Systems of Linear Equations (Little Mathematics Library) – Skornyakov

Posted on October 25, 2021 by The Mitr

In this post, we will see the book from the series Little Mathematics Library titled Systems of Linear Equations by L. A. Skornyakov.

About the book

The book contains a complete exposition of the theory of systems of linear equations employing only elementary operations on matrices. The method of complete mathematical induction is, formally, not used here. However, in some cases it is hidden behind the words “etc.”. Each section is followed by exercises. The main purpose of the exercises is to give the reader an opportunity to test his mastery of the material. The book is intended for a wide circle of readers, including pupils of senior classes of secondary schools, who are interested in mathematics.

The book was translated from Russian by Eugene Yankovsky and was published in 1988 by Mir.

A big thank you to @4evercla6 for this and two more books from LML series. See the comment in the LML taking stock post. We will see them in the next couple of posts.

Now only The Euler Characteristic by Yu. A. Shaskin remains from the list!

You can get the book here.

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Preface 6

1. Systems of Linear Equations and Their Solutions 7
2. Matrices and Their Elementary Transformations 11
3. A Method for Solving Systems of Linear Equations 22
4. The Rank of a Matrix 31
5. The Theorem on Principal Unknowns 39
6. Fundamental Systems of Solutions 48

Answers 56
Solutions 60

Posted in books, little mathematics library, mathematics, mir books, mir publishers | Tagged fundamental systems, high school, linear equations, little mathematics library, mathematics, matrices, mir books, rank of a matrix, solutions, solving, systems of linear equations, theorems | 8 Comments

The Dog Family / These Are All Dogs / ఇవన్నీ కుక్కలే – Akimushkin

Posted on October 24, 2021 by The Mitr

In this post, we will see the book The Dog Family aka These Are All Dogs by Igor Akimuskhin.

About the book

Wolves, jackals, and foxes all belong to one
family, the family of dogs. They are found on all the
continents except Antarctica. They live in the forest
and on the steppes, in the mountains and on the
plains, in the tundra and in the desert.

The legs of animals in this family are long and
well-shaped. The paws have strong, blunt claws. All
the animals run fast, some at a speed of 65
kilometers an hour!

The hair is thick and of various shades of gray or
red. Some of the animals are striped. One of the
African jackals is called the striped jackal. Some of
the animals are spotted. The African wild dog has
black, white and yellow spots. This is the only wild
animal that has hair of three colors.

The smallest animal in the dog family is the
fennec. It is like a kitten. The largest is the wolf. Big
wolves weigh 80 kilograms. Just imagine that!

This book will tell you about animals that are
close relatives of the dog.

The book was published by Raduga in 1976 translated from the Russian by Tracy Kuehu. Another print of the book by Malysh in 1979 has translation from Russian by E. Yankowskaya. The two translations have slight differences in the tone.

The fantastic illustrations are by A. Keleinikov.

There is a Telugu version of the book also, perhaps it was translated in other Indic languages also.

All credits to Guptaji, the Raduga version was from books donated by Mrs Purva Bharadwaj and Mrs. Anupama Jha.

You can get the The Dog Family here.

You can get the These Are All Dogs here.

You can get the Telugu version ఇవన్నీ కుక్కలే here.

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The Wolf

The Common Jackal

The Black Backed Jackal

The Coyote

The Arctic Fox

The Common Red Fox

The Racoon Dog

The Bush Dog

The Maned Wolf

The Wild Dog of Africa

The Red Wolf

The Corsac

The Fennec

The Big Eared Fox

Posted in books, children's books, children's stories, malysh publishers, raduga publishers, science | Tagged animals, arctic fox, big eared fox, bush dog, corsac, coyote, dog family, dogs, ecology, fennec, jackal, lives, malysh, maned wolf, popular science, racoon dog, raduga, red fox, red wolf, soviet books, telugu, wild, wild dogs, wolf, zoology | Leave a comment

Problems In Crystal Physics With Solutions – Perelomova, Tagieva

Posted on October 23, 2021 by The Mitr

Int this post, we will see the book Problems In Crystal Physics With Solutions by N. V. Perelomova and M. Tagieva.

About the book

This collection of problems in physical properties of crystals, first published in 1972, has survived a rigorous test of time and proved its merits for lecturers and students at the Moscow Institute of Steel and Alloys. The problems were compiled on the basis of university textbooks, special monographs, and journal articles. The book is intended for graduate and post-graduate students, as well as for engineers dealing with practical applications of crystals. It has been translated into German and French.

N. V. Perelomova, Cand.Sc. (Phys. and Math.), is a lecturer at the Chair of Crystallography of the Moscow Institute of Steel and Alloys. She is the author of the monograph “Acoustic Crystals” and of about 50 published works in crystal physics. M. M. Tagieva, Cand.Sc. (Phys. and Math.), is a senior instructor at the Chair of Crystallography of the Moscow Institute of Steel and Alloys, the author of 32 scientific papers.

The book was translated from Russian by and was published in .

Many thanks to CN for making this book available, may she RIP.

You can get the book here.

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Preface to English Edition 5
Editor’s Foreword 6
From the Preface to the First Russian Edition 7
Preface to the Second Russian Edition 8

List of Symbols 9

1. Matrix Representation of Symmetry Operations and Symmetry Classes 13
2. Symmetry Principle in Crystal Physics. Symmetry of Physical Phenomena and Properties of Crystals 22
3. Physical Properties of Crystals Described by Tensors of Rank One 35
4. Physical Properties of Crystals Described by Tensors of Rank Two 45
5. Stress and Strain in Crystals. Analysis of Stressed State 69
6. Piezoelectric Properties of Crystals. Electrostriction 87
7. Elastic Properties of Crystals. Hook’s law 115
8. Piezoresistivity in Semiconductor Crystals 136
9. Optical Properties of Crystals 151
10. Piezooptical Properties of Crystals 170
11. Electrooptical Properties of Crystals 181
12. Generation of Optical Harmonics 208
13. Rotation of Polarization Plane (Optical Activity) 225
14. Elastic Waves in Crystals 231
15. Thermodynamics of Crystals 274

Answers to Problems 290

References 295

Appendix

Table 1. Notation of 32 Symmetry Classes 296
Table 2. Symbols of Symmetry Elements on Stereographic Projections 297
Table 3. Rules for Setting of Crystals According to Symmetry System 298
Table 4. Symmetry Elements and Rules for Choosing Axes for 32
Table 5. Crystallographic Classes 298 Rules for Choosing Crystallophysical Axes 301
Table 6. Matrices of Piezoelectric Moduli (d_{ij}) and Piezoelectric Constants (g_{ij}) 302
Table 7. Matrices of Piezoelectric Constants (h_{ij}) and (e_{ij}) for Crystals in Which These Matrices Differ from (d_{ij}) and (g_{ij}) 304
Table 8. Matrices of Piezoelectric Moduli (d_{ij}) for Piezoelectric Textures 304
Table 9. Matrices of Elastic Compliances (s_{ij}) and Elastic Stiffnesses (c_{ij}) 304
Table 10. Matrices of Piezoresistivity Constants (𝚷_{ij}) 308
Table 11. Matrices of Piezooptical Constants (𝛑_{ij}) and Elastooptical Constants (p_{kl}) 310
Table 12. Matrices of Linear Electrooptical Effect Constants (r_{ij}) 314
Table 13. Matrices of Quadratic Electrooptical Effect Constants (R_{ij}) 317
Table 13.a Tensor [g_{ij}] 319
Table 14. Reference Data Required for Solving the Problems 321
Table 15. Units of Physical Quantities and Conversion Factors for the Corresponding Units in the SI and CGSE Systems 331
Table 16. Tensor of Physical Properties of Crystals Mentioned in the Book 336

Posted in books, mir books, mir publishers, physics, problem books | Tagged crystal, Crystallophysical Axes, elastic, hooke's law, notation, optical activity, physical properties, physics, piezo-electric, piezo-optic, Piezoelectric Moduli, properties, reference data, semiconducto, strain, stress, symbols, symmetry, tables, tensors, theromodynamics, units, waves | 1 Comment

Physics Of The 20th Century History And Outlook

Posted on October 22, 2021 by The Mitr

In this post, we will see the book Physics Of The 20th Century History And Outlook
edited by Ye. P. Velikhov, A. S. Borovik-Romanov, I. M. Khalatnikov, S. R. Mikulinsky, A. T. Grigor’yan, V. P. Vizgin.

About the book

To describe all the most important problems that motivated the physics of the 20th century would require many volumes. What the authors have sought to achieve in this book is to concentrate on the more fundamental issues and to trace their historical development. Whilst no aspect of modern physics is uninteresting, the topics covered here are certain to fascinate any reader, whether trained in physics or not. The achievements and promise of exciting fields — atomic physics, astrophysics, quantum theory, elementary particle physics, quantum electronics, and nonlinear physics — are covered.

No attempt has been made to restrain the authors to a dry presentation of the inception of a particular theme, they have striven to enlighten the logic of the evolution of each concept and foresee what direction the future may take.

The book was translated from Russian by Alexander Repyev and was published in 1987 by Mir.

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Quantum Theory. Origins and Growth by M.A. Elyashevich

The Origins and Development of Modern Atomistics by D.N. Trifonov

State-of-the-Art in ‘New Atom’ Research by V.I. Goldanskii and V.P. Shantarovich

Quantum Electronics by V.S. Letokhov

Nonlinear Physics. Stochasticity and Structures by A.V. Gaponov-Grekhov and M.I. Rabinovich

Physics and Astrophysics in the Late 20th Century. Development and Future Outlook by V.L. Ginzburg

Posted in books, history, mir books, mir publishers, philosophy, physics, science, soviet | Tagged astrophysics, atomiscists, future, history, mir, new atom, non-linear mechanics, non-linear physics, philosophy, problems, quantum electronics, quantum mechanics, quantum theory, random processes, science, soviet, stochastics, structures, theory | 1 Comment

A Handbook of Philosophy

Posted on October 21, 2021 by The Mitr

In this post, we will see the book A Handbook Of Philosophy edited by B. l. Syusyukalov; L. A. Yakovleva.

The team of authors is

B. J. Syusyukalov, M. M. Sidorov, L. P. Nikitin, I. B. Mikhailova. V. A. Popov, V. M. Chellini, L. A. Yakovleva, N. J. Ropakov, D. P. Zerkin, L.G. Yuldashev, Z. A. Berbeshkina, V. V. Ostryakov, S. I. Popov

About the book

This handbook sets out the basic concepts and categories of Marxist-Leninist philosophy (dialectical and historical materialism). It is intended for self-instruction. The methods recommended by the authors may also be useful to teachers and students of Marxist-Leninist philosophy in higher and secondary educational institutions.

The book was translated from Russian by Stepan Apresyan and Ludmila Lezhneva. The book was designed by Nikolai Senko and was published in 1984 by Progress.

Credits to the original uploader.

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PART I DIALECTICAL MATERIALISM

1. Philosophy: Its Subject-Matter and Role in Society 5

2. The Struggle between Materialism and Idealism in Pre-Marxist Philosophy 13

3. The Rise of Marxism — A Revolution in Philosophy. The Leninist Stage in the Development of Marxist Philosophy 28

4. Matter and the Basic Forms of Its Existence 35

5. Consciousness: Its Origin and Essence 38

6. Dialectics as the Science of Development and Universal Connection 41

7. The Basic Laws and ‘Categories of Dialectics 44

8. The Dialectical Materialist Theory of Knowledge 56

9. Critique of the Main Trends of Contemporary Bourgeois Philosophy 65

PART II HISTORICAL MATERIALISM

10. Materialist Conception of History 65

11. Society and Nature 73

12. Material Production as the Basis of Social Development 79

13. Socio-Economic Formations as Stages of Historical Development 82

14. Social Structure. Classes and Class Relations 87

15. Historical Forms of Human Community 90

16. Political System of Society 94

17. Social Revolution 102

18. Social Consciousness and Its Structure. Forms of Social Consciousness 107

19. Science and Its Role in Social Life 118

20. Culture and the Laws of Its Development 122

21. The Role of People and Personality in History. Personality and Society. Philosophical Problems of Humanism 126

22. Critique of Contemporary Bourgeois Sociology 131

23. Marxist-Leninist Philosophy — the Philosophical and Methodological Foundation of Scientific Cognition and Revolutionary Practice 138

Posted in books, philosophy, progress publishers, sociology, soviet | Tagged consciousness, culture, development, dialectics, epistemology, idealism, knowledge, leninst, marxist, materialism, philosophy, revolution, society | Leave a comment

Geometry – Shuvalova

Posted on October 20, 2021 by The Mitr

In this post, we will see the book Geometry by E. Z. Shuvalova.

About the book

The book provides a comprehensive treatment of basic geometrical concepts for high schools. The first chapter deals with properties of triangles. Chapter 2 gives a comprehensive introduction to structure of solid geometry. The chapter on parallelism in space details the concept in various contexts. Next three chapters dal with space, vectors and planes and their properties including dihedral and polyhedral angles. The last few chapters treat solids, polyhedrons and their properties such as areas volumes and sections by planes. There are worked problems and exercises for each chapter.

The book was translated from Russian by Leonid Levant and was published in 1980 by Mir.

Credits to the original uploader.

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Symbols Used in the Book 9

CHAPTER 1. BASIC RELATIONS BETWEEN THE ELEMENTS OF AN ARBITRARY TRIANGLE. SOLVING OBLIQUE TRIANGLES

Sec. 1. The Law of Sines 11
Sec. 2. The Law of Cosines 13
Sec. 3. Expressing the Tangent of a Half-Angle in Terms of the Sides of a Triangle and Radius of the Inscribed Circle (or the Incircle) 16
Sec. 4. Solving Oblique Triangles 17
Sec. 5. Measuring Distances Between “Inaccessible” 20
Sec. 6. Other Problems on Solving Oblique Triangles 23
Sec. 7. Worked Problems 28
Problems to Chapter 4 32

CHAPTER 2. LOGICAL STRUCTURE OF THE COURSE OF SOLID
GEOMETRY

Sec. 8. Structure of the Course of Solid Geometry. Notation and Terminology 36
Sec. 9. Axioms of Belonging 38
Sec. 10. Axioms of Distance 40
Sec. 11. Axioms of Order 42
Sec. 12. Axiom of Plane Mobility 45
Sec. 13. Axiom of Parallelism 47
Sec. 14. Corollaries Following from the Axioms 48

CHAPTER 3. PARALLELISM IN SPACE

Sec. 15. The Relative Position of Two Straight Lines in
Space. The Relative Position of a Plane and a Straight Line in Space 50
Sec. 16. Parallelism of a Straight Line and a Plane 51
Sec. 17. Parallel Planes 52
Sec. 18. Direction in Space. The Angle Between Two Lines 55
Sec. 19. Parallel Projecting 58
Sec. 20. Representation of Figures in Solid Geometry 61
Sec. 21. Worked Problems 63
Problems to Chapter 3 66

CHAPTER 4. TRANSFORMATION OF SPACE. VECTORS

Sec. 22. Transformation of Space 68
Sec. 23. Translation in Space 69
Sec. 24. The Vector Defined 70
Sec. 25. The Sum of Vectors 72
Sec. 26. Subtraction of Vectors. Multiplication of a Vector by a Number 75
Sec. 27. A Linear Combination of Vectors. The Conditions of Collinearity and Coplanarity 78
Sec. 28. Scalar Product of Vectors 81
Sec. 29. Arithmetic Properties of a Scalar Product 83
Sec. 30. Vector Product of Vectors 85
Problems to Chapter 4

CHAPTER 5. PERPENDICULARITY IN SPACE. DIHEDRAL AND POLYHEDRAL ANGLES

Sec. 31. A Perpendicular to a Plane 91
Sec. 32. An Inclined Line and Its Projection on a Plane. The Distance from a Point toa Plane 92
Sec. 33. The Theorem on Three Perpendiculars 94
Sec. 34. The Angle Between an Inclined Line and a Plane 97
Sec. 35. Dependence Between Parallelism and Perpendicularity of Straight Lines and Planes 98
Sec. 36. The Distance Between Skew Lines 101
Sec. 37. The Triple Product of Three Vectors. The Test for Coplanarity of Three Vectors 102
Sec. 38. Dihedral Angles 104
Sec. 39. The Angle Between Planes. Perpendicular Planes 106
Sec. 40. Orthogonal Projecting 108
Sec. 41. The Length of a Projection of a Line Segment. The Area of a Projection of a Plane Polygon 110
Sec. 42. The Area of a Projection of an Arbitrary Plane 113
Sec. 43. Polyhedral Angles 114
Sec. 44. Worked Problems 118
Problems to Chapter 5 123

CHAPTER 6. THE COORDINATE METHOD

Sec. 45. Rectangular Coordinate System 127
Sec. 46. Expressing a Scalar Product of Vectors in Terms of Their Coordinates. The Equation of a Plane 132
Sec. 47. Expressing the Vector Product of Two Vectors in Terms of Their Coordinates 135
Sec. 48. Expressing the Triple Product of Three Vectors in Terms of Their Coordinates 138
Sec. 49. Worked Problems 138
Problems to Chapter 6. 145

CHAPTER 7. POLYHEDRA, CYLINDERS, CONES

Sec. 50. The Polyhedron Defined 147
Sec. 51. Regular Polyhedra 147
Sec. 52. Eulers Theorem 149
Sec. 53. The Prism. 152
Sec. 54. A Cylindrical Surface. The Cylinder 156
Sec. 55. The Pyramid 159
Sec. 56. A Conical Surface. The Cone 160
Sec. 57. Homothety in бресе 163
Sec. 58. Properties of Parallel Sections of a Cone (Pyramid). Frustums of a Cone (Pyramid) 165
Sec. 59. Sections of Polyhedra 167
Sec. 60. Worked Problems 169

Problems to Chapter 7 174

CHAPTER 8. THE BALL

Sec. 61. A Sphere and a Ball Defined. A Sphere and a Ball Cut by a Plane 181
Sec. 62. A Tangent Plane. 182
Sec. 63. The Concept of a Spherical Triangle 183
Sec. 64. Worked Problems 485
Problems to Chapter 8. 189

CHAPTER 9. MEASURING VOLUMES

Sec. 65. General Properties of Volumes 191
Sec. 66. The Volume of a Rectangular Parallelepiped 192
Sec. 67. The Volume of a Right Cylindrical Solid 194
Sec. 68. The Volume of an Oblique Cylindrical Solid 195
Sec. 69. The General Formula for Computing the Volume of a Figure Using the Areas of Cross-Sections 196
Sec. 70. The Formulas for Computing the Volume of a Cone, a Ball and Its Parts. Simpson’s Formula 199
Sec. 71. Worked Problems 204

Problems to Chapter 9 209

CHAPTER 10. THE AREA OF SURFACE

Sec. 72. The Area of the Surface of a Polyhedron 215
Sec. 73. The Area of an Arbitrary Surface 218
Sec. 74. The Area of the Surface of a Right Circular Cylinder, a Circular Cone, and a Ball 219
Sec. 75. Worked Problems 223

Problems to Chapter 10 226

ANSWERS 232
INDEX 236

Posted in books, mathematics, mir books, mir publishers | Tagged areas, basis, cones, conic sections, cylinder, euler theorem, geometry, high school, mathematics, mir publishers, mirbooks, parallel lines, parallelism, polyhedra, projections, solid geometry, space vectors, sphere, transformations, triangles, volumes | 1 Comment

I Won’t Apologize – Sofia Prokofieva

Posted on October 19, 2021 by The Mitr

In this post, we will see the book I Won’t Apologize by Sofia Prokofieva.

About the book

The book tells a story about a boy named Vasya who after a fight with his mother runs away from his home. In the process he and has an adventure and finally realises his mistake.

The book was translated from Russian by Raissa Bobrova and the fantastic paintings are by G. A. W. Traugot was published in by Raduga in 1984.

All Credits to Guptaji.

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Posted in books, children's books, children's stories, raduga publishers, soviet | Tagged children's book, illustrated book, soviet, story book, vasya, winter | Leave a comment

Computational Mathematics – Danilina, Dubrovskaya, Kvasha, Smirnov

Posted on October 18, 2021 by The Mitr

In this post, we will see the book Computational Mathematics by N. I. Danilina; N. S. Dubrovskaya; O. P. Kvasha; G. L. Smirnov.

About the book

The rapid development of computer engineering in recent times has led to ail expansion of application of mathematics. Quantitative methods have been introduced into practically every sphere of human activity. The use of computers in the economy requires skilled specialists who have a command of the methods of computational mathematics.

Computational mathematics is one of the principal disciplines necessary for the preparation of specialists for various branches of economy. By studying it students acquire theoretical knowledge and practical skill to solve various applied problems with the aid of mathematical models and numerical methods that are realized on a computer.

This study aid assumes that the reader is aware of the elementary concepts of higher mathematics, i.e. continuity, the derivative and the integral. It covers three large divisions of mathematics: “Algebraic Methods” (Ch. 2-6), “Numerical Methods of Analysis” (Ch. 1, 7, 8) and “Numerical Methods of Solving Differential Equations” (Ch. 1), 10).
The theoretical material presented is illustrated by numerous examples. Each chapter is concluded by exercises for independent work.

The book was translated from Russian by Irene Aleksanova and was published in 1988 by Mir.

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Preface 5

Introduction 11

Chapter 1 Elementary Theory of Errors 14

1.1. Exact and Approximate Numbers. Sources and Classification of Errors 14
1.2. Decimal Notation and Rounding Off Numbers 16
1.3. Absolute and Relative Errors 17
1.4. Valid Significant Digits 20
1.5. The Connection Between the Number of Valid Digits and the Error of the Number 22
1.6. The Errors of a Sum and a Difference 23
1.7. The Error of a Product. The Number of Valid Digits in a Product 27
1.8. The Error of a Quotient. The Number of Valid Digits of a Quotient 32
1.9. The Errors of a Power and a Root 35
1.10. The Rules of Calculating Digits 36
Exercises 38

Chapter 2 Matrix Algebra and Some Data from the Theory of Linear Vector Spaces 39

2.1. Matrices and Vectors. Principal Operations Involving Matrices and Vectors 39
2.2. Transpose of a Matrix 46
2.3. The Determinant of a Matrix. The Properties of the Determinant and the Rules of Its Calculation 48
2.4. The Inverse Matrix 57
2.5. Solving Matrix Equations 63
2.6. Triangular Matrices. Expansion of a Matrix in a Product of Two Triangular Matrices 66
2.7. Inversion of a Matrix by Expanding It in a Product of Two Triangular Matrices 72
2.8 Step Matrices and Operations Involving them 78
2.9. Inversion of a Matrix by Partitioning it into Blocks 82
2.10. The Absolute Value and the Norm of a Matrix 89
2.11. The Rank of a Matrix and the Methods of Its Calculation 91
2.12. The Concept of a Linear (Vector) Space. The Linear Dependence of Vectors 95
2.13. The Basis of Space 98
2.14. The Transformation of the Coordinates of a Vector upon a Change in the Basis 104
Exercises 105

Chapter 3. Solving Systems of Linear Equations 108

3.1. Systems of Linear Equations 108
3.2. The Kronecker-Capelli Theorem 109
3.3. Cramer’s Rule for n Linear Equations in Unknowns 111
3.4. Solving Arbitrary Systems of Linear Equations 114
3.5. Homogeneous Systems of Linear Equations 118
3.6. Basic Elimination Procedure 120
3.7. Solving Systems of Linear Equations by the Gauss Elimination Method 124
3.8. Calculating Determinants by the Gauss Elimination Method 136
3.9. The Gaussian Elimination for Inversion of a Matrix 138
3.10. Cholesky’s Method 142
3.11 The Iterative Method (the Method of Successive Approximations) 148
3.12. The Conditions for Convergence of an Iterative Process 153
3.13. Estimation of the Error of the Approximate Process of the Iterative Method 154
3.14. Seidel’s Method. The Conditions for convergence of Seidel’s Process 156
3.15. Estimation of the Errors of Seidel’s Process 159
3.16. Reducing a System of Linear Equations to a Form Convenient for Iterations 160
Exercises 162

Chapter 4. Calculating the Values of Elementary Functions 165

4.1. Calculating the Values of Algebraic Polynomials 165
4.2. Calculating the Values of Analytic Functions 170
4.3. The Iterative Method of Calculating the Value of a Function 176
Exercises 178

Chapter 5. Methods of Solving Nonlinear Equations 179

5.1. Algebraic aud Transcendental Equations 179
5.2. Separating Roots 184
5.3. Computing Hoots with a Specified Accuracy. Trial and Error Method 192
5.4. Method of Chords 197
5.5. Newton’s Method of Approximation 203
5.6. Tho Combination of the Method of Chords and Newton’s Method 207
5.7. The Iterative Method 214
5.8. General Properties of Algebraic Equations. Determining the Number of Real Roots of an Algebraic Equation 223
5.9. Finding the Domains of Existence of the Roots of an Algebraic Equation 228
5.10. Horner’s Method of Approximating Real Roots of an Algebraic Equation 231

Exercises 235

Chapter 6 The Eigenvalues and Eigenvectors of a Matrix 237

6.1. The Characteristic Polynomial 237
6.2. The Method of Direct Expansion 241
6.3. Krylov’s Method of Expansion of a Characteristic Determinant 245
6.4. Using Krylov’s Method for Calculation of Eigenvectors 253
6.5. The Leverrier-Faddeev Method 254
6.6. Using the Leverrier-Faddeev Method for Calculation of Eigenvectors 258
6.7. Danilevsky’s Method 260
6.8. Using Danilevsky’s Method for Calculation of Eigenvectors 274
6.9. Using Iterative Methods to Find tho First Eigenvalue of a Matrix 277
6.10. Determining the Successive Eigenvalues and the Corresponding Eigenvectors 279
Exercises 281

Chapter 7 Interpolation and Extrapolation 283

7.1. The Function and the Methods of Its Representation 283
7.2. Mathematical Tables 285
7.3. The Approximation Theory 290
7.4. Interpolation by Polynomials 294
7.5. The Error of Interpolation Processes 297
7.6. Lagrange’s Interpolating Polynomial 202
7.7. Finite Differences 308
7.8. Stirling and Bessel Interpolating Polynomials 318
7.9. Newton’s First and Second Interpolating Polynomials 324
7.10. Divided Differences 329
7.11. Newton’s Interpolating Polynomial for an Arbitrary Net of Nodes 334
7.12. Practical Interpolation in Tables 338
7.13. Aitken’s Iterated Interpolation 330
7.14. “Optimal-Interval” Interpolation 342
7.15. Interpolation with Multiple Nodes 345
7.16. Mathematical Apparatus of Trigonometric 347
7.17. Trigonometric Interpolation 357
7.18. Numerical Methods of Determining the Fourier Coefficients 362
7.19. Backward Interpolation 366
Exercises 371

Chapter 8. Numerical Differentiation and Integration

8.1. Statement of a Problem and the Basic Formulas for Numerical Differentiation
8.2. Peculiarities of Numerical Differentiation
8.3. Statement of a Problem of Numerical Integration
8.4. Basic Quadrature Formulas
8.5. Newton-Cotes Quadrature Formulas
8.6. Quadrature Formulas of the Highest Algebraic Degree of Accuracy
8.7. Compounded Quadrature Formulas
Exercises

Chapter 9 Approximate Solution of Ordinary Differential Equations 423

9.1. Differential Equations 423
9.2. The Method of Successive Approximations (Picard’s Method) 426
9.3. Integrating Differential Equations by Means of Power Series 430
9.4. Numerical Integration of Differential Equations. Euler’s Method 434
9.5. Modifications of Euler’s Method 430
9.6. The Runge-Kutta Method 444
9.7. Adams’ Extrapolation Method 452
9.8. Milne’s Method 459
9.9. The Notion of the Boundary Value Problem for Ordinary Differential Equations 465
9.10. The Method of Finite Differences for Second-Order Linear Differential Equations 467
Exercises 469

Chapter 10 Approximate Methods of Solution of Partial Differential Equations 471

10.1. Classification of the Second-Order Differential Equations 471
10.2. Classification of Boundary Value Problems 473
10.3. Statement of the Simplest Boundary-Value Problems 477
10.4. The Method of Finite Differences. The Principal Concepts 483
10.5. Difference Schemes for Solving the Equation of Heat Conduction 494
10.6. Difference Schemes for Solving the Equation of Oscillation of a String 498

Exercises 500
Answers to Exercises 502
Index 507

Posted in books, mathematics, mir books, mir publishers, science, technology | Tagged adam's extrapolation method, approximate methods, approximate solutions, boundary value problems, Characteristic Polynomial, Cholesky's Method, computational methods, Danilevsky's Method, difference scheme, Eigenvalues and Eigenvectors of a Matrix, elementary functions, euler's method, extrapolation, Gauss Elimination Method, Horner's Method, interpolation, iterative methods, Krylov's Method, Leverrier-Faddeev Method, linear vector spaces, matrix algebra, method of finite differences, Methods of Solving Nonlinear Equations, milne's method, Newton's Method of Approximation, Newton-Cotes Quadrature Formulas, Numerical Differentiation and Integration, numerical methods, ordinary diff, ordinary differential equations, partial differential equations, picard's method, power series, quadrature formula, runge-kutta method, solutions, systems of linear equations, Theory of Errors | 1 Comment

Grandpa’s Glasses (দাদুর চশমা) by Georgi Yurmin

Posted on October 17, 2021 by The Mitr

In this post, we will see the book Grandpa’s Glasses by Georgi Yurmin.

About the book

In this book grandpa to a curious child explains different optical instruments and their uses. We come to know about lenses, spectacles, magnifying glasses, telescopes, microscopes, binoculars and periscopes.

The book was translated from Russian by Fainna Solasko and illustrated by Irina Kiselevskaya. The book was published in by Raduga.

All credits to Guptaji.

You can get the book here and here.

There is a Bengali version here and here.

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How Grandpa Lost His Glasses 5

Two Curved Shafts 7

What’s the good of a Long Nose? 9

Why-Why-Why? 11

I’m not scared of Mr. Fire-Eater 17

Which Glasses are the best? 19

Posted in books, children's books, children's stories | Tagged bengali, binocular, children's book, children's literature, lenses, microscope, Optical Instruments, optics, periscope, popular science, spectacles, telescopes | Leave a comment

Automation of Electrical Power Systems – Barzam

Posted on October 16, 2021 by The Mitr

In this post, we will see the book Automation In Electrical Power Systems by A. Barzam.

About the book

This is the third Russian edition of “Automation in Electrical Power Systems” which covers design and operation of automatic control devices intended to prevent and clear faults in electrical power systems and restore power to the loads in the event of breakdown thus assuring continuity of the supply.

The reliable and unfailing operation of such devices has been ensured through the research and development effort put into automatic power control systems. The book discusses automatic control in conjunction with protective relaying, since the required reliability and economy of power system operation can be achieved through the combined action of both groups of equipment, each cate ring for specific aspects in functioning of loads and generating sources.

The wide use of automatic control systems adds to the reliability, stability and economy of power supply systems and takes some burden from attending personnel.

The book is designed as a study guide for students of power engineering secondary schools. It may also interest engineers concerned with the operation, installation and design of protective relaying and automatic devices used in electric power stations and networks.

The book was translated from Russian by P. I. Zabolotny and was published in 1977 by Mir.

Credits to the original uploader.

You can get the book here.

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Preface 9

Introduction 11

I-1. Purpose of Automatic Power Control Systems 11
I-2. Elements of Automatic Control Systems 13
I-3. Automatic Control and Controllers 16
I-4. Relays and Relaying Devices 22
I-5. Elements of Logic Operations 24
I-6. Connection Diagrams 31
I-7. Conclusions 32
I-8. Review Questions 33

Chapter 1. Automatic Control of Synchronous Generator Excitation 35

1-1. Purpose of Automatic Excitation Control (AEC) Devices 35
1-2. Automatic Excitation Forcing of a Generator 38
1-3. Excitation Compounding with Cumulative Connection of Electromagnetic
Voltage Corrector 43
1-4. Excitation Controllers of Generators, Series TVV, with a High-Frequency Excitation System 49
1-5. Overaction Excitation Controllers 51
1-6. Conclusions 56
1-7. Review Questions 57

Chapter 2. Automatic Voltage Regulation 60

2-1. General 60
2-2. Use of AEC Devices 60
2-3. Group Control of Generator Excitation 65
2-4. na Devices for Changing the Transformation Ratio of Power Transformers 69
2-5. Devices for Automatic Capacity ‘Control of Capacitor Banks 75
2-6. Voltage Regulation by Booster Transformers 78
2-7. Voltage Regulation by Changing Excitation of Synchronous Capacitor 78
2-8. Voltage Ngulaan; By: Controlled Reactors 80
2-9. Conclusions 81
2-10. Review Questions 82

Chapter 3. Excitation Systems and Automatic Field pihage Devices of Synchronous Machines 83

3-1. General 83
3-2. Exciters Using Gas-Discharge Tubes and Thyristors 86
3-3. Brushless Excitation System 91
3-4. Excitation Systems of Large Turbogenerators 92
3-5. Field Discharge by Deion Grid Automatic Devices and by changing the Field Coil Supply to Inverter 94
3-6. Conclusions 99
3-7. Review Questions 100

Chapter 4. Automatic Controls for Maintaining Stability in Parallel Operation and Elimination of Asynchronous Operation 102

4-1. General 102
4-2. Principal Relations Determining Operation of Automatic Controls 103
4-3. Automatic Controls for Improvement of Steady-State Stability 109
4-4. Automatic Controls for Improvement of Transient Stability 124
4-5. Automatic Devices for Sectionalizing Power Systems to Prevent or Eliminate Asynchronous Operation 129
4-6. Separation of Small Thermal Power Stations from Large Hydroelectric Stations when Speed of Hydroelectric Generators Increases 143
4-7. Preventing Misoperation of Protective Relaying 144
4-8. Conclusions 158
4-9. Review Questions 159

Chapter 5. Automatic Frequency Control 161

5-1. Purpose and Specific Features of Automatic PENS Control (AFC) 161
5-2. Modern Principles of AFC 165
5-3. Short-Time Drops of Frequency 169
5-4. Choice of Parameters of FARC Devices and Work of Operators 175
5-5. AFC and FARC Circuits 176
5-6. Induction Frequency Relays 180
5-7. Frequency Relays, Type P4U-I, EAU Onne Semiconductor Blemenie 184
5-8 Conclusions 187
5-9. Review Questions 188

Chapter 6. Automatic Control of Frequency; Real Power and Power Flows in Power Systems 189

6-1. General 189
6-2. Frequency and Power Regulators 193
6-3. Devices to Control Power Output 195
6-4. Power Group Control at Thermal Stations 199
6-5. Power Group Control at Hydroelectric Stations 200
6-6. Frequency and Power Control in Integrated Power Systems 205
6-7. Magnetic Power Transducers 212
6-8. Conclusions 213
6-9. Review Questions 215

Chapter 7. Rapid Paralleling of Synchronous Generators and Parts of Power System 217

7-1. General 217
7-2. Precise Synchronization by Means of an ACT-4 Autosynchronizer 218
7-3. Self-Synchronization of Generators 227
7-4. Automatic Connection of Generators by Self-Synchronization 231
7-5. Speed Control Methods 236
7-6. Asynchronous Connection of Generators and Parts of Power System 238
7-7. Connection of Synchronous Motors, Preventing Their ace Out of a and
Resynchronization 241
7-8. Conclusions 247
7-9. Review Questions 248

Chapter 8. Three-Phase Automatic Reclosure 254

8-1. General 251
8-2. Single Lines ‘with Supply from One End 258
8-3. Single Tie Lines Between Power Stations and Substations with Svachronous Loads 268
8-4. Tie Lines and Parallel Links 287
8-5. TPARC Devices on Air Circuit Breakers 289
8-6. Conclusions 293
8-7. Review Questions 295

Chapter 9. One Phase Automatic Reclosure of Power Transmission Lines 297

9-1. Earth Fault and Tripping of One Phase 297
9-2. Types of Discriminating Elements of PARC Devices 306
9-3. PARC Circuit 312
9-4. Use of TPARC Device of Double-Shot Type and Pole-After-Pole Isolators in Place of a PARC Device on Lines 315
9-9. Conclusions 316
9-6. Review Questions 317

Chapter 10. Three Phase Automatic Reclosure of Transformers and Busbars 319

10-1. General 319
10-2. Automatic Testing of Busbars for Insulation 321
10-3. Power Supply to Consumers After Tripping of Busbars and Automatic
Reestablishing of Substation Connections 322
10-4. Automatic Reestablishing of Power Station Connections 324
10-5. Three-Phase ARC of Transformers 325
10-6. Conclusions 327
10-7. Review Questions 327

Chapter 11. Automatic Transfer to Reserve Supply and Equipment 328

11-1. General 328
11-2. ATS Device Circuits 331
11-3. ATS Devices Used by Substations Supplying Synchronous Loads 339
11-4. ATS Devices with Standardization Control Stations 341
41-5. Self-Starting of an Asynchronous Load 343
41-6. Conclusions 356
11-7. Review Questions 307

Chapter 12. Operation of ARC and ATS Devices in Conjunction with Protective Relaying 358

12-1. Acceleration of Protection Action Before ARC 308
12-2. Acceleration of Protection Action After ARC, ATS, and Remote Connection 359
12-3. High-Speed Selective Disconnection 360
12-4. Substations Without Circuit Breakers on the High-Tension Side 864
12-5. Simplifying Protective Relaying of Complex System Lines 367
12-6. Simplifying Primary Connection Circuits and Protective Relaying 369
12-7. Step-Down Transformers at Remote-Controlled Substations 373
12-8. Automatic Discriminating Redundancy 374
12-9. Conclusions 376
12-10. Review Questions 377

Chapter 13. Automatic Control Eliminating Overvoltages Across Equipment 378

13-1. General 378
13-2. Overvoltage Automatic Protection Controls
13-3. Increasing the Reset-to-Pickup Ratio of Voltage Relay
13-4. Conclusions

Chapter 14. Automatic Recording of Electrical Variables in Disturbances 392

14-1. General 392
14-2. Automatic Starting Devices for Oscillographs 396
14-3. Devices for Recording Electrical Variables with Automatic Acceleration of Recording Speeds During Disturbances 400
14-4. Automatic Oscillographs 403
14-5. Locating the Fault on Power Transmission Line from Fixing Instruments 406
14-6. Fixing Instruments 411
44-7. Conclusions 418
44-8. Review Questions 419

References 420
Index 428

Posted in books, engineering, mir books, mir publishers, physics, soviet, technology | Tagged Automatic Control, Automatic Frequency Control, automatic voltage regulation, electrical engineering, electrical systems, Electrical Variables, Excitation Systems, power systems, Power Transmission Lines, protective relaying, Synchronous Generator Excitation, Synchronous Generators, three phase, variables | 1 Comment

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The Wolf

The Common Jackal

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The Wild Dog of Africa

The Red Wolf

The Corsac

The Fennec

The Big Eared Fox

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