entraining Jet Model of Cumulus Convection
Chapter 4. Weather Chart Interpretation
4.1. The Time Section
4.2. The Surface Chart
4.3. The Upper-air Chart
4.4. Fields of Divergence and Vorticity
4.5. Air Masses
Chapter 5. Circulation and Synoptic Systems of the Tropics
5.1. The General Circulation 106
5.2. The Equatorial Trough 109
5.3. The Trade Winds 116
5.4. Antitrades 116
5.5. Low-latitude Disturbances 119
5.6. Monsoons 132
5.7. Interaction Between Motions of Different Scales 142
5.8. Heat and Moisture Transport Mechanisms 145
Chapter 6. Tropical Cyclones
6.1. Formation of Tropical Cyclones 152
6.2. The Life Cycle of a Storm 157
6.3. Structure of Tropical Cyclones 159
6.4. Relation Between Lowest Pressure and Highest Wind in Storms 167
6.5. Forecasting the Movement of Tropical Cyclones 175
6.6. Analysis and Prediction of Storm Intensity Using Satellite Data 181
6.7. Impact of Tropical Storms 192
Bibliography 198
Index 201
#1982 #airMass #atmosphere #cyclones #mirPublishers #monsoon #pressure #rains #sovietLiterature #weather #weatherElements
A huge collection of very high-quality #physics, #mathematics and other #science#books from the Soviet-era Mir Publishers, available for #free #download here in the format of your choice. These are worth their weight in gold today. Their hardcover/paperback versions are next to impossible to find. They have some the best introductory, mid-level and reference #textbooks on various scientific topics that I've seen over my entire scientific career, written by some of the greatest Russian scientists and mathematicians. Check out in particular the Little Mathematics Library. Enjoy!
Higher Algebra – Kurosh
In this post we see Higher Algebra by A. Kurosh.
The education of the mathematics major begins with the
study of three basic disciplines: mathematical analysis, analytic
geometry and higher algebra. These disciplines have a number of
points of contact, some of which overlap; together they constitute
the foundation upon which rests the whole edifice of modern
mathematical science.Higher algebra – the subject of this text – is a far-reaching and
natural generalization of the basic school course of elementary
algebra. Central to elementary algebra is without doubt the problem
of solving equations. The study of equations begins with the very
simple case of one equation of the first degree in one unknown. From
there on, the development proceeds in two directions: to systems of
two and three equations of the first degree in two and, respectively,
three unknowns, and to a single quadratic equation in one unknown and
also to a few special types of higher-degree equations which readily
reduce to quadratic equations (quartic equations, for example). Both
trends are further developed in the course of higher algebra, thus
determining its two large areas of study. One – the foundations of
linear algebra – starts with the study of arbitrary systems of
equations of the first degree (linear equations). When the number of
equations equals the number of unknowns, solutions of such systems
are obtained by means of the theory of determinants.The second half of the course of higher algebra, called the algebra
of polynomials, is devoted to the study of a single equation in one
unknown but of arbitrary degree. Since there is a formula for solving
quadratic equations, it was natural to seek similar formulas for
higher-degree equations. That is precisely how this division of
algebra developed historically. Formulas for solving equations of
third and fourth degree were found in the sixteenth century. The
search was then on for formulas capable of expressing the roots of
equations of fifth and higher degree in terms -of the coefficients of
the equations by means of radicals, even radicals within radicals. It
was futile, though it continued up to the beginning of the nineteenth
century, when it was proved that no such formulas exist and that for
all degrees beyond the fourth there even exist specific examples of
equations with integral coefficients whose roots cannot be written
down by means of radicals.
This book was translated from the Russian by George Yankovsky. The book was published by first Mir Publishers in 1972, with reprints in 1975, 1980 and 1984. The book below is from the 1984 reprint.
All credits to the original uploader.
You can get the book here.
and here
Update 3 June 2021: added The Internet Archive Link
Table of Contents
Introduction 7
Chapter 1.
Systems of linear equations. Determinants 15
1. The Method of Successive Elimination of Unknowns 15
2. Determinants of Second and Third Order. 22
3. Arrangements and Permutations 27
4. Determinants of nth Order 36
5. Minors and Their Cofactors 43
6. Evaluating Determinants 46
7. Cramer’s Rule 53
Chapter 2.
Systems of linear equations ( general theory) 59
8. n-Dimensional Vector Space 59
9. Linear Dependence of Vectors 62
10. Rank of a Matrix 69
11. Systems of Linear Equations. 76
12. Systems of Homogeneous Linear Equations 82
Chapter 3.
The algebra of matrices 87
13. Matrix Multiplication 87
14. Inverse Matrices 93
15. Matrix Addition and Multiplication of a Matrix by a Scalar 99
16. An Axiomatic Construction of the Theory of Determinants 103
Chapter 4.
Complex numbers 110
17. The System of Complex Numbers 110
18. A Deeper Look at Complex Numbers 112
19. Taking Roots of Complex Numbers 120
Chapter 5.
Polynomials and their roots 126
20. Operations on Polynomials 126
21. Divisors. Greatest Common Divisor 131
22. Roots of Polynomials. 139
23. Fundamental Theorem 142
24. Corollaries to the Fundamental Theorem 151
25. Rational Fractions 156
Chapter 6.
Quadratic forms 161
26. Reducing a Quadratic Form to Canonical Form 161
27. Law of Inertia. 169
28. Positive Definite Forms 174
Chapter 7
Linear spaces 178
29. Definition of a Linear Space. An Isomorphism 178
30. Finite-Dimensional Spaces. Bases 182
31. Linear Transformations 188
32. Linear Subspaces. 195
33. Characteristic Roots and Eigenvalues 199
Chapter 8
Euclidean spaces204
34. Definition of a Euclidean Space. Orthonormal Bases 204
35. Orthogonal Matrices, Orthogonal Transformations. 210
36. Symmetric Transformations. 215
37. Reducing a Quadratic Form to Principal Axes. Pairs of Forms 219
Chapter 9.
Evaluating roots of polynomials 225
38. Equations of Second, Third and Fourth Degree 225
39. Bounds of Roots 232
40. Sturm’s Theorem 238
41. Other Theorems on the Number of Real Roots 244
42. Approximation of Roots 250
Chapter 10.
Fields and polynomials 257
43. Number Rings and Fields 257
44. Rings 260
45. Fields 267
46. Isomorphisms of Rings (Fields). The Uniqueness of the Field of Complex Numbers 272
47. Linear Algebra and the Algebra of Polynomials over an Arbitrary Field 276
48. Factorization of Polynomials into Irreducible Factors 281
49. Theorem on the Existence of a Root 290
50. The Field of Rational Fractions 297
Chapter 11.
Polynomials in several unknowns 303
51. The Ring of Polynomials in Several Unknowns 303
52. Symmetric Polynomials. 312
53. Symmetric Polynomials Continued 319
54. Resultant. Elimination of Unknown. Discriminant 329
55. Alternative Proof of the Fundamental Theorem of the Algebra of
Complex Numbers 337
Chapter 12.
Polynomials with rational coefficients 341
56. Reducibility of Polynomials over the Field of Rationals 341
57. Rational Roots of Integral Polynomials 345
58. Algebraic Numbers 349
Chapter 13.
Normal form of a matrix 355
59. Equivalence of $\lambda$-matrices. 355
60. Unimodular $\lambda$-matrices. Relationship Between Similarity of
Numerical Matrices and the Equivalence of their Characteristic Matrices 362
61. JordanNormalForm 370
62. MinimalPolynomials 377
Chapter 14.
Groups. 382
63. Definition of a Group. Examples 382
64. Subgroups 388
65. Normal Divisors, Factor Groups, Homomorphisms 394
66. Direct Sums of Abelian Groups 399
67. Finite Abelian Groups 406
Bibliography 414
Index 416
Problems in Mathematical Analysis – Demidovich (Ed.)
We now come to Problems in Mathematical Analysis edited by B. P. Demidovich. The list of authors is G. Baranenkov, B. Demidovich, V. Efimenko, S. Kogan, G. Lunts, E. Porshneva, E. Sychera, S. Frolov, R. Shostak and A. Yanpolsky.
This collection of problems and exercises in mathematical analysis covers the maximum requirements of general courses in higher mathematics for higher technical schools. It contains over 3,000 problems sequentially arranged in Chapters I to X covering branches of higher mathematics (with the exception of analytical geometry) given in college courses. Particular attention is given to the most important sections of the course that require established skills (the finding of limits, differentiation techniques, the graphing of functions, integration techniques, the applications all of definite integrals, series, the solution of differential equations).
Since some institutes have extended courses of mathematics, the
authors have included problems on field theory, method, and the
Fourier approximate calculations. Experience shows that problems given in this book not only fully satisfies the number of the requirements of the student, as far as practical mastering of the various sections of the course goes, but also enables the instructor to supply a varied choice of problems in each section to select problems for tests and examinations.Each chapter begins with a brief theoretical introduction that
covers the basic definitions and formulas of that section of the
course. Here the most important typical problems are worked out in full. We believe that this will greatly simplify the work of the student. Answers are given to all computational problems; one asterisk indicates that hints to the solution are given in the
answers, two asterisks, that the solution is given. The are
frequently illustrated by drawings.This collection of problems is the result of many years of teaching higher mathematics in the technical schools of the Soviet Union. It includes, in addition to original problems and examples, a large number of commonly used problems.
This book was translated from the Russian by George Yankovsky. The book was published by first Mir Publishers in 1970.
All credits to the original uploader.
Thanks Siddharth for providing the link.
PDF | OCR | 15.2 MB | Pages: 511 |
Update 13 May 2018: The Internet Archive link
and here
You can get the book here
For magnet / torrent links go here.
Password if needed: mirtitles
4-shared link here
Password, if required, for 4shared files:
www.mirtitles.org
Facing problems while extracting? See FAQs
Table of Contents
Preface 9
Chapter I
INTRODUCTION TO ANALYSIS
Sec. 1. Functions 11
Sec. 2. Graphs of Elementary Functions 16
Sec. 3 Limits 22
Sec. 4 Infinitely Small and Large Quantities 33
Sec. 5. Continuity of Functions 36
Chapter II
DIFFERENTIATION OF FUNCTIONS
Sec. 1. Calculating Derivatives Directly 42
Sec. 2. Tabular Differentiation 46
Sec. 3 The Derivatives of Functions Not Represented Explicitly 56
Sec. 4. Geometrical and Mechanical Applications of the Derivative 60
Sec. 5. Derivatives of Higher Orders 66
Sec. 6. Differentials of First and Higher Orders 71
Sec. 7. Mean Value Theorems 75
Sec. 8. Taylor’s Formula 77
Sec. 9. The L’Hospital-Bernoulli Rule for Evaluating Indeterminate
Forms 78
Chapter III
THE EXTREMA OF A FUNCTION AND THE GEOMETRIC
APPLICATIONS OF A DERIVATIVE
Sec. 1. The Extrema of a Function of One Argument 83
Sec. 2. The Direction of Concavity. Points of Inflection 91
Sec. 3. Asymptotes 93
Sec. 4. Graphing Functions by Characteristic Points 96
Sec. 5. Differential of an Arc Curvature 101
Chapter IV
INDEFINITE INTEGRALS
Sec. 1. Direct Integration 107
Sec. 2. Integration by Substitution 113
Sec. 3. Integration by Parts 116
Sec. 4. Standard Integrals Containing a Quadratic Trinomial 118
Sec. 5. Integration of Rational Functions 121
Sec. 6. Integrating Certain Irrational Functions 125
Sec. 7. Integrating Trigoncrretric Functions 128
Sec. 8. Integration of Hyperbolic Functions 133
Sec. 9. Using Ingonometric and Hyperbolic Substitutions for
Finding integrals of the Form $\int R(x, \sqrt{ax^2 + bx + c}) dx$ R Where R
is a Rational Function
Sec. 10. Integration of Various Transcendental Functions 135
Sec. 11. Using Reduction Formulas 135
Sec. 12. Miscellaneous Examples on Integration 136
Chapter V
DEFINITE INTEGRALS
Sec. 1. The Definite Integral as the Limit of a Sum 138
Sec. 2. Evaluating Definite Integrals by Means of Indefinite Integrals 140
Sec. 3 Improper Integrals 143
Sec. 4. Change of Variable in a Definite Integral 146
Sec. 5. Integration by Parts 149
Sec. 6. Mean-Value Theorem 150
Sec. 7. The Areas of Plane Figures 153
Sec 8. The Arc Length of a Curve 158
Sec 9 Volumes of Solids 161
Sec 10 The Area of a Surface of Revolution 166
Sec. 11. Moments. Centres of Gravity. Guldin’s Theorems 168
Sec. 12. Applying Definite Integrals to the Solution of Physical
Problems 173
Chapter VI.
FUNCTIONS OF SEVERAL VARIABLES
Sec. 1. Basic Notions 180
Sec. 2. Continuity 184
Sec. 3. Partial Derivatives 185
Sec. 4. Total Differential of a Function 187
Sec. 5. Differentiation of Composite Functions 190
Sec. 6. Derivative in a Given Direction and the Gradient of a Function 193
Sec. 7. Higher -Order Derivatives and Differentials 197
Sec. 8. Integration of Total Differentials 202
Sec. 9. Differentiation of Implicit Functions 205
Sec. 10. Change of Variables 211
Sec. 11. The Tangent Plane and the Normal to a Surface 217
Sec. 12. Taylor’s Formula for a Function of Several Variables 220
Sec. 13. The Extremum of a Function of Several Variables 222
Sec. 14. Finding the Greatest and smallest Values of Functions 227
Sec. 15. Singular Points of Plane Curves 230
Sec. 16. Envelope 232
Sec. 17. Arc Length of a Space Curve 234
Sec. 18. The Vector Function of a Scalar Argument 235
Sec. 19. The Natural Trihedron of a Space Curve 238
Sec. 20. Curvature and Torsion of a Space Curve 242
Chapter VII.
MULTIPLE AND LINE INTEGRALS
Sec. 1. The Double Integral in Rectangular Coordinates 246
Sec. 2. Change of Variables in a Double Integral 252
Sec. 3. Computing Areas 256
Sec. 4. Computing Volumes 258
Sec. 5. Computing the Areas of Surfaces 259
Sec. 6 Applications of the Double Integral in Mechanics 260
Sec. 7. Triple Integrals 262
Sec. 8. Improper Integrals Dependent on a Parameter. Improper Multiple Integrals 269
Sec. 9. Line Integrals 273
Sec. 10. Surface Integrals 284
Sec. 11. The Ostrogradsky-Gauss Formula 286
Sec. 12. Fundamentals of Field Theory 288
Chapter VIII.
SERIES
Sec. 1. Number Series 293
Sec. 2. Functional Series 304
Sec. 3. Taylor’s Series 318
Sec. 4. Fourier’s Series 311
Chapter IX
DIFFERENTIAL EQUATIONS
Sec. 1. Verifying Solutions. Forming Differential Equations of Families of
Curves. Initial Conditions 322
Sec. 2. First-Order Differential Equations 324
Sec. 3. First-Order Diflerential Equations with Variables
Separable. Orthogonal Trajectories 327
Sec. 4. First-Order Homogeneous Differential Equations 330
Sec. 5. First-Order Linear Differential Equations. Bernoulli’s
Equation 332
Sec. 6 Exact Differential Equations. Integrating Factor 335
Sec 7 First-Order Differential Equations not Solved for the Derivative 337
Sec. 8. The Lagrange and Clairaut Equations 339
Sec. 9. Miscellaneous Exercises on First-Order Differential Equations 340
Sec. 10. Higher-Order Differential Equations 345
Sec. 11. Linear Differential Equations 349
Sec. 12. Linear Differential Equations of Second Order with Constant
Coefficients 351
Sec. 13. Linear Differential Equations of Order Higher than Two with
Constant Coefficients 356
Sec. 14. Euler’s Equations 357
Sec. 15. Systems of Differential Equations 359
Sec. 16. Integration of Differential Equations by Means of Power Series 361
Sec. 17. Problems on Fourier’s Method 363
Chapter X.
APPROXIMATE CALCULATIONS
Sec. 1. Operations on Approximate Numbers 367
Sec. 2. Interpolation of Functions 372
Sec. 3. Computing the Real Roots of Equations 376
Sec. 4. Numerical Integration of Functions 382
Sec. 5. Numerical Integration of Ordinary Differential Equations 384
Sec. 6. Approximating Fourier’s Coefficients 393
ANSWERS 396
APPENDIX 475
I. Greek Alphabet 475
II. Some Constants 475
III. Inverse Quantities, Powers, Roots, Logarithms 476
IV. Trigonometric Functions 478
V. Exponential, Hyperbolic and Trigonometric Functions 479
VI. Some Curves 480
Questions and Answers in School Physics – Tarasov and Tarasova
This book was planned as an aid to students preparing for an entrance examination in physics for admission to an engineering institute. It has the form of a dialogue between the author (the Teacher:) and an inquisitive reader (the Student:). This is exceptionally convenient for analysing common errors made by students in entrance examinations, for reviewing different methods of solving the same problems and for discussing difficult questions of physical theory.
The English edition of this book was published in 1973 and was translated from the Russian by Nicholas Weinstein.
Electronic copy typeset in LaTeX here and here.
You can download this wonderful book from here and here.
#circuits #conservationLaws #education #field #forces #gasLaws #highSchool #kinematics #mechanics #mirBooks #mirPublishers #ohmSLaw #optics #physics #problems #questions #schoolPhysics #solutions #thermodynamics
Science for Everyone – Physics and Geometry of Disorder – Percolation Theory
We now come to another gem in the Science For Everyone series, Physics and Geometry of Disorder – Percolation Theory by A. L. Efros.
This book is about percolation theory and its various applications, which occur mostly in physics and chemistry. The book is self-sufficient in that it contains chapters on elementary probability theory and Monte Carlo simulation. Most attention is paid to the relationship between the geometrical and physical properties of systems in the vicinity of their percolation thresholds. The theory is applied to examples of impurity semiconductors and doped ferromagnetics, which demonstrate its universality. Although written for students at high schools, the book is very good reading for college students and will satisfy the curiosity of a physicist for whom this will be a first encounter with percolation theory.
The book was translated from the Russian by V. I. Kisin and was first published by Mir in 1986.
The Internet Archive Link and here
Follow us on The Internet Archive: https://archive.org/details/@mirtitles
Write to us: [email protected]
Updated: 15 January 2019
Contents
Part I. Site Percolation Problem 14
Chapter 1. Percolation Threshold 14
Two Pundits Shred a Wire Mesh (14).
What Is a Random Variable? (17).
Mean Value and Variance (18).
Why a Large Wire Mesh? (23).
Exercises (27).
Chapter 2. Basic Rules for Calculating Probabilities Continuous Random Variables 28
Events and Their probabilities (28).
Addition of Probabilities (30).
Multiplication of Probabilities (33).
Exercises (37).
Percolation Threshold in a 2 x 2 Network (37).
Exercise (40).
Continuous Random Variables (40).
Exercises (44).
Percolation Threshold as a Continuous Random Variable (44).
Exercise (48).
Chapter 3. Infinite Cluster 48
Permanent Magnet (48).
Doped Ferromagnetics (53).
Formation of an Infinite Cluster (56).
Exercise (59).
Site Percolation Problem Revisited (59).
Clusters at a Low Concentration of Magnetic Atoms(63).
Exercises (67).
Chapter 4 Solution of the Site Percolation Problem by Monte Carlo Computer Techniques 68
Why Monte Carlo? (68).
What Is the Monte Carlo Method? (70).
How to Think Up a Random Number (74).
The Mid—Square Method (76).
Exercises (78).
Linear Congruent Method (78).
Exercises (79).
Determination of Percolation Threshold. by Monte Carlo Simulation on a Computer. Distribution of Blocked and Non-blocked Sites (81).
Exercise (84).
Search for Percolation Path (85).
Determination of the Threshold (86).
Exercise (89).
Part II. Various Problems of Percolation Theory and Their Applications
Chapter 5. Problems on Two-Dimensional Lattices 90
We Are Planting an Orchard (the Bond Problem) (90).
Exercise (95).
Inequality relating x_b to x_s (95).
Exercise (98).
Covering and Containing; Lattices (98).
“White” Percolation and “Black” Percolation (105).
Dual Lattices (110).
Exercise (115).
Results for Plane Lattices (116).
Exercise (117).
Directed Percolation (117).
Chapter 6. Three—Dimensional Lattices and Approximate Evaluation of Percolation Thresholds 120
Three-Dimensional Lattices (121).
Percolation Thresholds for 3D Lattices (126).
Factors Determining Percolation Threshold in the Bond Problem (127).
How to Evaluate Percolation Threshold in the Site Problem (129).
Exercise (134).
Chapter 7. Ferromagnetics with Long-Range Interaction. The Sphere Problem 135
Ferromagnetics with Long-Range Interaction (136).
Exercise (140).
The Sphere (Circle) Problem (140).
The Circle (Sphere) Problem Is the Limiting Case Of the Site Problem (144).
Chapter 8. Electric Conduction of Impurity Semiconductors. The Sphere Problem 147
Intrinsic Semiconductors (147).
Impurity Semiconductors (150).
Transition to Metallic Electric Conduction at Increased Impurity Concentrations (158).
The Mott Transition and Sphere Problem (161).
Exercise (166).
Chapter 9. Various Generalizations of the Sphere Problem 166
Inclusive Figures of Arbitrary Shape (166).
The Ellipsoid Problem (169).
Other Surfaces (173).
Another Experiment at the House Kitchen. The Hard-Sphere Problem (174).
Chapter 10. Percolation Level 179
“The Flood” (179).
How to Construct a Random Function (182).
Analogy to the Site Problem (185).
Percolation Levels in Plane and Three Dimensional Problems (186).
Impurity Compensation in Semiconductors (189).
Motion of a Particle with Nonzero Potential Energy (190).
Motion of an Electron in the Field of Impurities (192).
Part III. Critical Behavior of Various Quantities Near Percolation Threshold. Infinite Cluster Geometry 195
Chapter 11 The Bethe Lattice
Rumors (196).
Solution of the Site Problem on the Bethe Lattice (200).
Discussion (204).
Exercise (206).
Chapter 12. Structure of Infinite Clusters 206
The Shklovskii—de Gennes Model (206).
Role of the System’s Size (210).
Electric Conduction Near Percolation Threshold (215).
Exercise. (219).
Function P (X) Near Percolation Threshold. Role Played by Dead—Ends (219).
Universality of Critical Exponents (222).
Chapter 13. Hopping Electric Conduction 226
Mechanism of Hopping Conduction (227).
Resistor Network (229).
Properties of Resistor NetworK (231).
The Sphere` Problem Revisited (232).
Calculation of Resistivity (233). Discussion of the Result (235).
Chapter 14. Final Remarks 237
Some Applications (237).
What Is Percolation Theory, After All? (240)
Answers and Solutions 242
Chapter 1 (242). Chapter 2 (244). Chapter 3 (246).
Chapter 4 (249). Chapter 5 (250). Chapter 6 (256).
Chapter 7 (257). Chapter 8 (257). Chapter 11 (257).
Chapter 12 (258).
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