Sequences and Combinatorial Problems ( Pocket Mathematical Library Workbook 1)- Gelfand et al

Posted on December 19, 2021 by The Mitr

In this post, we will see the book Sequences And Combinatorial Problems (Pocket Mathematical Library Workbook 1) by S. I. Gelfand; M. L. Gerver; A. A. Kirillov; N. N. Konstantinov; A.G. Kushnirenko.

About the book

This book has a very simple structure. It begins with a brief section called “Preliminaries” presenting the modicum of background information needed to solve the 89 problems stated in the next section, called “Sample Problems.” These problems are, for the most part, equipped with hints or answers or both. But the nub of the book is the section called “Detailed Solutions,” where you will find all 89 sample problems worked out in full detail. In our opinion, just studying these solutions (after first spending a decent amount of time trying to solve the problems on your own!) is a perfectly plausible way of learning about sequences and combinatorial problems. Finally, to make sure you have mastered the subject matter of the book, you should attack all 37 problems in the section called “Test Problems.” In fact, think of this section as a (rather tough) final examination on which you must get at least a passing grade. Good luck!

The book was translated from Russian by Richard Silverman was published in 1969.

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Preface vii
Preliminaries 1
Sample Problems 8
Detailed Solutions 25
Test Problems 81

Posted in books, mathematics, problem books, soviet | Tagged combinatorics, differences, high school, mathematics, patterns, problem books, problems, problems and solutions, proof by induction, sequences, series, solutions, soviet, workbooks | 1 Comment

A Course of Mathematical Analysis (Vols 1 and 2) – Nikolsky

Posted on December 18, 2021 by The Mitr

In this post we will see the two volume Course in Mathematical
Analysis by S. M. Nikolsky.

About the book

The major part of this two-volume textbook stems from the
course in mathematical analysis given by the author for many
years at the Moscow Physico-technical Institute.

The first volume consisting of eleven chapters includes an
introduction (Chapter 1)which treats of fundamental notions of
mathematical analysis using an intuitive concept of a limit. With
the aid of visual interpretation and some considerations of a
physical character it establishes the relationship between the
derivative and the integral and gives some elements of differentiation and integration techniques necessary to those readers who are simultaneously studying physics.

The notion of a real number is interpreted in the first volume
(Chapter 2) on the basis of its representation as an infinite decimal. Chapters 3-11 contain the following topics: Limit of Sequence, Limit of Function, Functions of One Variable, Functions of Several Variables, Indefinite Integral, Definite Integral, Some Applications of Integrals, Series.

Volume 2 contains multiple integrals, field theory. Fourier series and Fourier integral, differential manifolds and differential forms, and the Lebesgue integral.

The books were translated from the Russian by V. M. Volosov. The
book was published by first Mir Publishers in 1977 with reprints in
1981, 1985 and 1987. The second volume below is from the 1987 print, while the first one is from 1977 one.

Note: Volume 2 is at a much better scan resolution. In an earlier post we had seen only Vol. 2, that post had dead links. This post with both volumes has cleaned scans and updated links. Earlier post has been updated.

Credits to the original uploaders.

You can get

Volume 1 here

and here

Volume 2 here

and here

Volume 1

Preface to the English Edition 5

Chapter 1. Introduction 13

Chapter 2. Real Numbers 45

Chapter 3. Limit of Sequence 68

Chapter 4. Limit of Function 90

Chapter 5. Differential Calculus. Functions of One Variable 127

Chapter 6. n-dimensional Space. Geometrical Properties of Curves 180

Chapter 7. Differential Calculus. Functions of Several Variables 215

Chapter 8. Indefinite Integral. Properties of Polynomials 314

Chapter 9. Definite Integral 351

Chapter 10. Some applications of integral. Approximate Methods 395

Chapter 11. Series 417

Name Index 453

Subject Index 455

Volume 2

Chapter 12. Multiple Integrals 9

Chapter 13. Scalar and Vector Fields. Differentiation and Integration
of Integral with Respect to Parameter. Improper Integrals 80

Chapter 14. Normed Linear Spaces. Orthogonal Systems 147

Chapter 15. Fourier Series. Approximation of Functions with Polynomials 188

Chapter 16. Fourier Integral. Generalized Functions 240

Chapter 17. Differentiable Manifolds and Differential Forms 289

Chapter 18. Supplementary Topics 326

Chapter 19. Lebesgue Integral 338

Name Index 437
Subject Index 438

Posted in books, mathematics, mir books, mir publishers, soviet | Tagged analysis, definite integral, differentiable manifolds, differential forms, field theory, Fourier integral, fourier series, Functions of One Variable, Functions of Several Variables, Fundamentals of Mathematical Analysis, indefinite integral, lebesgue integral, Limit of Function, mathematics, mir publishers, multiple integrals, Real Numbers Limit of Sequence, series, Some Applications of Integrals, soviet, vector field | 1 Comment

Thinking Machines – Gutenmacher

Posted on December 17, 2021 by The Mitr

In this post, we will see the book Thinking Machines by L. Gutenmacher.

About the book & the author

The book describes earliest computers, technologies and computing techniques and algorithms. The fundamental aspects of computation are well described in the book.
Gutenmacher was one of the earliest computer scientists in the Soviet Union. He pioneered the usage of computers to model cognitive and linguistic processes. His research papers covered such topics as data storage and retrieval, software development, and computerized telephony. A number of his works were translated into English, German, French, and Spanish.

The book was translated from Russian by A. Zdornykh and was designed by V. Yeryomin The book was published in 1960 by Foreign Languages Publishing House.

Original scan by DLI. Note: The scan is warped and not clear at places, but is mostly readable.

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General 3

Machines and Mechanisation 5
Specialisation and “Qualification” of Information and Logical Machines 9
Block Diagram of an Electronic Information and Logical Machine 12
Machine and Human Memory 14
Machine Problems 20
Machine Tests 25

Machine Memory 32

External Memory 32
Internal Memory 48
Long-time Capacity Memory 52
Inductive Long-time Memory 58
Photo-electronic Long-time Memory 59
Memory Elements of Volatile Memory 60
Magnetic Volatile Memory 64
Capacitive Volatile Memory 68

Machine Memory Address Systems 72

Multi-dimension Address System 72

Number Magnetic Address System 78

Associative (Word) Address System 87
Automatic Dictionary 91

Information Traffic in the Machine 96

Sequential-parallel Shifting of Information 96
Telelibrary 102
Information Machines and Telephone-telegraph Stations 108

Computer Elements Information Machines 115

“Logical” keys 115
Computer Units and Circuits 120

Machine Processing of Information 138

Machine Scientific and Technical Information 138
Machine Language 146
Processing Chemistry Literature 158
Processing Statistical and Planning Information 173

Posted in books, computers, engineering, foreign languages publishing, soviet, technology | Tagged algorithms, block diagrams, circuits, computers, informatio processing, logic, logical keys, logical machines, machine processing, memory | 1 Comment

Eight Lectures on Mathematical Analysis – Khinchin

Posted on December 16, 2021 by The Mitr

In this post, we will see the book Eight Lectures On Mathematical Analysis by A. Ya. Khinchin.

About the book

Eight Lectures on Mathematical Analysis is a translation and adaptation of a book by the outstanding Russian mathematician A. Ya. Khinchin. It is based on a series of lectures delivered at the University of Moscow by Professor Khinchin to improve the mathematical qualifications of engineers.

In this book, the reader will find a masterful outline of the fundamental ideas of mathematical analysis. Inessential details have purposely been omitted, and the resulting exposition is clear and easy to follow. The book should be accessible to anyone who has had even a sketchy introduction to the material. And yet, because it is a concise, lucid exposition of the most important concepts of mathematical analysis, the book should be of value to the student enrolled in a university course in analysis.

A. YA. KHINCHIN, until his death in 1959, was a professor at Moscow State University, a corresponding member of the Academy of Sciences, and a member of the Academy of Pedagogical Sciences of the RSFSR. The author of more than one hundred fifty mathematical research papers and books, he will be remembered as a world-renowned authority in mathematical analysis, probability theory, number theory, and mathematical statistics.

The book was translated from Russian by Irena Zygmud was published in 1965.

Credits to original uploader.

Note: This is one of the clearest exposition of these fundamental mathematical concepts that I have come across. Khinchin was a genius mathematician teacher who develops the concepts very gradually not assuming much and explains subtle points in the process which are usually missed out. Also, we never lose sight of what we are trying to achieve in a derivation with a clear logical path towards it and its consequences for the discussion. I hope you enjoy this book as much as I did.

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LECTURE 1. The Continuum 1

1. Why begin with the continuum? 1
2. Need for a theory of real numbers 3
3. Construction of the irrational numbers 7
4. Theory of the continuum 11
5. Fundamental lemmas of the real number system 16

LECTURE 2. Limits 22

6. What is a limit? 22
7. Some ways of tending toward a limit 24
8. The limit of a constant function 27
9. Infinitely small and infinitely large quantities 28
10. Cauchy’s condition for the limit of a function 31
11. A remark on the fundamental theorems on limits 33
12. Partial limits; the upper and lower limits 33
13. Limits of functions of several variables 40

LECTURE 3. Functions 44

14. What is a function? 44
15. The domain of a function 49
16. Continuity of a function 50
17. Bounded functions 52
18. Basic properties of continuous functions 55
19. Continuity of the elementary functions 60
20. Oscillation of a function at a point 63
21. Points of discontinuity 65
22. Monotonic functions 67
23. Functions of bounded variation 69

LECTURE 4. Series 71

24. Convergence and the sum of a series 71
25. Cauchy’s condition for convergence 74
26. Series with positive terms 75
27. Absolute and conditional convergence 81
28. Infinite products 84
29. Series of functions 88
30. Power Series 96

LECTURE 5. The Derivative 102

31. The derivative and derivates 102
32. The differential 108
33. Lagrange’s theorem (first mean value theorem) 113
34. Derivatives and differentials of higher order 116
35. Limits of ratios of infinitely small and infinitely large quantities 118
36. Taylor’s formula 121
37. Maxima and minima 125
38. Partial derivatives 127
39. Differentiating implicit functions 132

LECTURE 6. The Integral 137

40. Introduction 137
41. Definition of the integral 138
42. Criteria for integrability 144
43. Geometric and physical applications 148
44. Relation of integration to differentiation 152
45. Mean value theorems for integrals 154
46. Improper integrals 158
47. Double integrals 164
48. Evaluation of double integrals 169
49. The general operation of integration 173

LECTURE 7. Expansion of functions in series 177

50. Use of series in the study of functions 177
51. Expansion in power series 179
52. Series of polynomials and the Weierstrass theorem 183
53. Trigonometric series 190
54. Fourier coefficients 192
55. Approximation in the mean 194
56. Completeness of the system of trigonometric functions 197
57. Convergence of Fourier series for functions with a bounded integrable derivative 201
58. Extension to arbitrary intervals 203

LECTURE 8. Differential Equations 206

59. Fundamental concepts 206
60. The existence of a solution 211
61. Uniqueness of the solution 220
62. Dependence of the solution on parameters 222
63. Change of variables 226
64. Systems of equations of higher orders 230

Posted in books, mathematics, soviet | Tagged analysis, continuum, derivative, differential equations, discontinuities, expansion of series, fourier series, functions, fundamental ideas, implicit functions, integrals, lagrange's theorem, limits, mathematics, minima and maxima, partial derivatices, series, series convergence, solutions of differential equations, soviet, taylor's formula, trigonometric series | 2 Comments

The Origin of Life – Oparin

Posted on December 15, 2021 by The Mitr

In this post, we will see the book The Origin of Life by A. I. Oparin.

About the book

This book discusses the ideas of origin of life on Earth. Alexander Ivanovich Oparin was a Soviet biochemist notable for his theories about the origin of life, and for his book The Origin of Life. He also studied the biochemistry of material processing by plants and enzyme reactions in plant cells.

The book discusses the possible bio-chemical pathways, complex organic molecules, environmental conditions and geological factors for the origin and evolution of life. The book is a shortened version of his book The Origin of Life on Earth. On the whole, Oparin described a biochemical adventure marked by chemico-physics and natural selection, this latter working on microstructure. Oparin worked according to the canons of dialectic materialism applied to Nature by Friedrich Engels and did not give anything to divine and fantastic. In such context, proteins and enzymes were the dominant substances of life owing to their manifold activities

The book was translated from Russian was published in 1955 by Foreign Languages Publishing House. There are other translations as well notably by Dover published around the same time.

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CHAPTER ONE.
The Origin of Life—Materialism Versus Idealism and Religion 5

CHAPTER TWO.
The Primary Origin of the Most Elementary Organic Substances—Hydrocarbons and Their Derivatives 21

CHAPTER THREE.
The Origin of Proto-Proteins 40

CHAPTER FOUR.
The Origin of Primary Colloidal Formations 54

CHAPTER FIVE. The Organization of Living Protoplasm 64

CHAPTER SIX. The Origin of Primary Organisms 78

Conclusion 100

Posted in books, foreign languages publishing, geology, history, life sciences, popular science, soviet | Tagged biochemical pathways, chemical elements, complex organic molecules, darwin, evolution, geology, hydrocarbons, life origin, popular science, primary colloids, primary organisms, protoplasm | Leave a comment

The Teaching of Mathematics – Essays by A. Ya. Khinchin

Posted on December 14, 2021 by The Mitr

In this post, we will see the book The Teaching of Mathematics by A. Ya. Khinchin.

About the book

Khinchin was a teacher-genius before his time and a mathematician of outstanding calibre. The main contents of this book are four articles written by A. Ya. Khinchin for Russian mathematics teachers. 101 pages are devoted to four articles written between 1938 and 1949 by Khinchin (who died in 1959), the remainder of the book to biographical notes and an appendix on mathematics teaching in the Soviet school.

One of the best sections is the one on the concept of limit. The author traces the historical development of the limit concept to determine which approach is best suited for the schools.

In his first article on basic concepts, Professor Khinchin stresses the basic importance of teaching so as not to conflict with later learning. He favors simplification, but never falsification. He advocates precise language

The second article on Mathematical Definitions is excellent and should be read by high school teachers. The discussion of the difference between a definition and a description and when it is desirable to present each is particularly good. It is refreshing that a mathematician of Khinchin’s standing had such understanding of teaching problems.

Some absolute gems of advice and insight to consider if you are in education. Though written 80 years back the ideas of Khinchin are very relevant now.

The book was edited by B. V. Gnedenko and was translated from Russian by W. Cochrane and D. Vere-Jones. The book was published in 1968.

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Introduction by Ian N. Sneddon vii
Translators’ Foreword ix

B. V. Gnedenko

Introduction to the Russian edition xiii
Note for the English edition xx

A. Ya. Khinchin

Basic Concepts of Mathematics in the Secondary Schools 1
Section 1 The Concept of Number 1
Section 2 The Concept of Limit 20
Section 3 The Concept of Functional Dependence 31
Mathematical Definitions in the Secondary Schools 44
On Formalism in School Mathematics Teaching 60
On the Educative Effect of Mathematics Lessons 77

Appendix 1

B. V. Gnedenko and A. I. Markushevich 102
A. Ya. Khinchin: A Biographical Sketch 113
Bibliography of Publications 115

Appendix 2

D. Vere-Jones
Mathematics Teaching and the Soviet School 117

List of General References 165

Popular Lectures in Mathematics: Edited by I. N. Sneddon 166

Topics in Mathematics: Edited by A. L. Putnam and I. Wirszup 167

Posted in books, mathematics, soviet | Tagged khinchin, mathematical concepts, mathematical definitions, mathematical misconceptions, mathematics classroom, mathematics curriculum, mathematics textbooks, russian mathematics, soviet education, students, teachers, teaching of mathematics | 1 Comment

A Collection Of Problems On Mathematical Physics – Budak, Samarskii, Tikhonov

Posted on December 13, 2021 by The Mitr

In this post, we will see the book A Collection Of Problems On Mathematical Physics by B. M. Budak; A. A. Samarskii; A. N. Tikhonov.

About the book

THE PRESENT book is based on the practical work with equations of mathematical physics done in the Physics Faculty and the external section of Moscow State University. The problems set forth were used in the course “Equations of Mathematical Physics” by A. N. Tikhonov and A. A. Samarskii, and in “A Collection of Problems on Mathematical Physics” by B. M. Budak.

However, in compiling the present work the range of problems examined has been considerably enlarged and the number of problems several times increased. Much attention has been given to problems on the derivation of equations and boundary conditions. A considerable number of problems are given with detailed instructions and solutions. Other problems of similar character are given only with the answers. The chapters are divided into paragraphs according to the method of solution. This has been done in order to give students the opportunity, by means of independent work, of gaining elementary technical skill in solving problems in the principal classes of the equations of mathematical physics.

Therefore this book of problems does not claim to include all methods used in mathematical physics. For example, the operational method, variational and differential methods and the application of integral equations are not considered.

It is hoped, however, that this book will be useful not only to students but also to engineers and workers in research institutions.

The book was translated from Russian by A.R.M. Robson and translation was edited by D.M. Brink. The book was published in 1964.

Credits to original uploader.

Note: You might notice the page numbering in pdf is weird and not matching the original page numbers. In the original design of the book there is a section on problems first which is followed by the solutions part which deals with chapters as they are in the first part. In this copy, the problem chapters are immediately followed by solutions chapter. For example, Chapter 1 problems are originally with page numbers 1-3 and solutions of this chapter are in pages numbered 163-170. In this version pages 1-3 are followed by 163-170 for continuity in reading. Similarly for other chapters. The book is complete though. We will post a more coherent version later.

You can get the book here.

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Chapter I Classification and Reduction to Canonical Form of Second Order Partial Differential Equations

Chapter II Equations of Hyperbolic Type

Chapter III Equations of Parabolic Type

Chapter IV Equations of Elliptic Type

Supplement

I. Different Orthogonal System of Coordinates 741

II. Some Formulae of Vector Analysis 748

III. Special Functions 749

IV. Tables 755

Posted in books, mathematics, physics, soviet | Tagged boundary value problems, canonical forms, determinants, electric fields, elliptical, gamma function, heat conduction, heat transfer, hyperbolic, laplace's equation, mathematics, media, natural oscillations, oscillations, parabolic, partial differential equations, physics, problem books, propagation of sound, riemann's method, second order, solutions, soviet, special functions, temperature distribution, vibrations | 1 Comment

Fundamentals of Engineering Mechanics – Levinson

Posted on December 12, 2021 by The Mitr

In this post, we will see the book Fundamentals of Engineering Mechanics by L. Levinson.

About the book

The book provides an overview of various aspects of engineering mechanics. The first part (chapters 1 to 14) covers theoretical aspects of statics, kinematics and dynamics required for the later sections. The second part covers theory of machines including transmission mechanisms and connections. It also covers fundamental concepts of strain including strength of materials.

The book was translated from Russian by S. Klein was published in 1962 by Foreign Languages Publishing House. (Note: the date in the book is 1922, we know for sure it is not the case and FLPH version is from 1962. Is this a case of scanners/printers randomly changing digits in the scanned/printed documents?)

Credits to original uploader the Digital Library of India. Note: the original scan is by Digital Library of India project. The project though large in scale (millions of books digitised) it is like any other typical government project in execution. There is no quality control on the scans. In some cases the scans are barely legible while in others pages or text is missing. No colour scans. And even with black and white pdfs files size is in few hundred megs in some cases. This scan is not of good quality, there are pages which are barely readable. We will try to update this with a better scan in the future.

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PART ONE Theoretical Mechanics

Introduction 13
STATICS

Chapter I. Fundamentals of Force, and an Introduction to Statics

Chapter II. Coplanar System of Concurrent Forces

Chapter III. Coplanar Parallel Forces, and the Moment of a Force

Chapter IV. Centre of Gravity, and Stability of Bodies

Chapter V. Friction

KINEMATICS

Chapter VI. The Trajectory of a Particle. Displacement and Time

Chapter VII . Rectilinear Motion of a Particle

Chapter VIII. The Composition of Simple Motions of a Particle

Chapter IX. Curvilinear Motions of a Parliele Uniform and Non-Uniforin Curvilinear Motion of a Particle

Chapter X. Simple Motions of a Hard Body

DYNAMICS

Chapter XI. Fundamentals of Dynamics

Chapter XII. Introduction to Dynamics of a Material Point

Chapter XIII. Work and Power

Chapter XIV. Mechanical Energy

PART TWO
THE THEORY OF MACHINES AND FUNDAMENTAL CONCEPTS OF STRAIN

THE THEORY OF MACHINES

Chapter XV. The Inclined Plane, the Pulley, and the Windlass

Chapter XVI. Transmission of Power Between Parallel Shafts

Chapter XVII. Transmission Between Non-Parallel Spalls

Chapter XVIII. Conversion of Rotation into Linear Translation and Vice Versa

Chapter XIX. Auxiliary Ports Employed in Transmitting Rotation

STRENGTH OF MATERIALS

Chapter XXI. Basic Principles

Chapter XXII. Tension and Compression

Chapter XXIII. Shear and Torsion

Chapter XXIV. Bending

Chapter XXV. General Principles of Combined Strain

Supplements 331

Answers To Exercises 333

Posted in books, engineering, foreign languages publishing, mathematics, physics, soviet, technology | Tagged connectors, dynamics, engineering, engineering mechanics, kinematics, load, materials, mechanics, physics, power, pulley, statics, strain, stress, theory of machines, torsion, transmission, work | 3 Comments

Chestnut Grey – Bulatov

Posted on December 11, 2021 by The Mitr

In this post, we will see the book Chestnut Grey by M. Bulatov.

About the book

Ivan, youngest of three brothers is considered a fool by his elders. While on watchful duty to guard the wheat fields at night, Ivan earns the services of Chestnut-Grey — a magical stallion with a mane of silver and gold. How does Chestnut-Grey help Ivan to win the princess? Read the book to find out!

The book was translated from Russian and was illustrated by T. Mavrina. The book was published by Progress Publishers in 1977.

All credits to Guptaji.

You can get the book here (cleaned) and here.

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Posted in books, children's books, children's stories, folk tales, progress publishers, soviet | Tagged children's book, children's literature, folk tale, horse, illustrated book, ivan, magical horse, princess, progress publishers, russian, story book | Leave a comment

The Haughty Egg by Eno Raud

Posted on December 10, 2021 by The Mitr

In this post, we will see the book The Haughty Egg by Eno Raud.

About the book

One day Mother hen decides to lay an egg, but the egg disobeys and leaves the nest, rolling away. What happens to the egg? How will it survive on its own? Read this fun filled adventure of a mouse, a frog and a hedgehog to save the egg!

The book was translated from Estonian by Evi Mannermaa and was illustrated by Edgar Valter. The book was published in 1982 by Tallinn Perioodika.

All credits to Guptaji.

You can get the book here (cleaned) and here.

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Posted in books, children's books, children's stories, literature, soviet | Tagged animal story, chicken, children's book, crayfish, egg, estonian, frog, hedgehog, illustrated book, magpie, mouse, picture book, soviet literature, story book | Leave a comment

About the book

Contents

Preface vii Preliminaries 1 Sample Problems 8 Detailed Solutions 25 Test Problems 81

About the book

Contents

Volume 1

Preface to the English Edition 5

Chapter 1. Introduction 13

Chapter 2. Real Numbers 45

Chapter 3. Limit of Sequence 68

Chapter 4. Limit of Function 90

Chapter 5. Differential Calculus. Functions of One Variable 127

Chapter 6. n-dimensional Space. Geometrical Properties of Curves 180

Chapter 7. Differential Calculus. Functions of Several Variables 215

Chapter 8. Indefinite Integral. Properties of Polynomials 314

Chapter 9. Definite Integral 351

Chapter 10. Some applications of integral. Approximate Methods 395

Chapter 11. Series 417

Name Index 453

Subject Index 455

Volume 2

Chapter 12. Multiple Integrals 9

Chapter 13. Scalar and Vector Fields. Differentiation and Integration of Integral with Respect to Parameter. Improper Integrals 80

Chapter 14. Normed Linear Spaces. Orthogonal Systems 147

Chapter 15. Fourier Series. Approximation of Functions with Polynomials 188

Chapter 16. Fourier Integral. Generalized Functions 240

Chapter 17. Differentiable Manifolds and Differential Forms 289

Chapter 18. Supplementary Topics 326

Chapter 19. Lebesgue Integral 338

Name Index 437 Subject Index 438

About the book & the author

Contents

General 3

Machine Memory 32

Machine Memory Address Systems 72

Information Traffic in the Machine 96

Computer Elements Information Machines 115

Machine Processing of Information 138

About the book

Contents

LECTURE 1. The Continuum 1

LECTURE 2. Limits 22

LECTURE 3. Functions 44

LECTURE 4. Series 71

LECTURE 5. The Derivative 102

LECTURE 6. The Integral 137

LECTURE 7. Expansion of functions in series 177

LECTURE 8. Differential Equations 206

About the book

Contents

CHAPTER ONE. The Origin of Life—Materialism Versus Idealism and Religion 5

CHAPTER TWO. The Primary Origin of the Most Element­ary Organic Substances—Hydrocarbons and Their Deriv­atives 21

CHAPTER THREE. The Origin of Proto-Proteins 40

CHAPTER FOUR. The Origin of Primary Colloidal For­mations 54

CHAPTER FIVE. The Organization of Living Protoplasm 64

CHAPTER SIX. The Origin of Primary Organisms 78

Conclusion 100

About the book

Contents

B. V. Gnedenko

A. Ya. Khinchin

Appendix 1

Appendix 2

About the book

Contents

Chapter I Classification and Reduction to Canonical Form of Second Order Partial Differential Equations

Chapter II Equations of Hyperbolic Type

Chapter III Equations of Parabolic Type

Chapter IV Equations of Elliptic Type

Supplement

I. Different Orthogonal System of Coordinates 741

II. Some Formulae of Vector Analysis 748

III. Special Functions 749

IV. Tables 755

About the book

Contents

PART ONE Theoretical Mechanics

Introduction 13 STATICS

Chapter I. Fundamentals of Force, and an Introduction to Statics

Chapter II. Coplanar System of Concurrent Forces

Preface vii
Preliminaries 1
Sample Problems 8
Detailed Solutions 25
Test Problems 81

Chapter 13. Scalar and Vector Fields. Differentiation and Integration
of Integral with Respect to Parameter. Improper Integrals 80

Name Index 437
Subject Index 438

CHAPTER ONE.
The Origin of Life—Materialism Versus Idealism and Religion 5

CHAPTER TWO.
The Primary Origin of the Most Elementary Organic Substances—Hydrocarbons and Their Derivatives 21

CHAPTER THREE.
The Origin of Proto-Proteins 40

CHAPTER FOUR.
The Origin of Primary Colloidal Formations 54

Introduction 13
STATICS

PART TWO
THE THEORY OF MACHINES AND FUNDAMENTAL CONCEPTS OF STRAIN