Algunos libros de matemática en Español (Some mathematics books in Spanish)

While browsing through The Internet Archive I stumbled across a few mathematics books in Spanish. We have some of these titles in English, but not all.

All credits to The Internet Archive user @librosmir

Mir_Curso_de_Algebra_Superior_A._Kurosch_0000

Curso De Algebra Superior A. Kurosch

Mir_Algebra_Lineal_V._Voevodin_0000

Algebra Lineal V. Voevodin

Mir_Fundamentos_del_Análisis_Matemático_1_V._llín_&_E._Pozniak_0000

Fundamentos Del Análisis Matemático 1 V. Ilín & E. Pozniak

Mir_Fundamentos_del_Análisis_Matemático_2_V._Ilín_&_E._Pozniak_0000

Fundamentos Del Análisis Matemático 2 V. Ilín & E. Pozniak

Mir_Fundamentos_del_Análisis_Matemático_3_V._Ilín_&_E._Pozniak_0000

Fundamentos Del Análisis Matemático 3 V. Ilín & E. Pozniak

Mir_Geometría_Elemental_A._Pogorélov_0000

Geometría Elemental A. Pogorélov

LPM_(08)_Resolución_de_ecuaciones_en_números_enteros_A._Guelfond_0000

LPM ( 08) Resolución De Ecuaciones En Números Enteros A. Guelfond

MIR_LPM_Resolución_de_ecuaciones_en_números_enteros._A. O. Guelfond_0000

LPM Resolución De Ecuaciones En Números Enteros. A. O. Guelfond

Mir_Geometría_Superior_N._Efimov_0000

Geometría Superior N. Efimov

Mir_Problemas_de_Geometría_Analítica_D._Kletenik_0000

Problemas De Geometría Analítica D. Kletenik

Mir_Problemas_de_Geometría_Descriptiva_V._Gordon,_Y._Ivanov_&_T._Solntseva_0000

Problemas De Geometría Descriptiva V. Gordon, Y. Ivanov & T. Solntseva

Mir_Problemas_de_Geometría_Diferencial_A._Fedenko_0000

Problemas De Geometría Diferencial A. Fedenko

Mir_Geometría_Moderna_B._Dubrovin,_S._Nóvikov_&_A._Fomenko_0000

Geometría Moderna B. Dubrovin, S. Nóvikov & A. Fomenko

Mir_Geometría_Diferencial_A._Pogorélov_0000

Geometría Diferencial A. Pogorélov

Mir_Geometría_N._Yákovliev_0000

Geometría N. Yákovliev

Mir_Curso_Breve_de_Geometría_Analítica_N._Efimov_0000

Curso Breve De Geometría Analítica N. Efimov

 

Posted in books, Editorial Mir, mathematics, mir books, mir publishers | Tagged , , , , , , , , , , , | 1 Comment

Engineering Methods for Analysing Strength and Rigidity – Glushkov

In this post, we will see the book Engineering Methods for Analysing Strength and Rigidity by G. Glushkov.

Glushkov ENGINEERING METHODS FOR ANALYSING STRENGTH AND RIGIDITY-gc copy

About the book

The book is a theoretical treatise on the subject of higher order moments. The theory of moments developed into a specific branch of mathematics which became a useful tool for solving com­plicated problems in structural mechanics. A number of Soviet scientists developed the so-called moment-operational method, which has proved to be extremely efficient for solving various pro­blems of modern engineering. These problems arise when non-linear elasticity must be taken into account, when precise designing of non-uniform structural elements is required, when the loading of a structure is essentially non-uniform, etc.

The moment-operational method has been widely employed for compiling manuals containing numerous tables and formulas for designing beams, arches and frames. A number of scientific research works and textbooks present the theory of moments of higher order methods examples of problems solved by the moment-operational method.

The knowledge of the theory of higher moments as well as of the moment-operational method will serve to extend the field of their application to new problems.

The book was translated from the Russian by N. Lebedinsky and was published by Mir in 1974.

Many thanks to Akbar Azimi for providing the raw scans. We did the cleaning from 2-in-1 scans. There might be warping in some pages but the text overall is very readable.

The Internet Archive Link

Contents

Part 1 Moments of Higher Order: Theory and Application 9

Chapter 1. Theory of Moments 9

1. General Concept of Moments of Area 9
2. Moments as Geometric Characteristics of Beam Cross Sections 18
3. Uniaxial Moments of Point Forces and Couples 36
4. Uniaxial Moments of Balanced and Unbalanced Systems 40
5. Uniaxial Moments of Areas of Simple Figures 45
6. Uniaxial Moments of Areas of More Complicated Figures 52
7. Uniaxial Moments of Compound Loads 56
8. Moments of Higher Order and Generalized Forces 64

Chapter II. Application of Theory of Moments 73

9. Rigidity or Uniform Beams 73
10. Geometrical Interpretation of Moments 74
11. Calculation of Displacement Integrals in Rod Systems 83
12. Application of Higher Moments to Loading of Parabolic Influence Lines 92
13. Formulas for Statically Indeterminate Structures 94
14. Rigidity of Beams Composed of Prismatic Parts 140
15. Moments of Area of Flexibility Diagram for Non-Uniform Beams 145

Part II Moment-Operational Method: Theory and Application 160

Chapter III. Moment-Operational Method 160

16. Principles of Moment-Operational Method 160
17. Bimoments 162
18. Differential and Integral Bimoments 163
19. Application of Moment-Operational Method for Solving
Linear Differential Equations 170

Chapter IV. Rigidity of Non-Uniform Beams 173

20. Determination of Displacements by Coefficients of Flexibility Polynomial Expression 173
21. Determination of Displacements by Derivatives of Flexibility Analytical Expression 178
22. Determination of Displacements by Flexibility Integrals 182
23. Dermination of Displacements when Rigidity Follows Power 194
24. Determination of Displacement Integrals by Coefficients of Flexibility Polynomial 196
25. Determination of Displacement Integrals by Derivatives of Flexibility Analytical Expression 199

Chapter V. Multispan Non-Uniform Beams 202

28. Equation of Three Moments in Flexibility Polynomial Coeffi­cients 202
27. Equation of Three Moments in Derivatives of Analytically Expressed Flexibility 207
28. Equation of Three Moments in Flexibility Integrals 210
29. Mohrs Integrals for Non-Uniform Beams 219

Chapter VI. Beams on Elastic Foundation 223

30. General 223
31. Prismatic Beams on Foundation of Constant Rigidity 224
32. Prismatic Beams on Foundation of Linear Rigidity 227
33. Beams on Foundation of Hyperbolic Rigidity 229
34. Beams on Elastic Foundation with Moment Reaction 236

Chapter VII. Beams Under Combined Flexure and Compression 238

35. General 238
36. Prismatic Beams Under Arbitrary Transverse Loads and Constant Axial Forces 239
37. Rotating Rod of Constant Rigidity Under Compression and Flexure 255
38. Prismatic Beam Under Arbitrary Transverse Load and Uni­formly Distributed Axial Forces 260
39. Prismatic Beam Under Arbitrary Transverse Load and Linear Axial Forces 270
40. Prismatic Beam Under Arbitrary Transverse Load and Axial Law Distributed Along the Beam According to Polynomial 283

Chapter VIII. Application of Moment-Operational Method to Certain Complex Problems 285

41. Stability of Bars Under Axial Compression 285
42. Beams on Elastic Foundation Under Combined Compression and Bending 290
43. Non-Uniform Beam Under Axial Force 294
44. Higher Moments of Vector Quantities in Space 306
45. Rigidity of Beams: General Case of Non-Linear Stress-Strain Relationship 320

Chapter IX. Application of Moment-Operational Method to Structural Mechanics of Ships 331

46. Flexure of Irregular Decks 331
47. Non-Uniform Beams on Elastic Foundation 341
48. Stability and Vibration of Irregular Decks 346

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Questions and Answers in School Physics – Tarasov and Tarasova (LaTeX version)

In this post, we will see the book Questions and Answers in School Physics by Lev Tarasov and Aldina Tarasova. This post is for the LaTeX version of the book, earlier scanned book can be found here.
Tarasov-Tarasova-Questions-And-Answers-In-School-Physics-MirTitles-2020 copy

This book holds a special place for me, as this book helped me understand many subtle points in physics. Also, this was the first book that I have ever scanned and had added to gigapedia when it was extant. Also, this was one of the first books that I took to typeset in LaTeX, almost a decade back, but gave up after many attempts and the project was untouched for several years. At end of 2019 I restarted the work and here we are.

One major challenge remains to convert the 130 odd diagrams to purely LaTeX using TikZ. I have done this for some figures (~6-7), but most of them are from the scans. I will do it as and when time allows. And of course you are free to contribute as well. Any help in this regard would be highly appreciated.

I have done a round of copy-editing, but still minor typos may exist here and there, (hopefully there are no major typos or screw-ups). So do report if you find any. Earlier scan had two pages which were missing (pages 36-37), they have been added in the current version, so this version is complete. We have also re-scanned the full page figures of section heads and coloured them. Many thanks to psmitak for the scans!

About the typesetting
The typesetting was fun, and I am pleased with the results. A lot of help was derived from questions on tex.stackexchange.com.

The main font used isURW-Garamond with mathdesign, while the sans font is TeX Gyre Adventor. The template used for the typesetting is tufte-book and the paper size is b5. The colour scheme used is Maroon and SteelBlue from svgnames of xcolor package of LaTeX along with DarkGray. I have, at times, highlighted questions using Maroon and answers or pedagogically significant remarks using SteelBlue. This is mostly done, if not completely done. Hope that this typeset version is helpful!

The Internet Archive Link

Gitlab Link for project files

PS: Next in line is Tarasov’s Basic Concepts of Quantum Mechanics – one round is done, final copy-editing is currently in progress. A few glimpses from that project:

Posted in books, mir books, mir publishers, physics, problem books | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Structural Design – Baikov, Strongin

In this post, we will see the book Structural Design by Baikov and Strongin.

Rydnik-ABCs-of-Quantum-Mechanics-Mir-2020 copy

About the book

The book presents a systematic and step-by-step approach to the physical and mechanical properties of concrete, reinforcing steel, reinforced concrete, masonry, and struc­tural steel.

The theoretical basis and design principles for reinforced concrete, masonry, and steel structures have been brought in line with new standards which were put in force in the Soviet Union since January, 1977. The material is presented with emphasis on Soviet, practice in highly industrialized precast reinforced concrete, type-design structural elements, and high-strength materials.

A good deal of attention is given to special engineering structures for water supply, sewage disposal, and heat supply systems, including tanks, settlers, aeration filters, aeration tanks, water lowers, buried conduits and headers, and heat-pipeline structures.

Carefully worked design examples are shown throughout the book, and an appendix gives a selection of design charts associated with the basic Soviet codes of practice.

Intended as textbook for students of building, civil, and structural engineering, the book will also be of interest to students in other departments and practising engineers.

The book was published by Mir in 1980 and was from the Russian by Alexander Kuznetsov.

Many thanks to Akbar Azimi for providing the original scans. We cleaned the 2-in-1 scan and created the pdf. There might be some warping in few of the pages, but overall it is very readable.

The Internet Archive Link

CONTENTS

Preface 8

Chapter One. Basics of Structural Design. 9

I.1. Limit States. 9
I.2. Design Factors. 10
I.3. Characteristic and Design Loads and Strength. 11
I.4. Limit-State Design. 13
I.5. Units of Measure. 15

Chapter Two. Reinforced Concrete as a Construction Material. 16

II.1. General. 16
II.2. Concrete. 19
II.3. Reinforcing Steel. 25
II.4. Main Properties of Reinforced Concrete. 35

Chapter Three. Analysis and Design of Reinforced Concrete Members. 37

III.1. General. 37
III.2. Design of Prestressed Concrete Structures. 40
III.3. Practical Hints for Design and Engineering. 47
III.4. Engineering Hints for Prestressed Members. 51

Chapter Four. Members in Axial Compression. 55

IV.1. Constructional Features. 55
IV.2. Design Under Accidental Eccentricity. 57

Chapter Five. Reinforced Concrete Members in Axial Tension 62

V.l. Constructional Features. 62
V.2. State of Stress and Design of Nonprestressed Members. 63
V.3. State of Stress and Design of Prestressed Members. 67

Chapter Six. Reinforced Concrete Members in Bending. 72

VI. 1. Constructional Features. 72
VI.2. Stale of Stress in Bending Members. 80
VI.3. Normal-Section Strength Analysis of Members. 85
VI.4. Inclined-Section Shear Strength Analysis. 98
VI.5. Incipient-Cracking Resistance of Prestressed Members. 108
VI.6. Sag Analysis. 114
VI.7. Crack-Opening Analysis. 118

Chapter Seven. Reinforced’ Concrete Members in Eccentrical Compression and Tension. 120

VII.1. Constructional Features of Members in Eccentrical Compression. 120
VI1.2. Design of Members in Eccentrical Compression. 123
VII.3. Members in Eccentrical Tension. 132

Chapter Eight. Masonry and Reinforced Masonry Structures. 135

VIII.1. Masonry Materials and Strength. 135
VIII.2. Design of Masonry Members in Compression. 138
VIII.3. Reinforced Masonry Structures. 142
VIII.4. Design of Masonry Structures. 145
VIII.5. Worked Examples for Design of Masonry Members. 147

Chapter Nine. Metal Structures. 152

IX.1. Materials for Metal Structures. 152
IX.2. Joints in Metal Structures. 157
IX.3. Design and Proportioning of Beams. 164
IX.4. Design and Proportioning of Columns. 175
IX.5. Design and Proportioning of Trusses. 188
IX.6. Prestressed Steel Structures. 191

Chapter Ten. Design of Buildings. 193

X.l. Principles of Building Layout. 193
X.2. Reinforced Concrete Floors. 196
X.3. Reinforced Concrete Column Footings. 219
X.4. Prefab Reinforced Concrete One-Storey Industrial Buildings. 227
X.5. Buildings for Water Supply and Sewage Disposal Systems and Boilers. 237

Chapter Eleven. Special Structures for Water Supply and Sewage Disposal Systems. 246

XI.1. General. 246
XI.2. Construction Types of Circular Reinforced Concrete Tanks. 249
XI.3. Design of Circular Tanks. 260
XI.4. Construction Types of Reinforced Concrete Rectangular Tanks. 273
XI.5. Design of Rectangular Tanks. 285
XI.6. Construction Types and Design of Steel Circular Tanks. 292
XI.7. Reinforced Concrete Pipes and Wells for Water Supply and Sewage Disposal Systems. 296
XI.8. Construction Types and Design of Water Towers. 300

Chapter Twelve. Design of Reinforced Concrete Structures. Worked Examples. 306

XII.l. General. 306
XII.2. Nonprestrossod Ribbed Roof Slab. 306
XII.3. Prestressed Ribbed Roof Slab. 317
XII.4. Squaro Roof Slab. 324
XII.5. Roof Girder. 329
XII.6. Column and Footing. 337
XII.7. Wall of a Precast Reinforced Concrete Rectangular Tank. 342
XII.8. Wall of a Precast Circular Tank. 348

Chapter Thirteen. Structures for Heat Supply Systems. 355

XIII.1. General. 355
XIII.2. Construction Types of Conduits and Headers. 357
XIII.3. Servicing Chambers, Compensating Niches, and Supports for Heat Pipelines. 367
XIII.4. Heat Pipelines Laid without Conduits. 378
XIII.5. Overhead Heat Pipelines. 379
XIII.6. Design Principles for Heat Pipeline Structures.386

Appendices. 395

Index. 413

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ABC’s of Quantum Mechanics – Rydnik (LaTeX version)

We have already seen this book earlier. But this post is to bring to your notice the electronic version of the book typeset using LuaLaTeX.

Rydnik-ABCs-of-Quantum-Mechanics-Mir-2020 copy

The book has come out nicely. Of course, it could have been better! I have typeset it in A5 paper, with 12 pt font with LuaLaTeX. The font used is EB Garamond. I have tried to maintain the typesetting of the original book with no chapter numbers or section numbers.

The table of elementary particles and their properties was one of the more challenging tasks in this otherwise simple book to typeset. It took me almost a day to just typeset this table. The rest was easy.

Screenshot 2020-04-04 at 18.40.17I have also created the front and back covers using TikZ, the first time I have tried this. Though they could have been done better.

The Internet Archive Link

The source files can be found at the gitlab project page:

https://gitlab.com/mirtitles/rydnik-abc-qm

Note: The original scan (by itanveer) which we had cleaned and posted had two pages (258-259) missing. I had already made a draft post asking for help for these two pages from people who might have the book, as I do not currently have the access to my physical collection. Except for these two pages, the rest of the book was processed and ready. Serendipitously, just a couple of days back Hemant Garach commented on the earlier post saying that he has this book! I requested him to scan these two missing pages and thanks to him we now have the complete book!

TODO: What remains to be done (in order of need):

  1. One more round of copy-editing. Though I tried my best, there will be many small typos here and there. I hope I have not screwed up in any major way. A thousand eyes are better than just two!
  2. Recreating figures (and front cover) using TikZ or other tools, so that it becomes completely electronic. For this release, I have used the scanned raster figures. Some actual photos of cloud chambers and particle tracks can be used instead of the current ones.
  3.  There has been much increase in our knowledge of particle physics (both empirical and theoretical) ever since the book was written in the 1960s. The book itself might be expanded as much of the information might seem dated to a particle physicist. Perhaps a new expanded edition of the book covering the era from the 1970s to present? Anyone interested?!
Posted in books, mir books, mir publishers, physics, science | Tagged , , , , , , , , | 6 Comments

Collection of Problems on the Dynamics of a Point in a Central Force Field – Polyakhova

In this post, we will see the book by Ye. N. Polyakhova titled Collection of Problems on the Dynamics of a Point in a Central Force Field.

About the book

The collection is a detailed selection of problems on the dynamics of the motion of a material point acted on by a central gravitational force, in particular, the dynamics of space flight. As an exception, the book presents several problems on the motion of a point acted on central non-gravitational forces. The book is written mainly for correspondence students. Topics covered include Kepler’s laws, the integral of areas, Binet’s formulas for central forces, the energy balance and velocity along a space trajectory, time of motion along a space trajectory, conditions for the existence of elliptical trajectories, transfer from orbit to orbit, sphere of action, third escape velocity problems, two-body problem, and the generalized third law of Kepler, along with miscellaneous problems.

This collection is a textbook for the course of theoretical mechanics (“Point Dynamics” section). students in correspondence departments of Leningrad State University and other higher educational institutions used in part by students in the day and evening departments. Moreover, the problem book may prove useful for beginning instructors in providing practical exercises mechanics, particularly, when they prepare modifications of test problems.

Most of the collection is a detailed sampling of problems on the dynamics of a material point acted on by gravitational force, in particular, problems on the elementary dynamics of space flight. Several problems on the motion of a point acted on by central non-gravitational forces are presented. Altogether, the collection includes about 200 problems of varying degrees of difficulties, with solutions.

Translation of Sbornik zadach po dinamike tochki v pole tsentral’nykh sil, Leningrad, Leningrad University Press, 1974, pp. 1-145. The book was published by NASA in May 1975 under its technical translation programme (NASA TT F-16,263).

The Internet Archive Link

Contents

Foreword iv
Table of Contents vi
Chapter One. Central Forces. Force of Gravity and Its Dynamic Characteristics 1
Chapter Two. Kepler’s Laws 11
Chapter Three. Integral of Areas 19
Chapter Four. Binet’s Formulas for Central Forces 26
Chapter Five. Energy Balance and Velocity Along a Space Trajectory 36
Chapter Six. Time of Motion in a Space Trajectory 63
Chapter Seven. Conditions for the Existence of Elliptical Trajectories 77
Chapter Eight. Transfer from Orbit to Orbit 90
Chapter Nine. Sphere of Action. Problems of Third Escape Velocity 109
Chapter Ten. Two-Body Problem. Third Kepler’s Law Generalized 118
Chapter Eleven. Miscellaneous Problems 127
References 163

Posted in astronomy, books, NASA Technical Translations, physics, problem books | Tagged , , , , , , , , | 1 Comment

Linear Algebra And Multi Dimensional Geometry – Efimov, Rozendorn

In this post, we will see the book Linear Algebra And Multi Dimensional Geometry by
N. V. Efimov, E. R. Rozendorn

Efimov, Rozendorn - Linear Algebra and Multi-Dimensional Geometry - Mir fc

About the book

This book was conceived as a text combining the course of linear algebra and analytic geometry. It originated as a course of lectures delivered by N. V. Efimov at Moscow State University (mechanics and mathematics department) in 1964-1966. However, the material of these lectures has been completely reworked and substantially expanded. We have tried to bear in mind the requi­rements of other mathematical disciplines and also of mechanics and physics. We hope that all parts of the text will be useful. The only preparation required for this text can be given an a first- semester course of analytic geometry and algebra at the most ele­mentary level. All that is needed is a firm grasp of the elements of these subjects. For Chapter XII the student should be ac­quainted with projective transformations and the projective pro­perties of figures in the plane. Also, in Chapter X the reader may simplify his task by skipping Subsections 13 to 23 (Section 3) and Subsection 10 of Section 7. What is left of Chapter X can serve as a minimal algebraic basis for the theory of multidimensional in­tegration.
It may be noted in conclusion that the first five chapters already contain material with broad applications in mathematics, mecha­nics, and physics. These chapters, supplemented with some of the material of subsequent chapters, can be utilized in higher tech­nical schools with a more advanced mathematics curriculum.

 

The book was translated from the Russian by George Yankovsky and published by Mir in 1975.

Many thanks to shankar.leo for providing the scans and the pdf.

The Internet Archive Link

Note: I tried to optimise the file for size, but somehow the archive kept on rejecting for some error in the pdf. I could have tried a few more things, but didn’t get time for that, hence the delay in post. For now, hence this large file (~120M) was uploaded. This file is OCRed but without bookmarks and pagination.

I will try to update a smaller file in the future, or if someone can add a link to a smaller file,  it would be great.

Preface 9

Introduction 11

Chapter I. Linear Spaces

1. Axioms in linear space 15
2. Examples Of linear spaces 17
3. Elementary corrolaries to the axioms of a linear space 23
4. Linear combinations. Linear dependence.25
5. Lemma on the basis minor 27
6. Basic lemma on two systems of vectors 30
7. The rank of a matrix 32
8. Finite-dimensional and infinite-dimensional spaces. Bases 34
9. Linear operations in components 36
10. Isomorphism between linear spaces 38
11. Correspondence between complex and real spaces 40
12. Linear subspace 42
13. Linear hull 44
14. Sum of subspaces. Direct sum 47

Chapter II. Linear Transformations of Variables. Transformations of Coordinates

1. Abbreviated notation for summation 53
2. Linear transformation of variables. The product of linear
transformations of variables and matrix products 56
3. Square matrices and nonsingular transformations 60
4. The rank of a product of matrices 64
5. Transformation of coordinates in a change of basis 66

Chapter III. Systems of Linear Equations. Planes In Affine Space

1. Affine space 70
2. Affine coordinates 71
3. Planes 73
4. Systems of first-degree equations 77
5. Homogeneous systems 81
6. Nonhomogeneous systems 88
7. Mutual positions of planes 91
8. Systems of linear inequalities and convex polyhedrons 98

Chapter IV. Linear, Bilinear and Quadratic Forms

1. Linear forms 108
2. Bilinear forms 112
3. The matrix of a bilinear form 116
4. Quadratic forms 118
5. Reducing a quadratic form to canonical form by Lagrange’s method 121
6. The normal form of a quadratic form 124
7. The law of inertia of quadratic forms 125
8. Reducing a quadratic form to canonical form by Jacobi’s method 127
9. Positive definite and negative definite quadratic forms 129
10. Gram’s determinant. The Cauchy-Bunyakovsky inequality 132
11. Zero subspaces of a bilinear and a quadratic form 134
12. The zero cone of a quadratic form.137
13. Elementary examples of zero cones of quadratic forms 139

Chapter V. Tensor Algebra

1. Reciprocal bases. Contravariant and covariant vectors 142
2. Tensor product of linear spaces 149
3. Basis in a tensor product. Components of a tensor 153
4. Tensors of bilinear forms 159
5. Multiple-order tensors. Tensor product 162
6. Components of multiple-order tensors 166
7. Multilinear forms and their tensors 168
8. Symmetrization and antisymmetrization (alternation). Skewsymmetric forms 170
9. An alternative description of the tensor product of two linear spaces 174

Chapter VI. Groups and Some Applications

1. Groups and subgroups. Distribution of bases into classes
with respect to a given subgroup of matrices. Orientation 180
2. Transformation groups. Isomorphism and homomorphism of groups 186
3. Invariants. Axial invariants. Pseudoinvariants 191
4. Tensor quantities 197
5. The oriented volume of a parallelepiped. The discriminant tensor 201

Chapter VII. Linear Transformations of Linear Spaces

1. Generalities 207
2. A linear transformation as a tensor 210
3. The geometrical meaning of the rank and determinant of a linear transformation. The group of nonsingular linear transformations.213
4. Invariant subspaces 216

5. Examples of linear transformations 218
6. Eigenvectors and the characteristic polynomial of a transformation 224
7. Basic theorems on the characteristic polynomial and eigenvectors 227
8 Nilpolent transformations. The general structure of singular
transformations 229
9. The canonical basis of a nilpotent transformation 233
10. Reducing a transformation matrix to the Jordan normal form 242
11. Transformations of a simple structure 248
12. Equivalence of matrices 250
13. The Hamilton-Cayley formula 252

Chapter VIII. Spaces with Quadratic Metric

1. Scalar products 254
2. The norm of a vector 256
3. Orthonormal bases 258
4. Orthogonal projection. Orthogonalization 259
5. Metric isomorphism 265
6. ^-orthogonal matrices and ^ orthogonal groups 266
7. The group of Euclidean rotations 270
8. The group of hyperbolic rotations 278
9. Tensor algebra in quadratic-metric spaces 287
10. The equation of a hyperplane in quadratic-metric space 295
11. Euclidean space. Orthogonal matrices. Orthogonal group 297
12. The normal equation of a hyperplane in Euclidean space 302
13. The volume of a parallelepiped in Euclidean space. The discriminant tensor. Vector product 304

Chapter IX. Linear Transformations of Euclidean Space

1. Adjoint of a transformation 308
2. Lemma on the characteristic roots of a symmetric matrix 310
3. Self-adjoint transformations 311
4. Reducing a quadratic form to canonical form in an orthonormal basis 317
5. The joint reduction to canonical form of two quadratic forms 319
6. Skew-adjoint transformations 322
7. Isometric transformations 325
8. The canonical form of an isometric transformation 330
9. The motion of a rigid body with one fixed point 335
10. The curvature and torsion of a space curve 338
11. The decomposition of an arbitrary linear transformation into the product of a self-adjoint and an isometric transformation 340
12. Applications to the theory of elasticity. The strain tensor and the stress tensor 343

Chapter X. Multivectors and Outer Forms

1. Alternation 346
2. Multivectors. Outer product 351
3. Bivectors 357
4. Simple multivectors 366
5. Vector product 370
6. Outer forms and operations on them 376
7. Outer forms and covariant multivectors 379
8. Outer forms in three-dimensional Euclidean space 386

Chapter XI. Quadric Hypersurfaces

1. The general equation of a quadric hypersurface 391
2. Changes in the left member of the equation under translation of the origin 392
3. Changes in the left member of the equation for a change in the orthonormal basis 395
4. The centre of a quadric hypersurface 397
5. Reducing to canonical form the general equation of a quadric hypersurface in Euclidean space 399
6. Classification of quadric hypersurfaces in Euclidean space 402
7. Affine transformations. 410
8. Affine classification of quadric hypersurfaces 414
9. The intersection of a straight line with a quadric hypersurface. Asymptotic directions 415
10. Conjugate directions.418

Chapter XII. Projective Space

1. Homogeneous coordinates in affine space. Points at infinity 422
2. The concept of a projective space 425
3. A bundle of planes in affine space 435
4. Central projection 443
5. Projective equivalence of figures 446
6. Projective classification of quadric hypersurfaces 453
7. The intersection of a quadric hypersurface and a straight line. Polars 459

Appendix 1. Proof of the theorem on the classification of linear quantities 467

Appendix 2. Hermitian forms. Unitary space.471

Bibliography. 484

Index. 486

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At the Crossroads of Infinities – Parnov

In this post, we will see the book At the crossroads of infinities by E. I. Parnov.

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About the book

At the Crossroads of Infinities is a story about the struggle of ideas out of which the modern physical picture of the world was born. Can anything move faster than light? Is the uni­verse finite or infinite? Is time revers­ible? What lies at the basis of the realities which we perceive as space, time or matter? These are the questions taken up in this book. And more, for it also tells of the roads of know­ledge, of the way man has probed the mysteries of the infinitely large and infinitely small, yet at root in­tegral world. (From the Front Jacket)

The book is a tour of the development of ideas of modern physics at the beginning of the 20th century. The book covers historical as well as philosophical issues which are at the core of modern physics. The struggle of ideas which the creators and developers of quantum mechanics and special relativity had to deal with is described very well.

The book was translated from the Russian by Vladimir Talmy and was published by Mir in 1971.

The Internet Archive Link

Contents

FACE TO FACE WITH THE UNIVERSE 7

PART I. LOOKING BACK 11

PART II. BUILDING BLOCKS OF THE UNIVERSE 86

PART III. AT THE THRESHOLD OF  A UNIFIED THEORY 200

PART IV. SPACE. TIME. VACUUM 252

PART V. THE MEGAWORLD 297

PART VI. THE UNIVERSE AND INFINITY 361

 

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Origin and Chemical Evolution of the Earth (Science for Everyone) – Voitkevich

In this post, we will see the book Origin and Chemical Evolution of the Earth by G.V. Voitkevich.  Earlier, we had seen Origin and Development of Life on Earth by the same author, which can be seen as a companion volume to the one in this post.

This is a book in the Science for Everyone Series. With this post, we have almost completed this series. As of now, we have updated all the dead links with Internet Archive ones. Next, we will update the Little Mathematic Library.

Now only ONE book in this series remains (Earth, Sweet Earth by Ekaterina Radkevich (1990)). Many people contributed to this collection becoming almost complete, a big thanks to all those who have contributed to making this possible.

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About the book

One of the most important problems in modern science is the origin of the Earth and formation of its shell. Modern views on the chemical composition of meteorites, planets and other bodies of the Solar System are pres­ented in this book. On the basis of recent achievements in cosmochemistry, the author, who is one of the leading scientists in the field of geochemistry, geophysics, describes the most probable processes that determined the chemical composition of the Earth in the remote past. Prof. George Voitkevich is also a winner of the Kar­pinsky Prize, which is given to a scientist for outstand­ing work in geology by the USSR Academy of Sciences. (From the back cover)

In this book the author attempts to describe in popular form some problems of the Earth’s origin and its chemical changes over its long geological history on the basis of cosmochem­ical, geochemical and geophysical data ob­tained in recent years. The chemical evolu­tion of the Earth is part of the chemical evolu­tion of Space. Modern cosmochemical and geo­chemical data reveal that the chemical history of the Earth as well as of other bodies of the Solar System is associated not only with pre­served stable and nonstable isotopes but also with extinct radioactive isotopes, including the isotopes of transuranium elements. (From the Introduction)

The book was translated from the Russian by V. F. Agranat and V. F. Pominov and was first published by Mir in 1988.

The Internet Archive Link

Contents

Preface 5

The Distribution of Elements in the Solar System and Their Geochemical Properties 9

Evidence of the Early History of the Solar System 31

The Nature and Chemical Composi­tion of Planets 45

Composition and Constitution of the Earth 71

The Present and Past Radioactivity of the Earth 87

The Birth of Atoms in Space 97

Chemical Evolution of the Protoplanetary Material 112

Formation of the Earth’s Principal Shells 136

Origin and Evolution of the Ocean and Atmosphere 152

Principal Trends in the Chemical Changes in the Earth’s Crust and Biosphere 181

The Chemical Evolution of the Earth’s Crust 202

Conclusion 223

Bibliography 232

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Puppets Without Strings (Science for Everyone) – Varshavsky, Pospelov

In this post, we will see the book Puppets Without Strings: Reflections on the Evolution
and Control of Some Man-Made Systems by V. I. Varshavsky, D. A. Pospelov. This is another book in the Science For Everyone series.

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About the book

Paradoxes in the evolution of technological systems. Who designed the global telephone and communication network? The whole is the sum of the parts plus their interactions. Is a simple data register really simple? Automata exploring unknown worlds. Optimum or expediency? Random interactions and information exchange. Daydreaming and cynical automata.

“I thought he thought I thought he. .. .” Heterogeneity in a group of automata is a key to success. Are we haunted by the ghost of Erehwon City? Puppets without strings: who is the puppeteer? Boundaries of centralization. How do systems evolve?
A fresh look at design. Evolution goes on. (from the Back Cover)

We seek to present a popular account of the control problems that arise in complex systems which are more generally called large-scale systems in control theory. In systems of this kind, centralized control often gives way to decentralized control, the transition being a penalty for the system’s complexity. This is because the system’s complexity makes centralized con­trol either inefficient or impracticable. How do large-scale systems arise, and is it possible that the category of large-scale system is merely a far-fetched nothing? We have tried to show in this book that large-scale man-made systems which sur­round us are steadily becoming more nu­merous and still more complex. The evolu­tion of man-made systems out of the already existing ones goes on in much the same way as living organisms evolve. Decen­tralized control is but a natural product of this evolution. We hope to convince our readers that it is just so. (from Instead of a Preface)

The book was translated from the Russian by A. Kandaurov and was first published by Mir in 1988.

The Internet Archive Link

Contents

Instead of a Preface 8

Chapter 1. Decentralized Control: the Whys and Wherefores 11

1.1. The Man-Made World 11
1.2. Systems That Have Never Been Designed as a Whole 17
1.3. A Few Instructive Examples 23
1.4. Analysis of the Examples 28
1.5. Why Decentralization? 33

Chapter 2. Is It Easy to Exist in a Contradictory World? 40

2.1. The Pros and Cons of Com­mon Sense 40
2.2. A “Small Animal” 45
2.3. Reaping the Fruits of Linear Tactics 49
2.4. Smart Machines: Reckless and Cautious 55
2.5. How to Live in a Transient World 60
2.6. Hungry Bats and Aerobatics 76
2.7. Put Your Heads Together 81

Chapter 3. “How Comes This Gentle Concord in the World? 86

3.1. The Sukharev Tower Pact 86
3.2. When Everybody Is Alike 103
3.3. Distribution of Limited Resources 119
3.4. What Shall ’ We Do with Random Interactions? 127
3.5. He Thought I Thought He 141
3.6. Optimists and Pessimists in the World of Automata 150
3.7. Three More Simple Models 161

Chapter 4. Jump the Queue and Call It Fair! 170

4.1. Where Do All the Queues Come From? 170
4.2. Barbers, Clients, and Prior­ities 178
4.3. How to Learn to Be a Foreman 187
4.4. One Circus Ring Is Not Enough 194
4.5. Problem Faced by Housing Board and Similar Problems 200
4.6. “Stubborn” Automata and Vot­ing 212

Chapter 5. Stringless Puppets Make a Show 223

5.1. Wait and See Them Fire 223
5.2. Have Them Fire All at Once 227
5.3. Marching and Wandering Au­tomata 236
5.4. Praise Be to Homogeneous Structures 241
5.5. Why Yoga Is Not Our Way? 255

Chapter 6. Dialectics of the Simple and the Complex 262

6.1. Synthesogenesis and Integra­tion of Efforts 262
6.2. Segregatiogenesis and Its Ef­fects 272
6.3. Evolution in the Erehwon City 282
6.4. Instead of a Conclusion. Evo­lution Goes on 287

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