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Chemical Thermodynamics by M.Kh. Karapetyants

The book is primarily aimed at students in higher education specialising in chemistry, particularly future engineers. The author has avoided unnecessary abstraction and overly complex mathematics to ensure the material remains practical and accessible, while still providing a solid theoretical foundation. The content includes approximate laws that allow for quick, practical problem-solving, even when precise values are unavailable. The author integrates empirical thermodynamics with the periodic table to make thermodynamic concepts more comprehensible, particularly entropy, which students often find difficult to grasp.

The book also addresses the importance of connecting thermodynamics with other branches of chemistry, such as general and inorganic chemistry, to enhance students’ understanding for later courses. The primary focus is on the thermodynamics of gaseous systems, with less emphasis on solutions and electrolytes. Numerous examples, mainly related to inorganic substances and chemical processing, help students apply theory to practical problems, with calculations that can be compared to experimental data. The book also includes many tables and figures derived from various sources to support these applications.

Translated from the Russian by G. Leib

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Contents

List of Tables 11
Preface 13
Chapter 1. INTRODUCTION 15
1.1. The Subject and Method of Thermodynamics 15
1.2. Basic Concepts and Definitions 17
1.2.1. Systems and Their Classification 17
1.2.2. Thermodynamic Parameters 18
1.2.3. Work and Heat 22
1.2.4. Reversible and Irreversible Processes 23
1.2.5. Mathematical Relations Between the Parameters of State 28
1.3. Terms and Symbols 33
Chapter 2. THE FIRST LAW OF THERMODYNAMICS 35
2.1. Content of the First Law 35
2.1.1. Cyclic Processes 35
2.1.2. Non-Cyclic Processes. Internal Energy 36
2.2. Enthalpy 41
Chapter 3. HEAT EFFECTS AND HEAT CAPACITIES 45
3.1. Hess’s Law 45
3.2. Standard Heat Effects 49
3.3. Some Methods of Calculating Heat Effects 53
3.3.1. Heats of Formation 53
3.3.2. Heats of Combustion 57
3.3.3. Comparative Calculation of Heat Effects 58
3.4. Heat Capacity 58
3.4.1. Heat Capacity in Different Processes 58
3.4.2. Temperature Dependence of Heat Capacity 61
3.4.3. Certain Laws 71
3.5. Temperature Dependence of Heat Effect 73
3.5.1. Kirchhoff Equation 73
3.5.2. Equation AH = <p(T) in Its Final Form 77
3.5.3. Heat Balance 84
Chapter 4. THE SECOND LAW OF THERMODYNAMICS 87
4.1. Content of the Second Law 87
4.1.1. The Carnot Cycle 87
4.1.2. Thermodynamic Temperature Scale 91
4.1.3. Impossibility of a Perpetual Motion Machine 92
4.2. Entropy 94
4.2.1. Change in Entropy in Reversible Processes 95
4.2.2. Change in Entropy in Irreversible Processes 97
4.2.3. Change in Entropy as a Criterion of the Equilibrium and Spontaneity of Processes 98
4.2.4. Relation Between Entropy and Other Thermodynamic Parameters and Some Relationships Between Derived Functions 102
4.3. Substantiation of the Second Law 106
4.3.1. Thermodynamic Probability of a State 106
4.3.2. Phase Space 106
4.3.3. Relationship Between Entropy and Thermodynamic Probability 108
4.3.4. Fluctuations 110
4.3.5. The Invalidity of the “Theory of Heat Death” of the Universe 112
Chapter 5. THERMODYNAMIC AND CHEMICAL POTENTIALS. THE GENERAL CONDITIONS OF EQUILIBRIUM 114
5.1. Thermodynamic Potentials 114
5.1.1. Change in Thermodynamic Potential as a Criterion of the Equilibrium and Spontaneous Nature of a Process 119
5.1.2. Various Thermodynamic Relationships 121
5.2. Characteristic Functions 123
5.3. Chemical Potential 128
5.4. General Conditions of Equilibrium 131
5.4.1. Stable and Unstable Equilibria 132
5.4.2. Equilibrium Coexistence of Phases. The Gibbs Phase Rule 134
5.4.3. Principle of Displacement of Equilibrium 139
Chapter 6. ONE-COMPONENT HOMOGENEOUS SYSTEMS 141
6.1. Ideal Gas 141
6.2. Equations of State of a Real Gas 150
6.3. Fugacity 159
6.3.1. Standard State 160
6.3.2. Temperature Dependence of Fugacity 162
6.3.3. Methods of Calculating Fugacity 163
6.4. Throttling 168
6.5. Calculation of Properties of Gases According to Experimental Data 175
6.5.1. Calculations Using the Relationships p-V-T and Cp = q>(T) 175
6.5.2. Calculations Using the Relationships Cp = <p(p, T) or H = q(p, T) and VT> = 9 (p) 184
6.5.3. Calculations Using (ij and C9 185
6.5.4. Influence of Pressure on the Heat Effect of a Reaction 185
6.6. A Generalized Method of Calculating Selected Properties of Gases and Liquids at Pressures above Atmospheric 186
6.6.1. Gases 186
6.6.2. Liquids 199
Chapter 7. ONE-COMPONENT HETEROGENEOUS SYSTEMS 205
7.1. Relationship Between Temperature and Pressure with Coexisting Phases 205
7.1.1. Clapeyron-Clausius Equation 205
7.1.2. Approximate Relationships 209
7.2. Methods for the Comparative Calculation of the Temperature Dependence of the Saturated Vapour Pressure 214
7.2.1. Straight Line Method 215
7.2.2. Method of Comparing Boiling Points of Given and Standard Substances at Equal Vapour Pressures 216
7.2.3. Method of Comparing Vapour Pressures of Various Substances at Equal Boiling Points 218
7.2.4. Method of Comparing Vapour Pressures of Various Substances at Equal Reduced Boiling Points 220
7.3. Critical State 221
7.4. Heat Capacities of Coexisting Phases and Heats of Phase Transitions 227
7.4.1. Heat Capacities of Coexisting Phases 227
7.4.2. Heats of Phase Transitions 232
7.5. Influence of Total Pressure on Saturated Vapour Pressure 244
7.6. Influence of Surface Curvature on Saturated Vapour Pressure 247
7.7. Second-Order Phase Transitions 249
Chapter 8. SOLUTIONS 251
8.1. Fundamental Concepts and Definitions 251
8.2. Partial Molar Quantities 255
8.2.1. Basic Equations 257
8.2.2. Methods of Calculation 260
8.3. Heat Capacities and Enthalpies of Solutions 264
8.3.1. Partial Molar Heat Capacities 264
8.3.2. Partial Molar Enthalpies 265
8.4. Ideal Solutions 272
8.5. Infinitely Dilute Solutions 278
8.5.1. Partial Molar Quantities 279
8.5.2. Henry’s Law 281
Chapter 9. BINARY SOLUTION-PURE COMPONENT EQUILIBRIUM 285
9.1. Relationship Between Temperature and Concentration 285
9.1.1. Solution-Solid Component Equilibrium 287
9.1.2. Analysis of Solubility Diagrams 292
9.1.3. Solution-Gas Equilibrium 304
9.2. Relationship Between Pressure and Concentration 305
9.2.1. Solution-Solid Component Equilibrium 306
9.2.2. Solution-Gas Equilibrium 307
9.3. Gas Mixture-Pure Component Equilibrium 317
9.4. Influence of Dispersion on Solubility 318
Chapter 10. SOLUTION-SOLUTION EQUILIBRIUM IN BINARY MIXTURES 319
10.1. Liquid-Gas Equilibrium for Completely Miscible Liquids at Low Pressures 319
10.1.1. Ideal Solution-Mixture of Ideal Gases 319
10.1.2. Non-Ideal Solution-Mixture of Ideal Gases 322
10.1.3. Separation of Solution Components 332
10.2. Liquid-Gas Equilibrium for Completely Miscible Liquids at High Pressures 334
10.2.1. Critical Phenomena 341
10.3. Equilibrium in Systems with Incompletely Miscible Liquids 349
10.3.1. Liquid-Gas Equilibrium 349
10.3.2. Liquid-Liquid Equilibrium 351
10.3.3. Gas-Gas Equilibrium 352
10.4. Liquid-Gas Equilibrium for Immiscible Liquids 355
Chapter 11. EQUILIBRIUM IN THREE- AND FOUR-COMPONENT SYSTEMS 359
11.1. Depicting Composition 359
11.1.1. Three-Component Systems 359
11.1.2. Four-Component Systems 361
11.2. Liquid-Solid Equilibrium in Three-Component Systems 362
11.2.1. Substances Forming No Compounds 362
11.2.2. Substances Forming Compounds 366
11.2.3. Isotherms of Aqueous Solutions of Two Common-Ion Salts 367
11.3. Mutual Solubility of Three Liquids 385
11.4. Liquid-Gas Equilibrium in Ternary Systems 391
11.4.1. Isotherm 391
11.4.2. Is

obaric Systems 399
Chapter 12. THE PRINCIPLE OF MAXIMUM ENTROPY 405
12.1. Entropy as a Thermodynamic Function 405
12.2. Method of Maximum Entropy 410
12.3. Application of the Maximum Entropy Principle in Thermodynamics 414
Chapter 13. MODERN CONCEPTS OF THERMODYNAMICS 419
13.1. Thermodynamic Models 419
13.2. Relations with Other Areas of Science 421
13.3. Role of Thermodynamics in Physical Chemistry 424
13.4. Applications of Thermodynamics in Industry 427
13.5. Advanced Topics in Thermodynamics 430

Chapter 14. EQUILIBRIUM TRANSFORMATION 518

14.1. Direction of a Process 518

14.2. Calculation of Equilibrium Transformation 527

14.2.1. Reactions in the Gaseous Phase 528

14.2.2. Reactions in Solutions 531

14.2.3. Heterogeneous Reactions 533

14.2.4. Electrochemical Reactions 537

14.3. Influence of Various Factors on the Extent of a Reaction 541

14.3.1. Temperature 541

14.3.2. Pressure 545

14.3.3. Presence of an Inert Gas 548

14.3.4. Ratio of Reactants 549

14.3.5. Change in Surface Area 550

14.3.6. Kind of Reaction 552

14.4. Equilibrium in Complex Chemical Systems 553

14.5. Sources of Errors in Calculating Equilibrium 562

14.5.1. Errors Due to Inaccuracy of Experimental Data 562

14.5.2. Errors Connected with the Processing of Experimental Data 564

14.6. Theoretical and Practical Extents of a Reaction 566

Chapter 15. FUNDAMENTALS OF QUANTUM STATISTICAL CALCULATIONS OF THERMODYNAMIC FUNCTIONS AND CHEMICAL EQUILIBRIUM FROM SPECTROSCOPIC DATA 568

15.1. Introduction 568

15.2. Thermodynamic Properties of Gases Due to Translational Degrees of Freedom 572

15.3. Thermodynamic Properties of Gases Due to Intramolecular Degrees of Freedom 575

15.3.1. Rotational Partition Function 577

15.3.2. Vibrational Partition Function 583

15.3.3. Partition Function for Electronic Excitation 587

15.3.4. Nuclear Spin 588

15.3.5. Effect of Isotopic Composition 589

15.3.6. Group of Properties 589

15.4. Calculation of Chemical Equilibrium 592

APPENDICES 599

List of Symbols 599

Heat Capacities, Standard Enthalpies and Gibbs Energies of

Semiconductor Physics by P.S. Kireev

This textbook originates from lectures delivered by the author to students of the Semiconductor Materials and Devices Faculty at the Moscow Institute of Steel and Alloys. It assumes prior knowledge of subjects like Crystallography and Quantum Mechanics, allowing the material to focus exclusively on semiconductor physics without revisiting crystal lattice structures or atomic bonding. Leveraging students’ understanding of quantum mechanics, the textbook employs rigorous methods to address topics such as energy band structures and charge carrier transitions, including their interactions with lattice defects, phonons, and photons. Detailed intermediate calculations and experimental data further enhance comprehension.

While the material is presented at a high level, it remains accessible, supported by clear derivations and illustrations. Group theory methods are introduced to simplify problem-solving but are confined to an appendix, as this subject is typically not part of technical college curricula. The book deliberately avoids covering the operation of specific semiconductor devices, treating Semiconductor Physics as a distinct discipline with a focus on fundamental principles.

Translated from the Russian by Mark Samokhvalov

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CONTENTS
Preface 9

Chapter I. Introduction. Electron Theory of Conductivity 11

Electron Theory of Conductivity. Ohm’s Law 11
Mean-Free Time and Free-Path Distribution Functions 16
Electron Distribution Function. Mean Values of Physical Quantities 20
Semiconductors. The Classification of Materials According to Their Conductivity 31
Semiconductor Conductivity Models. The Concept of a Hole 35
Intrinsic and Extrinsic Conductivities 39
Chapter II. The Fundamentals of the Band Theory of Semiconductors 42
7. The Schrödinger Equation for the Crystal 42
8. The Adiabatic Approximation 45
9. Single Electron Approximation 50
10. Periodic Field of the Crystal Lattice. Translational Operator 54
11. Quasimomentum 59
12. The Effective Mass of the Electron 64
13. Relation Between Velocity and Quasimomentum 70
14. Acceleration Operator 73
15. Brillouin Zones 80
16. Normalising Inside a Potential Box and the Discrete Nature of Quasimomentum 85
17. Theory of the Quasifree Electron 90
18. Theory of the Quasibound Electron 105
19. Effective Mass Method. Influence of External Fields on Energy Spectrum of a Crystal 119
20. Localised States 125
21. Elementary Theory of Impurity States 130
22. Surface States 138
23. Quantisation of Electron Energy in a Magnetic Field. Landau Levels 141
24. Pauli Principle. Concept of Metal, Semiconductor, and Dielectric 146
25. Main Features of the Hole 153
26. Band Structure of Some Semiconductors. Calculation Methods 158
27. Quasiparticle Concept 175

Chapter III. Electron and Hole Statistics in Semiconductors 180
28. Density of States 180
29. Electron and Hole Concentrations 189
30. Electric Neutrality Equation 197
31. Intrinsic Semiconductor 200
32. Extrinsic Semiconductor. Impurity of One Type 205
33. Semiconductor Doped with Both Acceptor and Donor Impurities 215
34. Degenerate Semiconductor 221
35. Density of States in a Magnetic Field 225

Chapter IV. Kinetic Phenomena in Semiconductors 234
36. Boltzmann’s Kinetic Equation 234
37. Relaxation Time 241
38. Electric Current Density and Energy Flux Density 249
39. Kinetic Coefficients 253
40. Conductivity of Semiconductors 261
41. Galvanomagnetic Effects 270
42. Hall Effect in Extrinsic Conductivity Range 280
43. Hall Effect in a Substance with Several Types of Charge Carriers 288
44. Magnetic Field Dependence of Hall Coefficient 294
45. Magnetoresistive Effect 302
46. Heat Conductivity of Semiconductors 311
47. Thermoelectric Phenomena 318
48. Thermomagnetic Phenomena 334
49. General Analysis of Kinetic Phenomena 338
50. On Kinetic Phenomena in Semiconductors with Tensor Effective Masses 348
51. Tensorsensitive Effect. Tensorsensitivity 352
52. Piezoresistive Effect. Piezoresistance Coefficients 359

Chapter V. The Theory of Charge Carrier Scattering 369
53. Effective Scattering Cross Section 369
54. Relationship Between Relaxation Time and Effective Cross Section 378
55. Elements of Quantum Transition Theory 383
56. Impurity Ion Scattering 390
57. Scattering by Neutral Impurity Atoms 398
58. Lattice Vibrations. Normal Coordinates, Phonons 401
59. Acoustical and Optical Lattice Vibrations 409
60. Lattice Specific Heat. Phonon Statistics 422
61. Scattering by Thermal Lattice Vibrations. Method of Deformation Potential 432
62. Temperature Dependence of Charge Carrier Mobility 441
63. Dependence of Relaxation Time on External Fields. Deviations from Ohm’s Law 452

Chapter VI. Charge Carrier Recombination 461
64. Continuity Equation. Lifetime 461
65. Recombination Mechanism. Linear Recombination 472
66. Diffusion and Drift of Nonequilibrium Charge Carriers 484
67. Surface Recombination 492

Chapter VII. Contact Phenomena in Semiconductors 497
68. Debye Length 497
69. Work Function 510
70. Contact Potential Difference. Metal-Metal Contact 515
71. Metal-Semiconductor Contact 519
72. Inhomogeneous Semiconductor, p-n Junction 525

Chapter VIII. Optical and Photoelectrical Phenomena in Semiconductors 532
73. Light-Absorption Spectrum 532
74. Light Absorption by Free Charge Carriers 536
75. Cyclotron Resonance 546
76. Intrinsic Light Absorption 555
77. Absorption of Light by the Lattice 573
78. Light Absorption by Electrons in Localised States 579
79. Influence of the Ambient on Absorption Spectrum 586
80. Photoresistive Effect 590
81. Dember Effect. Photovoltaic Effect 599
82. Photomagnetoelectric Effect 608
83. Faraday Effect 613
84. Spin-Orbital Splitting of Energy Bands 623

Appendix. Introduction to the Theory of Groups 633

Space Transformations 633
Group of Symmetry Transformations. Properties of Group Elements 639
Relation Between Groups 643
Representation of Groups 646
The Properties of Irreducible Representations 649
The Basis of a Representation 652
Direct Product of Representations 655
Point Groups 659
Translational Groups. Brillouin Zones 665
The Wave Vector Group 671
Schrödinger Equation 680
Twin Groups. Time Inversion 684
Recommended Literature 694

Theory Of Stellar Spectra by V.V. Sobolev

The only source of our information on stars is their radiation. From stellar spectra we judge the structure of stellar atmospheres, their chemical composition, and physical processes taking place there. Spectrograms are interpreted on the basis of the theory of stellar spectra, wherein lies its enormous value for astrophysics. Until recently astronomers could observe stellar radiation only in a very small range of frequencies making up the visible region of the spectrum. However, about 20 years ago radio astronomy came into being which permits investigating the radiation of celestial bodies in a completely different spectral region.

Quite recently, in connection with the launching of satellites and rockets, there arose the theoretical possibility of obtaining stellar spectra in any frequency range. So far, highly useful spectrograms of stars and the sun have been obtained in the so-called rocket ultraviolet. It is obvious that this broadening of observational data will even further increase the significance of the theory of stellar spectra. At the same time it is necessary to improve and extend this theory.

The surface layers of stars, out of which their spectra arise, represent
strongly ionized gases, i.e., plasma. Plasma studies are also being carried out in physics laboratories, having increased in intensity of late. Methods used by physicists in studying plasmas are in many respects similar to methods used by astrophysicists in studying stellar atmospheres. Therefore, the theory of stellar spectra is of interest not only to astrophysicists but also to physicists.

An excellent example of the broad interest in the theory of stellar spectra is the summer seminary on problems of this theory, organized by the
Astronomical Council of the Academy of Sciences of the USSR and the Leningrad University and held in Leningrad in June 1964* About 150 young astrophysicists and physicists of the Soviet Union participated in the sessions. This book was written on the basis of the lectures given at that time.
The first part of the book examines atomic processes associated with the
formation of spectra, with special emphasis on calculation of the energy levels of the atom and the probability of transitions between these levels. The second part deals with the theory of radiation transfer, which forms an important aspect of the theory of stellar spectra. The next two parts discuss the most essential problems in the formation of spectra of different types of stars and nebulae. The last part, devoted to ultraviolet spectra of celestial bodies, mainly gives a review of observational data and their qualitative interpretation (since, as yet, no quantitative theory of these spectra has been established).
The diversity of the problems of the modern theory of stellar spectra makes it impossible to present them with sufficient completeness in a single monograph.
The authors of this book have endeavored to acquaint the reader with the most important of these problems.

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Preface …………………………………………… iii
PART I. PHYSICAL PROCESSES CONNECTED WITH THE FORMATION OF SPECTRA ………… 1
Plasma Spectroscopy (S.E. Frish) …………………….. 1
Calculations of Atomic Energy Levels (A.P. Yutsis and Ya.I. Vizbarayte) …………… 23
Theory of Atomic Transitions (G.F. Drukarev) ……….. 35

PART II. THEORY OF RADIATIVE TRANSFER ……………………… 64
Certain Nonlinear Problems of the Theory of Radiative Transfer (V.A. Ambartsumyan) ……. 64
Radiative Diffusion in Gases (V.V. Sobolev) …………. 75
Determination of the Populations of Excited Levels in an Optically Thick Gas Layer (V.V. Ivanov) ……….. 92
Nonstationary Radiation Field (I.N. Minin) …………. 116
Randomized Problem of Diffuse Reflection (R.V. Ambartsumyan) ………… 135

PART III. SPECTRA OF FIXED STARS ……………………….. 140
Models of Stellar Atmospheres (V.V. Sobolev) ………. 140
Continuous Spectra of Hot White Dwarfs (A.K. Kolesov) ……. 147
Model Atmospheres of Main-Sequence Stars of Class M (V.G. Buslavskiy) …….. 152
Determination of the Chemical Composition of Stellar Atmospheres (A.A. Boyarchuk) ……….. 160

PART IV. SPECTRA OF NONSTATIONARY STARS AND INTERSTELLAR MATTER ………… 170
Spectra of Nonstationary (Variable) Stars (V.G. Gorbatskiy) ……….. 170
Analysis of the Emission Spectra of Nonstationary Stars (A.A. Boyarchuk) ………… 194
Spectra of Interstellar Matter (S.A. Kaplan) ………… 203
Radio Observations of Planetary Nebulae (Yu. N. Pariyskiy) ………. 216

PART V. SPECTRA OF CELESTIAL BODIES IN THE FAR ULTRAVIOLET REGION ……….. 220
Spectra of Celestial Bodies in the Far Ultraviolet Region (G.A. Gurzadyan) ………. 220

ଆଲେକ୍ସେଇ କ୍ରିଲୋଭ From Bonfire To Reactor (In Odia by Alexei Krylov)

A popular science book for children explaining various sources of energy and how we can harness them from nature.

Some really fantastic full page drawings by Andrei Platonov

Translated to Oriya

Why do airplanes fly?
What makes cars and trains run?
Why is electricity provided to our homes and to factories? Why do people eat? Indeed, why and what for?

ତିହାସ

– ଚିତ୍ରାଙ୍କନ – ଆଦେଲ ପ୍ଲାଟୋନୋଭ୍

ଅନୁବାଦ – ଅରୁଣ ଢୁମାର ମହାନ୍ତ
– ମୁଖ୍ୟ ପରିବେଶକ – ନବଯୁଗ ଗ୍ରନ୍ଥାଳୟ

ବଜ୍ରକବାଟି ରୋତ୍

କଟକ – ୭୫୩୦୦୧

ଶିଶୁମାନଙ୍କ ପାଇଁ ଏକ ଲୋକପ୍ରିୟ ବିଜ୍ଞାନ ପୁସ୍ତକ, ଯାହାରେ ଉର୍ଜାର ବିଭିନ୍ନ ସ୍ରୋତ ଏବଂ ପ୍ରକୃତିରୁ ସେଗୁଡ଼ିକୁ କିପରି ଅଧିଗମନ କରାଯାଇପାରେ, ସେବିଷୟରେ ବିସ୍ତାରରେ ବ୍ୟାଖ୍ୟା କରାଯାଇଛି।

ଆନ୍ଦ୍ରେଇ ପ୍ଲାଟୋନଭଙ୍କ ଦ୍ୱାରା ଆକର୍ଷଣୀୟ ପୃଷ୍ଠା ପୃଷ୍ଠା ଅଙ୍କନରେ ଭରିଥିବା ପୃଷ୍ଠାଗୁଡ଼ିକ ପୁସ୍ତକକୁ ଆରୋ ଆକର୍ଷଣୀୟ କରିଛି।

ଏହି ପ୍ରଶ୍ନଗୁଡ଼ିକ ଜିଜ୍ଞାସାକୁ ଜଗାଇ ଦିଏ:
ଏୟାରପ୍ଲେନ୍ କାହିଁକି ଉଡେ?
କାହିଁକି ଗାଡ଼ି ଏବଂ ଟ୍ରେନ୍ ଚାଲେ?
ଆମ ଘର ଏବଂ କାରଖାନାଗୁଡ଼ିକୁ ବିଦ୍ୟୁତ୍ କାହିଁକି ଯୋଗାଇ ଯାଏ?
ଲୋକମାନେ କାହିଁକି ଖାଉଛନ୍ତି?
ସତରେ, କାହିଁକି ଏବଂ କଣ ପାଇଁ?

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रासायनिक मूलद्रव्यांचा शोध – दमी. त्रीफोनोव, व. त्रीफोनोव (Chemical Elements How They Were Discovered In Marathi by D. N. Trifonov, V. D. Trifonov )

या पुस्तकामध्ये आपण रसायनशास्त्रातील “मुळाक्षरां “ची कशी रचना झाली, तसेच आपल्या चौकस बुद्धिमत्तेतून संशोधकांनी एकामागोमाग एकेका नव्या मूलद्रव्याचा शोध कसा लावला याचे विवेचन करणार आहोत.

बहुतेक सर्व रासायनिक मूलद्रव्यांवर अनेक पुस्तके लिहिली गेली आहेत. त्यांची संख्या एवढी प्रचंड आहे की त्यांचे एक स्वतंत्र ग्रंथालयच होईल. त्या पुस्तकांमध्ये, मूलद्रव्यांचा अंतर्भाव असणारे खडक व खनिजे, त्यांच्या नि- एकर्षणाच्या विविध पद्धती, मूलद्रव्यांचे भौतिक आणि रासायनिक गुणधर्म यांचा आढावा घेतलेला असतो. काही मूलद्रव्ये आश्चर्य वाटण्याएवढी मुबलक आहेत. त्यांचे उपयोगही अनपेक्षित वाटावेत एवढ्या भिन्नभिन्न क्षेत्रात केलेले आढळतील. खरे तर आजच्या प्रगत वैज्ञानिक युगात प्रत्येक मूलद्रव्याचा काहीना काहीतरी महत्त्वपूर्ण उपयोग आहेच आहे असेच दिसेल. प्रत्येक मूलद्रव्याचे त्याचे स्वतःचे असे खास “चरित्र” असून ती सारी आपापल्या परीने वैशिष्ट्यपूर्णही आहेत हे खरे की मूलद्रव्यांच्या शोधांच्या इतिहासाबाबत अद्यापीही बरीच संदिग्धता आहे व इतिहासकारांना न सुटलेले प्रश्न अजूनही सोडविता आलेले नाहीत. कुणी सांगावे, त्यांच्यापैकी एखादा- दुसरा इतिहासकार तुम्हीही असू शकाल !

अनुवाद : राजेंद्र सहस्रबुद्धे

You can get the book here and here

Follow us on

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

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Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles

रासायनिक मूलद्रव्यांचा शोध – दमी. त्रीफोनोव, व. त्रीफोनोव (Chemical Elements How They Were Discovered In Marathi by D. N. Trifonov, V. D. Trifonov )

या पुस्तकामध्ये आपण रसायनशास्त्रातील “मुळाक्षरां “ची कशी रचना झाली, तसेच आपल्या चौकस बुद्धिमत्तेतून संशोधकांनी एकामागोमाग एकेका नव्या मूलद्रव्याचा शोध कसा लावला याचे विवेचन करणार आहोत.

बहुतेक सर्व रासायनिक मूलद्रव्यांवर अनेक पुस्तके लिहिली गेली आहेत. त्यांची संख्या एवढी प्रचंड आहे की त्यांचे एक स्वतंत्र ग्रंथालयच होईल. त्या पुस्तकांमध्ये, मूलद्रव्यांचा अंतर्भाव असणारे खडक व खनिजे, त्यांच्या नि- एकर्षणाच्या विविध पद्धती, मूलद्रव्यांचे भौतिक आणि रासायनिक गुणधर्म यांचा आढावा घेतलेला असतो. काही मूलद्रव्ये आश्चर्य वाटण्याएवढी मुबलक आहेत. त्यांचे उपयोगही अनपेक्षित वाटावेत एवढ्या भिन्नभिन्न क्षेत्रात केलेले आढळतील. खरे तर आजच्या प्रगत वैज्ञानिक युगात प्रत्येक मूलद्रव्याचा काहीना काहीतरी महत्त्वपूर्ण उपयोग आहेच आहे असेच दिसेल. प्रत्येक मूलद्रव्याचे त्याचे स्वतःचे असे खास “चरित्र” असून ती सारी आपापल्या परीने वैशिष्ट्यपूर्णही आहेत हे खरे की मूलद्रव्यांच्या शोधांच्या इतिहासाबाबत अद्यापीही बरीच संदिग्धता आहे व इतिहासकारांना न सुटलेले प्रश्न अजूनही सोडविता आलेले नाहीत. कुणी सांगावे, त्यांच्यापैकी एखादा- दुसरा इतिहासकार तुम्हीही असू शकाल !

अनुवाद : राजेंद्र सहस्रबुद्धे

You can get the book here and here

Follow us on

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

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Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles

रासायनिक मूलद्रव्यांचा शोध – दमी. त्रीफोनोव, व. त्रीफोनोव (Chemical Elements How They Were Discovered In Marathi by D. N. Trifonov, V. D. Trifonov )

या पुस्तकामध्ये आपण रसायनशास्त्रातील “मुळाक्षरां “ची कशी रचना झाली, तसेच आपल्या चौकस बुद्धिमत्तेतून संशोधकांनी एकामागोमाग एकेका नव्या मूलद्रव्याचा शोध कसा लावला याचे विवेचन करणार आहोत.

बहुतेक सर्व रासायनिक मूलद्रव्यांवर अनेक पुस्तके लिहिली गेली आहेत. त्यांची संख्या एवढी प्रचंड आहे की त्यांचे एक स्वतंत्र ग्रंथालयच होईल. त्या पुस्तकांमध्ये, मूलद्रव्यांचा अंतर्भाव असणारे खडक व खनिजे, त्यांच्या नि- एकर्षणाच्या विविध पद्धती, मूलद्रव्यांचे भौतिक आणि रासायनिक गुणधर्म यांचा आढावा घेतलेला असतो. काही मूलद्रव्ये आश्चर्य वाटण्याएवढी मुबलक आहेत. त्यांचे उपयोगही अनपेक्षित वाटावेत एवढ्या भिन्नभिन्न क्षेत्रात केलेले आढळतील. खरे तर आजच्या प्रगत वैज्ञानिक युगात प्रत्येक मूलद्रव्याचा काहीना काहीतरी महत्त्वपूर्ण उपयोग आहेच आहे असेच दिसेल. प्रत्येक मूलद्रव्याचे त्याचे स्वतःचे असे खास “चरित्र” असून ती सारी आपापल्या परीने वैशिष्ट्यपूर्णही आहेत हे खरे की मूलद्रव्यांच्या शोधांच्या इतिहासाबाबत अद्यापीही बरीच संदिग्धता आहे व इतिहासकारांना न सुटलेले प्रश्न अजूनही सोडविता आलेले नाहीत. कुणी सांगावे, त्यांच्यापैकी एखादा- दुसरा इतिहासकार तुम्हीही असू शकाल !

अनुवाद : राजेंद्र सहस्रबुद्धे

You can get the book here and here

Follow us on

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

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Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles

रासायनिक मूलद्रव्यांचा शोध – दमी. त्रीफोनोव, व. त्रीफोनोव (Chemical Elements How They Were Discovered In Marathi by D. N. Trifonov, V. D. Trifonov )

या पुस्तकामध्ये आपण रसायनशास्त्रातील “मुळाक्षरां “ची कशी रचना झाली, तसेच आपल्या चौकस बुद्धिमत्तेतून संशोधकांनी एकामागोमाग एकेका नव्या मूलद्रव्याचा शोध कसा लावला याचे विवेचन करणार आहोत.

बहुतेक सर्व रासायनिक मूलद्रव्यांवर अनेक पुस्तके लिहिली गेली आहेत. त्यांची संख्या एवढी प्रचंड आहे की त्यांचे एक स्वतंत्र ग्रंथालयच होईल. त्या पुस्तकांमध्ये, मूलद्रव्यांचा अंतर्भाव असणारे खडक व खनिजे, त्यांच्या नि- एकर्षणाच्या विविध पद्धती, मूलद्रव्यांचे भौतिक आणि रासायनिक गुणधर्म यांचा आढावा घेतलेला असतो. काही मूलद्रव्ये आश्चर्य वाटण्याएवढी मुबलक आहेत. त्यांचे उपयोगही अनपेक्षित वाटावेत एवढ्या भिन्नभिन्न क्षेत्रात केलेले आढळतील. खरे तर आजच्या प्रगत वैज्ञानिक युगात प्रत्येक मूलद्रव्याचा काहीना काहीतरी महत्त्वपूर्ण उपयोग आहेच आहे असेच दिसेल. प्रत्येक मूलद्रव्याचे त्याचे स्वतःचे असे खास “चरित्र” असून ती सारी आपापल्या परीने वैशिष्ट्यपूर्णही आहेत हे खरे की मूलद्रव्यांच्या शोधांच्या इतिहासाबाबत अद्यापीही बरीच संदिग्धता आहे व इतिहासकारांना न सुटलेले प्रश्न अजूनही सोडविता आलेले नाहीत. कुणी सांगावे, त्यांच्यापैकी एखादा- दुसरा इतिहासकार तुम्हीही असू शकाल !

अनुवाद : राजेंद्र सहस्रबुद्धे

You can get the book here and here

Follow us on

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

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Tumblr https://www.tumblr.com/mirtitles

Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles

रासायनिक मूलद्रव्यांचा शोध – दमी. त्रीफोनोव, व. त्रीफोनोव (Chemical Elements How They Were Discovered In Marathi by D. N. Trifonov, V. D. Trifonov )

या पुस्तकामध्ये आपण रसायनशास्त्रातील “मुळाक्षरां “ची कशी रचना झाली, तसेच आपल्या चौकस बुद्धिमत्तेतून संशोधकांनी एकामागोमाग एकेका नव्या मूलद्रव्याचा शोध कसा लावला याचे विवेचन करणार आहोत.

बहुतेक सर्व रासायनिक मूलद्रव्यांवर अनेक पुस्तके लिहिली गेली आहेत. त्यांची संख्या एवढी प्रचंड आहे की त्यांचे एक स्वतंत्र ग्रंथालयच होईल. त्या पुस्तकांमध्ये, मूलद्रव्यांचा अंतर्भाव असणारे खडक व खनिजे, त्यांच्या नि- एकर्षणाच्या विविध पद्धती, मूलद्रव्यांचे भौतिक आणि रासायनिक गुणधर्म यांचा आढावा घेतलेला असतो. काही मूलद्रव्ये आश्चर्य वाटण्याएवढी मुबलक आहेत. त्यांचे उपयोगही अनपेक्षित वाटावेत एवढ्या भिन्नभिन्न क्षेत्रात केलेले आढळतील. खरे तर आजच्या प्रगत वैज्ञानिक युगात प्रत्येक मूलद्रव्याचा काहीना काहीतरी महत्त्वपूर्ण उपयोग आहेच आहे असेच दिसेल. प्रत्येक मूलद्रव्याचे त्याचे स्वतःचे असे खास “चरित्र” असून ती सारी आपापल्या परीने वैशिष्ट्यपूर्णही आहेत हे खरे की मूलद्रव्यांच्या शोधांच्या इतिहासाबाबत अद्यापीही बरीच संदिग्धता आहे व इतिहासकारांना न सुटलेले प्रश्न अजूनही सोडविता आलेले नाहीत. कुणी सांगावे, त्यांच्यापैकी एखादा- दुसरा इतिहासकार तुम्हीही असू शकाल !

अनुवाद : राजेंद्र सहस्रबुद्धे

You can get the book here and here

Follow us on

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

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Internet Archive https://archive.org/details/mir-titles

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"How did #SovietAuthors treat the #Holocaust? How did it differ from work elsewhere? And what are some of the challenges translating these works into English?"

#HarrietMurav and #SashaSenderovich discuss the new collection of #shortStories they edited and translated, #InTheShadowOfTheHolocaust: Short Fiction by #JewishWriters from the #SovietUnion

https://www.euraknot.org/soviet-holocaust-literature/
#SovietJews #JewishHistory #WWII #SovietLiterature #HolocaustLiterature #books @bookstodon

"How did #SovietAuthors treat the #Holocaust? How did it differ from work elsewhere? And what are some of the challenges translating these works into English?"

#HarrietMurav and #SashaSenderovich discuss the new collection of #shortStories they edited and translated, #InTheShadowOfTheHolocaust: Short Fiction by #JewishWriters from the #SovietUnion

https://www.euraknot.org/soviet-holocaust-literature/
#SovietJews #JewishHistory #WWII #SovietLiterature #HolocaustLiterature #books @bookstodon

"How did #SovietAuthors treat the #Holocaust? How did it differ from work elsewhere? And what are some of the challenges translating these works into English?"

#HarrietMurav and #SashaSenderovich discuss the new collection of #shortStories they edited and translated, #InTheShadowOfTheHolocaust: Short Fiction by #JewishWriters from the #SovietUnion

https://www.euraknot.org/soviet-holocaust-literature/
#SovietJews #JewishHistory #WWII #SovietLiterature #HolocaustLiterature #books @bookstodon

"How did #SovietAuthors treat the #Holocaust? How did it differ from work elsewhere? And what are some of the challenges translating these works into English?"

#HarrietMurav and #SashaSenderovich discuss the new collection of #shortStories they edited and translated, #InTheShadowOfTheHolocaust: Short Fiction by #JewishWriters from the #SovietUnion

https://www.euraknot.org/soviet-holocaust-literature/
#SovietJews #JewishHistory #WWII #SovietLiterature #HolocaustLiterature #books @bookstodon

"How did #SovietAuthors treat the #Holocaust? How did it differ from work elsewhere? And what are some of the challenges translating these works into English?"

#HarrietMurav and #SashaSenderovich discuss the new collection of #shortStories they edited and translated, #InTheShadowOfTheHolocaust: Short Fiction by #JewishWriters from the #SovietUnion

https://www.euraknot.org/soviet-holocaust-literature/
#SovietJews #JewishHistory #WWII #SovietLiterature #HolocaustLiterature #books @bookstodon

The Turning Point by Otto Lacis

When farmers lease plots of land in abandoned villages today, the state of desolation they find there is amazing. Those villages are found in areas that were occupied by the enemy during the war and also in regions that the enemy did not reach. The desolation and neglect have nothing to do with the war. They were caused by the Great Turn imposed on the nation by Stalin—the turn that crushed the peasants’ initiative, diligence and desire to work.

You can get the book here and here

Follow us on

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Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles

The Turning Point by Otto Lacis

When farmers lease plots of land in abandoned villages today, the state of desolation they find there is amazing. Those villages are found in areas that were occupied by the enemy during the war and also in regions that the enemy did not reach. The desolation and neglect have nothing to do with the war. They were caused by the Great Turn imposed on the nation by Stalin—the turn that crushed the peasants’ initiative, diligence and desire to work.

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

The Turning Point by Otto Lacis

When farmers lease plots of land in abandoned villages today, the state of desolation they find there is amazing. Those villages are found in areas that were occupied by the enemy during the war and also in regions that the enemy did not reach. The desolation and neglect have nothing to do with the war. They were caused by the Great Turn imposed on the nation by Stalin—the turn that crushed the peasants’ initiative, diligence and desire to work.

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

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The Turning Point by Otto Lacis

When farmers lease plots of land in abandoned villages today, the state of desolation they find there is amazing. Those villages are found in areas that were occupied by the enemy during the war and also in regions that the enemy did not reach. The desolation and neglect have nothing to do with the war. They were caused by the Great Turn imposed on the nation by Stalin—the turn that crushed the peasants’ initiative, diligence and desire to work.

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The Turning Point by Otto Lacis

When farmers lease plots of land in abandoned villages today, the state of desolation they find there is amazing. Those villages are found in areas that were occupied by the enemy during the war and also in regions that the enemy did not reach. The desolation and neglect have nothing to do with the war. They were caused by the Great Turn imposed on the nation by Stalin—the turn that crushed the peasants’ initiative, diligence and desire to work.

You can get the book here and here

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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.

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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
Exercises

Chapter 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
Exercises

Chapter 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
Exercises

Chapter 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
Exercises

Chapter 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
Exercises

Chapter 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
Exercises

Chapter 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
Exercises

Chapter 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
Exercises

Chapter 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 – 169

Chapter 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 – 196

Chapter 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 – 230

Chapter 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 – 247

Chapter 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 – 272

Chapter 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 – 299

Chapter 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 – 322

Chapter 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 – 332

Chapter 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 – 349

Chapter 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 – 373

Chapter 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 – 393

Chapter 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 – 428

Chapter 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 – 479

Chapter 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 – 557

Chapter 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 – 588

Chapter 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 – 603

B. 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 – 614

C. 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 – 636

Chapter 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 – 645

APPENDICES
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 – 671

ANSWERS – 674
SUBJECT INDEX – 684

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

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

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 Mazanav

Released 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

Twitter: @MirTitles
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Translators 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