We now come to the much anticipated “Problem Books” series and start with Problems in Physics by V. Zubov and V. Shalnov. This will be a good material for those who are preparing for Olympiads and other competitive exams.

For the most part, this is a collection of modified problems
discussed in extracurricular circles and at tutorials and
Olympiads at the Moscow University.
In selecting and preparing the problems for this collection
the authors attempted to focus the attention of the reader
on those postulates and laws of physics where students make
the most mistakes. Some problems were specially selected
to explain comprehensively the application of the most
important laws – something which students often fail to
grasp properly. A number of problems concern the subjects
usually omitted in secondary school text-book problems.
Some problems are intended for discussion in extracurricular
circles or for independent study by those wishing to
acquaint themselves with material beyond the scope of the
school syllabus.
The most difficult problems and the problems outside
the scope of the secondary school syllabus are provided
with detailed explanations in order to give the student
a better understanding of the general principles of solution.
With this end in view, some sections are also supplemented
with brief information about the most frequent mistakes
and the simplest means of solution.

The book was translated from the Russian by A. N. Troitsky and the translation was edited
by J. B. Williams. Mir Publishers published this book first time in 1974 with a second reprint in 1985. The link below is for the second print.

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Contents

Preface
Chapter I. MECHANICS (Problems 9 | Answers and Solutions 141)

1. Rectilinear Uniform Motion ( 9 | 141 )
2. Rectilinear Uniformly Variable Motion ( 15 | 148 )
3. Curvilinear Motion ( 18 | 152 )
4. Rotational Motion of a Solid Body ( 19|154 )
5. Dynamics of the Rectilinear Motion of a Point (20|155)
6. Power Impulse. Momentum (28|164)
7. Work. Energy. Power (33|169)
8. Dynamics of a Point Moving in a Circle (37|176)
9. Statics (45|188)
10. Universal Gravitational Forces (53|194)
11. Oscillations (54|197)
12. Hydro- and Aerostatics (56|201)

Chapter II. HEAT AND MOLECULAR PHYSICS (Problems 63 | Answers and Solutions 207)

13. Thermal Expansion of Bodies (63|207)
14. Quantity of Heat. Heat Exchange (65|210)
15. The Gas Laws (66|211)
16. Surface Tension (73|219)
17. Humidity of Air (77|224)

Chapter III. ELECTRICITY (Problems 78 | Answers and Solutions 224)

18. Coulomb’s Law (78|224)
19. Electric Field. Field Intensity (81|229)
20. Work Done by Forces in an Electrostatic Field. Potential (85|235)
21. Electric Field in a Dielectric (88|239)
22. Capacitance and Capacitors (89|241)
23. The Laws of Direct Current (93|244)
24. Thermal Effect of Current Power (102 | 255)
25. Permanent Magnets (105 | 257)
26. Magnetic Field of a Current (112 | 263)
27. Forces Acting in a Magnetic Field on Current-Carrying Conductors (116 | 267)
28. Electromagnetic Induction (120 | 270)

Chapter IV. OPTICS (Problems 124 | Answers and Solutions 271)

29. The Nature of Light (124 | 271)
30. Fundamentals of Photometry (126 | 273)
31. The Law of Rectilinear Propagation and Reflection of Light 128 275
32. Spherical Mirrors (133 | 279)
33. Refraction of Light at Plane Boundary (136 | 283)
34. Lenses and Composite Optical Systems (137 | 285)

When solving a problem, first of all establish the physical
laws which it is based on. Then use the formulas expressing
these laws to solve the problem in symbols, and finally 
substitute the numerical data in one system of units.

We now come to another book in the Problem Book series by Wolkenstein titled Problems in General Physics.

This collection of problems is based on the International System
of Units preferred today in all the fields of’ science, engineering
and economy. Other units can be converted to 51 units with the aid of the relevant tables given in this book.
Each section is preceded by a brief introduction describing the
fundamental laws and formulas which are used to solve the problems. The solutions to the problems and the reference data are appended at the end of the book.

The book was translated from the Russian by A. Troitsky and was edited by G. Leib. The book was first printed by Mir Publishers in 1971, and fourth reprint appeared in 1987. The link below is for the 1987 edition. Incidentally there is a Hindi translation of this book. I do not know if it was translated in other Indian languages.

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Contents

Introduction
1. International System of Units (SI)
2. Methods of Solving Problems

PROBLEMS

1. Physical Fundamentals of Mechanics
Mechanical Units
Examples of Solutions

1. Kinematics
2. Dynamics
3. Rotational Motion of Solids
4. Mechanics of Fluids

Chapter 2. Molecular Physics and Thermodynamics

Thermal Units
Examples of Solutions

5. Physical Fundamentals of the Molecular-Kinetic Theory and Thermodynamics
6. Real Gases
7. Saturated Vapours and Liquids
8. Solids

Chapter 3. Electricity and Magnetism

Electrical and Magnetic Units
Examples of Solutions
9. Electrostatics
10. Electric Current
11. Electromagnetism

Chapter 4. Oscillations and Waves

Acoustic Units
Examples of Solutions
12. Harmonic Oscillatory Motion and Waves
13. Acoustics
14. Electromagnetic Oscillations and Waves

Chapter 5. Optics

Light Units
Examples of Solutions
15. Geometrical Optics and Photometry
16. Wave Optics
17. Elements of the Theory of Relativity
18. Thermal Radiation

Chapter 6. Atomic and Nuclear Physics

Units of Radioactivity and Ionizing Radiation
Examples of Solutions
19. Quantum Nature of Light and Wave Properties of Particles
20. Bohr’s Atom. X-Rays
21. Radioactivity
22. Nuclear Reactions
23. Elementary Particles. Particle Accelerators

ANSWERS AND SOLUTIONS

1. Physical Fundamentals of Mechanics
2. Molecular Physics and Thermodynamics
3. Electricity and Magnetism
4. Oscillations and Waves
5. Optics
6. Atomic and Nuclear Physics

Appendix

Induction B versus Intensity H of a Magnetic Field for a Certain Grade of Iron
Relationship between Rationalized and Non-Rationalized Equations of an Electromagnetic Field

Tables

I. Basic Physical Quantities
II. Astronomic Quantities
III. Data on the Planets of the Solar System
IV. Diameters of Atoms and Molecules
V. Critical Values of T_cr and P_cr
VI. Pressure of Water Vapour Saturating a Space at Various Temperatures
VII. Specific Heat of Vaporization of Water at Various Temperatures
VIII. Properties of Some Liquids
IX. Properties of Some Solids
X. Elastic Properties of Some Solids
XI. Thermal Conductivity of Some Solids
XII. Dielectric Constant (Relative Permittivity) of Dielectrics
XIII. Resistivity of Conductors
XIV. Mobility of Ions in Electrolytes
XV. Work of Exit of Electrons from Metals
XVI. Refractive Indices
XVII. Boundary of K-Series of X-Rays for Various Materials of the Anti- cathode
XVIII. Spectral Lines of Mercury Arc
XIX . Masses of Some Isotopes
XX. Half-Lives of Some Radioactive Elements
XXI. Common Logarithms
XXII. Sines and Cosines
XXIII. Tangents and Cotangents

I believe that if you have solved or studied the solution of a 
large number of problems, the basics of the physical method of 
thinking have become clearer.

We now come to A Collection of Questions and Problems in Physics by L. A. Sena.

The aim of the present collection of questions and problems is to develop practical skills during study of one of the fundamental sciences, physics. The Collection is intended for the self-instruction of students of technical colleges. The best way to use it is to solve the problems while preparing for term exams.

The Collection contains more than 400 questions and problems covering all the sections of the physics course. All questions and problems have detailed answers and solutions. For this reason the two main sections of the book, Questions and Problems and Answers and Solutions, have identical headings and numbering: each chapter in the first section has a corresponding chapter in the second, and the numbering of answers corresponds to the numbering of problems.

A special feature of the Collection is the drawings and diagrams for most of the questions and answers. The diagrams use a variety of scales: linear, semilog, log-log, and quadratic.

Arrangement of the material in this Collection corresponds to the structure most commonly used in college physics textbooks. One exception is the questions and problems involving the special theory of relativity. These are placed in different chapters, starting from the one dealing with mechanics.

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

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Update: The book is in print and available here. Price is INR 80.

Contents

Introduction 7

Questions and Problems 10

1. Fundamentals of Mechanics to
2. Molecular Physics and Thermodynamics
3. Electrostatics 42
4. Direct Current 54
5. Electromagnetism 67
6. Oscillatory Motion and Waves 80
7. Alternating Current 92
8. Optics 95
9. Atomic and Nuclear Physics t09

Answers and Solutions 121

1. Fundamentals of Mechanics 121
2. Molecular Physics and Thermodynamics
3. Electrostatics 188
4. Direct Current 213
5. Electromagnetism 233
6. Oscillatory Motion and Waves 254
7. Alternating Current 275
8. Optics 286
9. Atomic and Nuclear Physics 316

Postface 335

We now come to Problems in Physics by A. A. Pinksy. This is the accompanying “Problem Book” to the  two volume set Fundamentals of Physics by A. A. Pinksy and B. M. Yavorvsky (which we might see soon!), who is also the co-author of A Modern Handbook of Physics and Handbook of Physics with A. A. Detlaf.

This book offers the reader over 750 problems concerning the same subject matter as is treated in the two volumes of  the “Fundamentals of Physics”. The order of presentation of the theoretical material is also the same.
The availability of a great number of problem books based on the traditional school physics curriculum prompted us to enlarge those sections which are absent from traditional problem books, namely the dynamics of a rotating rigid body, the elements of the theory of relativity and of quantum and statistical physics, of solid-state physics, wave optics, atomic and nuclear physics, etc. Problems dealing with astrophysics illustrate the application of the laws of physics to celestial bodies.
The book contains a few problems requiring elementary
skill in differentiating and integrating, as well as some problems
to be solved with the aid of numerical methods, which
nowadays are being increasingly used.

The book was translated from the Russian by Mark Samokhvalov and was first published by Mir Publishers in 1980.

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Contents

Preface
Some Practical Hints
Part One. Motion and Forces
(Problems 17 | Solutions 123| Answers and Hints 306)
1. Kinematics of a Particle
2. Force
3. Particle Dynamics
4. Gravitation. Electrical Forces
5. Friction
6. Theory of Relativity

Part Two. Conservation Laws
(Problems 30| Solutions 148| Answers and Hints 309)
7. The Law of Conservation of Momentum. Centre of Mass
8. Total and Kinetic Energy
9. Uncertainty Relation
10. Elementary Theory of Collisions
11. Potential Energy. Potential
12. The Law of Conservation of Energy in Newtonian Mechanics
13. The Law of Conservation of Energy
14. Rotational Dynamics of a Rigid Body
15. Non-inertial Frames of Reference and Gravitation

Part Three. Molecular-kinetic Theory of Gases
(Problems 44| Solutions 183| Answers and Hints 312)
16. An Ideal Gas
17. The First Law of Thermodynamics
18. The Second Law of Thermodynamics
19. Fundamentals of Fluid -Dynamics

Part Four. Molecular Forces and States of Aggregation of Matter
(Problems 55| Solutions 201| Answers and Hints 314)
20. Solids
21. Liquids
22. Vapours
23. Phase Transitions

Part Five. Electrodynamics
(Problems 61| Solutions 211| Answers and Hints 315)
24. A Field of Fixed Charges in a Vacuum
25. Dielectrics
26. Direct Current
27. A Magnetic Field in a Vacuum
28. Charges and Currents in a Magnetic Field
29. Magnetic Materials
30. Electromagnetic Induction
31. Classical Electron Theory
32. Electrical Conductivity of Electrolytes
33. Electric Current in a Vacuum and in Gas

Part Six. Vibrations and Waves
(Problems 87| Solutions 245| Answers and Hints 320)
34. Harmonic Vibrations
35. Free Vibrations
36. Forced Vibrations. Alternating Current
37. Elastic Waves
38. Interference and Diffraction
39. Electromagnetic Waves
40. Interference and Diffraction of Light
41. Dispersion and Absorption of Light
42. Polarization of Light
43. Geometrical Optics
44. Optical Instruments

Part Seven. Fundamentals of Quantum Physics
(Problems 110| Solutions 281| Answers and Hints 324)
45. Photons
46. Elementary Quantum Mechanics
47. Atomic and Molecular Structure
48. Quantum Properties of Metals and of Semiconductors

Part Eight. Nuclear and Elementary Particle Physics
(Problems 119| Solutions 299| Answers and Hints 327)
49. Nuclear Structure
50. Nuclear Reactions

Tables 329

1. Astronomical Data
2. Mechanical Properties of Solids
3. Thermal Properties of Solids
4. Properties of Liquids
5. Properties of Gases
6. Electrical Properties of Materials (20 °C)
7. Velocity of Sound (Longitudinal Waves)
8. Refractive Indexes
9. Masses of Some Neutral Atoms (amu)
10. Fundamental Physical Constants

It should be noted that most of the problems, chosen for this
collection, are not only an illustration of the theoretical 
material, but are well in accord with the materials which serve
as a bridge between theoretical mechanics and intermediate 
sciences.

We now come to another Problem Book in Physics this one is exclusively for theoretical mechanics: Collection of Problems in Theoretical Mechanics by I. V. Meshchersky.

The present edition embraces all basic principles of theoretical
mechanics usually taught during the first two years of studies in
higher and secondary technical schools. The material in this book is presented consistently, i, e., proceeding from the particular to the general. The same method is applied to the order of paragraphs and the arrangement of the text.

…

It should be noted that most of the problems, chosen for this
collection, are not only an illustration of the theoretical material, but are well in accord with the materials which serve as a bridge between theoretical mechanics and intermediate sciences.

The primary objective of the book was to present to the reader
problems of practical value by giving the examples in such fields as the operation of machines and mechanisms, hydrodynamics, resistance of materials, and other branches of science and engineering. All this has made the book widely popular among the Soviet students of technical schools.

…

The material collected in this book will aid students in the
practical application of laws and methods of theoretical mechanics in their engineering practice.

The book was translated from the Russian by N. M. Sinelnikova and edited by A. I. Lurie and the supplementary material: Solutions of Some Typical Problems is written by V. I. Kuznetsov. The other contributors to this edition are S. A. Sorokov (statics), N. N. Naugolnaya and A. S. Kelson (kinematics), A. S. Kelson (dynamics of a particle), M. I. Baty (dynamics of a system), G. J. Djanelidze (analytical statics, dynamics of bodies having variable masses, stability of motion). The book is an abridged version of the 28th edition of the book by Meshchersky published in 1962. This book was published by Higher School Publishing House in the 1968 (as per worldcat record, no date in the book). Dover also published this book in 1965.

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Contents

Preface 7
Part I. Statics of Rigid Bodies

I. Coplanar Force System
1. Collinear Forces 9
2. Concurrent Forces 10
3. Parallel Forces and Couples 19
4. Arbitrary Coplanar Force Systems 26
5. Graphical Statics 40
II. Statics in Space
6. Concurrent Forces 43
7. Reduction of a System of Forces to Its Simplest Possible Form 47
8. Equilibrium of an Arbitrary System of Forces 48
9. Centre of Gravity 56

Part II. Kinematics

III. Motion of a Particle
10. Equation of Motion and Path of a Particle 59
11. Velocity of a Particle 61
12. Acceleration of a Particle 63
IV. Simplest Motions of a Rigid Body
13. Rotation of a Rigid Body about a Fixed Axis 68
14. Conversion of Simplest Motions of a Rigid Body 70
V. Composition and Resolution of Motions of a Particle
15. Equations of Motion and Path of the Resultant Motion of a Particle 74
16. Composition of Velocities of a Particle 76
17. Composition of Accelerations of a Particle Undergoing Translatory Motion of Transport 79
18. Composition of Accelerations of a Particle Performing Rotational Motion of Transport about a Fixed Axis 82
VI. A Rigid Body Motion in a Plane
19. Equations of Motion of a Body and Its Particles in a Plane 87
20. Velocity of a Point of a Body Which Performs Motions in a Plane. Instantaneous Centres of Velocities. 89
21. Space and Body Centrodes 96
22. Accelerations of a Point on a Body Which Performs Motions in a Plane. Instantaneous Centres of Accelerations 99
23. Composition of Motions of a Body in a Plane 102
VII. Motion of a Rigid Body about a Fixed Point
24. Rotation of a Rigid Body about a Fixed Point 105
25. Composition of Rotations of a Rigid Body about Intersecting Axes 105

Part III. Dynamics

VIII. Dynamics of a Particle
26. Determination of Force Acting During Motion 113
27. Differential Equations of Motion 117
28. Theorem on Change of Momentum of a Particle. Theorem on Change of Angular Momentum of a Particle. Motion under the Action of Central Forces 125
29. Work and Power 128
30. Theorem on Change of Kinetic Energy of a Particle 130
31. Review Problems 134
32. Oscillations 138
33. Relative Motion 145
IX. Dynamics of a System
34. Principles of Kinetics and Statics 148
35. Principle of Virtual Displacements 155
36. General Equation of Dynamics 160
37. Theorem on the Motion of the Centre of Mass of a System 167
38. Theorem on the Change of Linear IV\omentum of a System 170
39. Theorem on the Change of Principal Angular Moment of a System Differential Equation of Rotation of a Rigid Body about a Fixed Axis. Elementary Theory on Gyroscopes 173
40. Theorem on the Change of Kinetic Energy of a System 188
41. Plane Motion of a Rigid Body 199
42. Forces Acting on Axis of a Rota ting Body 202
43: Review Problems 205
44. Impact 209
45. Dynamics of a System of Variable Mass 214
46. Analytical Statics 217
47. Lagrange’s Equations 221
X. Theory of Oscillations
48. Small Oscillations of Systems with a Single Degree of Freedom 235
49. Small Oscillations of Systems with Several Degrees of Freedom 247
50. Stability of Motion 256
Supplement. Solutions of Some Typical Problems 261

We now come to Problems in Elementary Physics by B. Bukhovtsev, V. Krivchenkov, G. Myakishev, and V. Shalnov.

This collection of 816 problems is based on the textbook “Elementary Physics” edited by Academician G. S. Landsberg. For this reason the content and nature of the problems and their arrangement mainly conform with this textbook. There is no section devoted to “Atomic Physics”, however, since the exercises in Landsberg’s book illustrate the relevant material in sufficient detail. Some problems on this subject have been included in other chapters.
The problems, most of which are unique, require a fundamental knowledge of the basic laws of physics, and the ability to apply them in the most diverse conditions. A number of problems in the book have been revised from those used at the annual
contests organized by the Physics faculty of the Moscow University.
The solutions of all the difficult problems are given in great
detail. Solutions are also given for some of the simpler ones.
The book is recommended for self-education of senior pupils
of general and special secondary and technical schools. Many
problems will be useful for first and second year students of
higher schools.

The book was translated from the Russian by A. Troitsky and was edited by G. Leib. Mir Publishers published this book first in 1971 and was reprinted again in 1978. The link below is for the 1978 edition.

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Contents

Chapter 1. Mechanics (Problems: 7 | Answers and Solutions: 160)

1-1. Kinematics of Uniform Rectilinear Motion
1-2. Kinematics of Non-Uniform and Uniformly Variable Rectilinear Motion
1-3. Dynamics of Rectilinear Motion
1-4. The Law of Conservation of Momentum
1-5. Statics
1-6. Work and Energy
1-7. Kinematics of Curvilinear Motion
1-8. Dynamics of Curvilinear Motion
1-9. The Law of Gravitation
1-10. Hydro and Aerostatics
1-11. Hydro and Aerodynamics

Chapter 2. Heat. Molecular Physics (Problems: 68| Answers and Solutions: 268)

2-1. Thermal Expansion of Solids and Liquids
2-2. The Law of Conservation of Energy. Thermal Conductivity
2-3. Properties of Gases
2-4. Properties of Liquids
2-5. Mutual Conversion of Liquids. and Solids
2-6. Elasticity and Strength
2-7. Properties of Vapours

Chapter 3. Electricity and Magnetism (Problems: 87| Answers and Solutions: 294)

3-1. Electrostatics
3-2. Direct Current
3-3. Electric Current in Gases and a Vacuum
3-4. Magnetic Field of a Current. Action of a Magnetic Field on a Current and Moving Charges
3-5. Electromagnetic Induction. Alternating Current
3-6. Electrical Machines

Chapter 4. Oscillations and Waves (Problems: 127| Answers and Solutions: 365)

4-1. Mechanical Oscillations
4-2. Electrical Oscillations
4-3. Waves

Chapter 5. Geometrical Optics (Problems: 135| Answers and Solutions: 380)

5-1. Photometry
5-2. Fundamental Laws of Optics
5-3. Lenses and Spherical Mirrors
5-4. Optical Systems and Devices

Chapter 6. Physical Optics (Problems: 151| Answers and Solutions: 421)

6-1. Interference of Light
6-2. Diffraction of Light
6-3. Dispersion of Light and Colours of Bodies

In this post we see Higher Algebra by A. Kurosh.

The education of the mathematics major begins with the
study of three basic disciplines: mathematical analysis, analytic
geometry and higher algebra. These disciplines have a number of
points of contact, some of which overlap; together they constitute
the foundation upon which rests the whole edifice of modern
mathematical science.

Higher algebra – the subject of this text – is a far-reaching and
natural generalization of the basic school course of elementary
algebra. Central to elementary algebra is without doubt the problem
of solving equations. The study of equations begins with the very
simple case of one equation of the first degree in one unknown. From
there on, the development proceeds in two directions: to systems of
two and three equations of the first degree in two and, respectively,
three unknowns, and to a single quadratic equation in one unknown and
also to a few special types of higher-degree equations which readily
reduce to quadratic equations (quartic equations, for example). Both
trends are further developed in the course of higher algebra, thus
determining its two large areas of study. One – the foundations of
linear algebra – starts with the study of arbitrary systems of
equations of the first degree (linear equations). When the number of
equations equals the number of unknowns, solutions of such systems
are obtained by means of the theory of determinants.

The second half of the course of higher algebra, called the algebra
of polynomials, is devoted to the study of a single equation in one
unknown but of arbitrary degree. Since there is a formula for solving
quadratic equations, it was natural to seek similar formulas for
higher-degree equations. That is precisely how this division of
algebra developed historically. Formulas for solving equations of
third and fourth degree were found in the sixteenth century. The
search was then on for formulas capable of expressing the roots of
equations of fifth and higher degree in terms -of the coefficients of
the equations by means of radicals, even radicals within radicals. It
was futile, though it continued up to the beginning of the nineteenth
century, when it was proved that no such formulas exist and that for
all degrees beyond the fourth there even exist specific examples of
equations with integral coefficients whose roots cannot be written
down by means of radicals.

This book was translated from the Russian by George Yankovsky. The  book was published by first Mir Publishers in 1972, with reprints in  1975, 1980 and 1984. The book below is from the 1984 reprint.

All credits to the original uploader.

DJVU | OCR | 15.8 MB | Pages: 432 |
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Table of Contents

Introduction 7
Chapter 1.
Systems of linear equations. Determinants 15

1. The Method of Successive Elimination of Unknowns 15
2. Determinants of Second and Third Order. 22
3. Arrangements and Permutations 27
4. Determinants of nth Order 36
5. Minors and Their Cofactors 43
6. Evaluating Determinants 46
7. Cramer’s Rule 53

Chapter 2.
Systems of linear equations ( general theory) 59

8. n-Dimensional Vector Space 59
9. Linear Dependence of Vectors 62
10. Rank of a Matrix 69
11. Systems of Linear Equations. 76
12. Systems of Homogeneous Linear Equations 82

Chapter 3.
The algebra of matrices 87

13. Matrix Multiplication 87
14. Inverse Matrices 93
15. Matrix Addition and Multiplication of a Matrix by a Scalar 99
16. An Axiomatic Construction of the Theory of Determinants 103

Chapter 4.
Complex numbers 110

17. The System of Complex Numbers 110
18. A Deeper Look at Complex Numbers 112
19. Taking Roots of Complex Numbers 120

Chapter 5.
Polynomials and their roots 126

20. Operations on Polynomials 126
21. Divisors. Greatest Common Divisor 131
22. Roots of Polynomials. 139
23. Fundamental Theorem 142
24. Corollaries to the Fundamental Theorem 151
25. Rational Fractions 156

Chapter 6.
Quadratic forms 161

26. Reducing a Quadratic Form to Canonical Form 161
27. Law of Inertia. 169
28. Positive Definite Forms 174

Chapter 7
Linear spaces 178

29. Definition of a Linear Space. An Isomorphism 178
30. Finite-Dimensional Spaces. Bases 182
31. Linear Transformations 188
32. Linear Subspaces. 195
33. Characteristic Roots and Eigenvalues 199

Chapter 8
Euclidean spaces204
34. Definition of a Euclidean Space. Orthonormal Bases 204
35. Orthogonal Matrices, Orthogonal Transformations. 210
36. Symmetric Transformations. 215
37. Reducing a Quadratic Form to Principal Axes. Pairs of Forms 219

Chapter 9.
Evaluating roots of polynomials 225

38. Equations of Second, Third and Fourth Degree 225
39. Bounds of Roots 232
40. Sturm’s Theorem 238
41. Other Theorems on the Number of Real Roots 244
42. Approximation of Roots 250

Chapter 10.
Fields and polynomials 257

43. Number Rings and Fields 257
44. Rings 260
45. Fields 267
46. Isomorphisms of Rings (Fields). The Uniqueness of the Field of Complex Numbers 272
47. Linear Algebra and the Algebra of Polynomials over an Arbitrary Field 276
48. Factorization of Polynomials into Irreducible Factors 281
49. Theorem on the Existence of a Root 290
50. The Field of Rational Fractions 297

Chapter 11.
Polynomials in several unknowns 303

51. The Ring of Polynomials in Several Unknowns 303
52. Symmetric Polynomials. 312
53. Symmetric Polynomials Continued 319
54. Resultant. Elimination of Unknown. Discriminant 329
55. Alternative Proof of the Fundamental Theorem of the Algebra of
Complex Numbers 337

Chapter 12.
Polynomials with rational coefficients 341

56. Reducibility of Polynomials over the Field of Rationals 341
57. Rational Roots of Integral Polynomials 345
58. Algebraic Numbers 349

Chapter 13.
Normal form of a matrix 355

59. Equivalence of $\lambda$-matrices.  355
60. Unimodular $\lambda$-matrices. Relationship Between Similarity of
Numerical Matrices and the Equivalence of their Characteristic Matrices 362
61. JordanNormalForm  370
62. MinimalPolynomials  377

Chapter 14.
Groups. 382

63. Definition of a Group. Examples 382
64. Subgroups 388
65. Normal Divisors, Factor Groups, Homomorphisms 394
66. Direct Sums of Abelian Groups 399
67. Finite Abelian Groups 406

Bibliography 414
Index 416

In this post we will see Problems and Exercises in the Calculus of
Variations by M. L. Krasnov, G. I. Makarenko, A. I. Kiselev .

The calculus of variations is one of the most important divisions of
classical mathematical analysis as regards applications.The authors’
aim was to supply the reader with a certain minimum of problems
covering the basic divisions of the classical calculus of variations,
and they deliberately avoided questions pertaining to the theory of
optimal control.

This book was translated from the Russian by George Yankovsky. The book was published by first Mir Publishers in 1975.

All credits to the original uploader.

DJVU | 3.1 MB | Pages: 221 | Bookmarked | OCR
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Table of Contents
CONTENTS
Introduction 6
Preliminary Remarks 7

CHAPTER I.
THE EXTREMUM OF A FUNCTION OF MANY VARIABLES

1. Absolute Extremum 9
2. Conditional Extremum 19

CHAPTER II.
EXTREMA OF FUNCTIONALS

3. The Functional. The Variation of a Functional and Its Properties 27
4. An Elementary Problem in the Calculus of Variations. Euler’s Equation 54
5. Generalizations of the Elementary Problem of the Calculus of Variations 75
6. Invariance of Euler’s Equation 85
7. Field of Extremals 88
8. Sufficient Conditions for the Extremum of a Functional 102
9. Conditional Extremum 118
10. Moving Boundary Problems 137
11. Discontinuous Problems. One-Sided Variations  151
12. The Hamilton-Jacobi Theory. The Variational Principles of Mechanics

CHAPTER III.
DIRECT METHODS IN THE CALCULUS OF VARIATIONS

13. Euler’s Finite-Difference Method 177
14. Ritz Method. Kantorovich Method 179
15. Variational Methods for Finding Eigenvalues and Eigenfunctions 188

ANSWERS AND HINTS 202

BIBLIOGRAPHY 215

INDEX 217

In this post we will see another problem book in mathematics titled Problems in Elementary Mathematics by V. Lidsky, L. Ovsyannikov, A. Tuliakov and M. Shabunin.

This book is written by a group of Soviet mathematicians under the guidance of Professor Victor Lidsky D.Sc. (Phys. & Maths). It includes advanced problems in elementary mathematics with hints and solutions.

In each section – algebra, geometry and trigonometry – the problems are arranged in the order of increasing difficulty. There are 658 problems in all.

The text can be used in mathematical schools and school mathematical societies.

This book was translated from the Russian by V. Vosolov and was first published by Mir Publishers in 1973.

All credits to the original uploader.

A note on the quality of the book: When the book was picked up from the net, it needed cleaning. We did some cleaning, OCR and bookmarking.

PDF | OCR | Cover | Bookmarked | 25.5 MB (20.5 MB Zipped) | 382 pages | Paginated

Get the book here. (Password, if needed: mirtitles)

For magnet links / torrents go here.

See the FAQs for extraction problems.

Contents

CONTENTS
Algebra
Problems / Solutions
1. Arithmetic and Geometric Progressions (1-23) 7/87
2. Algebraic Equations and Systems of Equations (24-95) 10/95
3. Algebraic Inequalities (96-123) 20/134
4. Logarithmic and Exponential Equations, Identities and Inequalities ( 124-169) 24/142
5. Combinatorial Analysis and Newton’s Binomial Theorem (170-188) 29/157
6. Problems in Forming Equations ( 189-228) 32/162
7. Miscellaneous Problems (229-291) 38/180
Geometry
A. Plane Geometry
1. Computation Problems (292-324) 47/202
2. Construction Problems (325-338) 51/217
3. Proof Problems (339-408) 52/223
4. Loci of Points (409-420) 59/254
5. The Greatest and Least Values (421-430) 61/260
B. Solid Geometry
1. Computation Problems (431-500) 62/256
2. Proof Problems (501-523) 70/209
3. Loci of Points (524-530) 72/322
4. The Greatest and Least Values (531-532) 72/325
Trigonometry

1. Transforming Express ions Containing Trigonometric Functions (533-554) 74/327
2. Trigonometric Equations and Systems of Equations (555-618) 77/333
3. Inverse Trigonometric Functions (619-628) 82/363
4. Trigonometric Inequalities (629-645) 83/366
5. Miscellaneous Problems (646-658) 85/372

This one I have been searching for a while. I had read reference to this work in some book (which I don’t remember now),  and ever since was trying to find it. Luckily today I landed on a page which had link to this book, thanks to Alex for putting up this book.

The ‘book’ seems to be is a part of a larger book, maybe selected/complete works Collected Papers of of P. L. Kapitza last chapter (32) of last volume (4). Also see comment of Alex). I do not know the original source. It has but 19 pages and there are 224 problems, and no solutions. But don’t be fooled by the number of pages. These are some of the most interesting and difficult problems you will encounter, and you will perhaps need all your wits to get through them. But they are fun, and you will enjoy doing them, even if some are very difficult. So don’t be disheartened if, you cannot solve them at all. But they will certainly set you thinking for sure.

This is what Kapitza writes about them:

The problems published in this collection were compiled by me for students of the Moscow Physical-Technical Institute, where I taught a course in general physics in 1947-1949. The collection also includes problems given at examinations for postgraduate studies at the Institute of Physical Problems at the USSR Academy of Sciences.

And on the characteristics of the problems:

I strove to achieve this end by formulating the majority of questions in the following manner. A small problem is presented, and the student, using the known laws of physics, must analyse and describe quantitatively the natural phenomenon involved. These natural phenomena were selected in terms of their scientific or practical interest within the scope of the students’ level of knowledge.

A characteristic feature of our problems is that they have no definite answer because the student is allowed to proceed further and further with the analysis of the problem posed, depending on his own abilities and inclinations.

Most of the problems have another distinctive trait. They do not contain numerical values of physical constants or parameters, and the student has to choose them personally.

And on how they were conducted

In the examinations, the students were always given complete freedom to use literature for solving the problems. Usually a few (up to 5) problems were given per examination, so as to enable the students to choose 23 of them. Thus, the inclinations of a student could be gauged from his selection of problems. For postgraduate examinations, new and more complex problems were prepared; in these cases, however, the student was allowed not only use of literature but also freedom to seek advice. Indeed, the scientist must cultivate the skill of using the advice of others, apart from learning the use of literature. In scientific work, discussions and consultations with colleagues and instructors are essential for success; this) however, requires a proper training from the very beginning of the studies.

We usually allowed about one hour for the solution of each problem. All problems have to be solved in writing, but the capabilities and character of the student become evident mostly 1n the course of a verbal discussion of the written text.

In this post we will look at a very special problem book by Shaskol’skaya and El’tsin.

This extremely popular problem book was translated outside the erstwhile USSR.

THE present collection of problems is a further development and revision of our book Selected Physics Problems, which was published in 1949 and was soon sold out. The basis of our earlier book was formed’ by problems set over a number of years in the “Olympic” examinations set in Physics .to schoolchildren. by the Physics Faculty of the Lomonosov State University in Moscow. A large number of teachers and a number of the students of the Physics Faculty of the Moscow State University took part in composing and selecting the. “Olympic” problems.

What’s special about the book is that the solutions offered are not cryptic and do not rely solely on “formulas”/”recipes” but are in a discussion form. The authors try to convey their reasoning to the reader and only after convincing the reader do they write equations. Thus the book presents a very conceptual and process-oriented approach to understanding physics through solving insightful problems.

Most of these problems can be solved from the knowledge of physics acquired in school; but we have not felt ourselves confined within the limits of the secondary-school syllabus, but have counted on pupils who have an interest in physics and are widening their knowledge by independent reading. The solution of such problems, or even an attentive analysis of the solutions given, should help schoolchildren to learn to apply their knowledge when grappling with concrete problems.

TOC:

I. Kinematics
II. The dynamics of motion in a straight line
III. Statics
IV. Work: Power: Energy: The law of conservation
of momentum: The law of conservation of energy
V. The dynamics of motion in a circle
VI. The universal theory of gravitation
VII. Oscillation: Waves: Sound
VIII. The mechanics of’liquids and gases
IX. Heat and capillary phenomena
X. Electricity
XI. Optics

Single-page layout done, OCR-ed, bookmarked and clean cover added by damitr.

Size: 14.8 MB.

You can get the book here and here.

password: mirtitles

In this post we take a stock of all the “Problem Books in Physics” that we have and the ones which we don’t have.

The ones in green text we already have but they are not prepared (except one). Red ones we do not have, any help in locating these would be greatly appreciated.

Let me know if any have been missed out.

Questions and Answers in School Physics
Lev Tarasov, Aldina Tarasova

Aptitude Test Problems in Physics
Krotov (Ed.)

Physical Problems for Robinsons
V. Lange

Problems in General Physics
V. S. Wolkenstein, G. Leib, A. Troitsky

Problems in Physics
V. G. Zubov, V. P. Shalnov

Problems in Physics
A.A. Pinsky

Collection of Problems in Theoretical Physics
Meshchersky

Physical Paradoxes and Sophisms V. N. Lange

Problems in General Physics
I.E. Irodov

A Collection of Questions and Problems in Physics
L. A. Sena

Problems in Elementary Physics
B. Bukhovtsev

Problems in Atomic and Nuclear Physics
I.E. Irodov

A Collection of problems on the equations of mathematical physics
A.V. Bitsadze, D.F. Kalinichenko (To be uploaded)

Problems in elementary physics
I.P. Gurskii (To be done)

Problems in Theoretical Physics
L. G. Grechko et al (To be done)

Problems of Crystal Physics with Solutions
N. V.Perelomova, M. M. Tagieva (To be done)

Problems of Fundamentals of Hydraulic and Thermal Engineering
V.G. Erojin and M.G. Majanko (To be done)

Problems in School Physics
I.V. Savelyev (Don’t have)

Collected problems in physics
S. Kozel, E. Rashda, S. Slavatinskii (Don’t have)

General Methods of Solving Physics Problems
B.S. Belikov (Don’t have)

Physics problems for the technician
R.A. Gladkova, L.S. Zhdanov (Don’t have)

Selected questions and problems in physics
R. Gladkova and N. Kutylovskaya (Don’t have)

Selected problems on physics
S. P. Myasnikov, T. N. Osanova (Don’t have)

Physics problems and questions
N. I. Goldfarb, Svetlana Landau (Don’t have)

In this post we will see Problems in Linear Algebra by I. V. Proskuryakov.

From the Preface:

In preparing this book of problems the author attempted firstly, to give a sufficient number of exercises for developing skills in the solution of typical problems (for example, the computing of determinants with numerical elements, the solution of systems of linear equations with numerical coefficients, and the like), secondly, to provide problems that will help to clarify basic concepts and their interrelations (for example, the connection between the properties of matrices and those of quadratic forms, on the one hand and those of linear transformations, on the other), thirdly to provide for a set of problems that might supplement the course of lectures and help to expand the mathematical horizon of the student (instances are the properties of the Pfaffian of the skew-symmetric determinant, the properties of associated matrices, and so on).

Compared with other problem book, this one has few new basic features. They include problems dealing with polynomial matrices (Sec. 13), linear transformations of affine and metric spaces (Secs. 18 and 19), and a supplement devoted to group rings, and fields. The problems of the supplement deal with the most elementary portions of the theory. Still and all, I think it can be used in pre-seminar discussions in the first and second years of study.

Starred numbers indicated problems that have been worked out or provided with hints. Solutions are given for a small number of problems.

The book was translated from the Russian by George Yankovsky and was first published by Mir Publishers in 1978.

Note: Though the file size is large (~ 2^ M) the scan quality is really poor and is barely readable at times. 2-in-1 page scan with lot of warping. We tried to rectify this but were unable to do so. There is a weird colour hue (pink and blue) on many of the pages. If any one has access to a better copy please let us know.

All credits to original uploader.

You can get the book here.

Password, if needed: mirtitles

Contents

Preface 5

Chapter I
DETERMINANTS
Sec. 1. Second and third-order determinants 9
Sec. 2. Permutations and substitutions 17
Sec. 3. Definition and elementary properties of determinants of any order 22
Sec. 4. Evaluating determinants with numerical elements 31
Sec. 5. Methods of computing determinants of the th order 33
Sec. 6. Monirs, cofactors and the Laplace theorem 65
Sec. 7. Multiplication of determinants 74
Sec. 8. Miscellaneous problems 86

Chapter II
SYSTEMS OF LINEAR EQUATIONS

Sec. 9. Systems of equation solved by the Cramer rule 95
Sec. 10. The rank of a matrix. The linear dependence of vectors and linear forms 105
Sec. 11. Systems of linear equations 115

Chapter III
MATRICES AND QUADRATIC FORMS

Sec. 12. Operations involving matrices 131
Sec. 13. Polynomial matrices 155
Sec. 14. Similar matrices, characteristic and minimal polynomials. Jordan and diagonal forms of a matrix. Functions of matrices. 166
Sec. 15. Quadratic forms 182

Chapter IV
VECTOR SPACES AND THEIR LINEAR TRANSFORMATIONS

Sec. 16. Affine vector spaces 195
Sec. 17. Euclidean and unitary vector spaces 205
Sec. 18. Linear transformations of arbitrary vector spaces 220
Sec. 19. Linear transformations of Euclidean and unitary vector spaces 236
Sec. 20. Groups 251
Sec. 21. Rings and fields 265
Sec. 22. Modules 275
Sec. 23. Linear spaces and linear transformations (appendices to Secs. 10 and 16 to 19) 280
Sec. 24. Linear, bilinear, and quadratic functions and forms (appendix to Sec. 15) 284
Sec. 25. Affine (or point-vector) spaces 288
Sec. 26. Tensor algebra 295

ANSWERS

Chapter I. Determinants 312
Chapter II. Systems of linear equations 342
Chapter III. Matrices and quadratic forms 359
Chapter IV. Vector spaces and their linear transformations 397
Supplement 427

Index 449

In this post we see yet another problem and solution book in mathematics titled Problems and Exercises in Integral Equations by M. Krasnov, A. Kiselev, G. Makarenko.

About the book:

As the name suggests the book is about integral equations and methods of solving them under different conditions. The book has three chapters. Chapter 1 covers Volterra Integral Equations in details. Chapter 2 covers Fredholm integral equations. Finally in Chapter 3, Approximate Methods for solving integral equations are discussed. There are plenty of solved examples in the text to illustrate the methods, along with problems to solve. This will be a useful resource book for those studying integral equations.

The book was translated from the Russian by George Yankovsky and was first published by Mir Publishers in 1971.

PDF | OCR | 600 dpi | Bookmarked | Paginated | Cover | 224 pp | 7.3 MB  (Zipped 6.7 MB)
(Note: IA file parameters maybe different.)

You can get the book here (IA) and here (filecloud).

Password, if needed: mirtitles

See FAQs for password related problems.

Contents

CONTENTS
PRELIMINARY REMARKS 7

CHAPTER I.
VOLTERRA INTEGRAL EQUATIONS 15

1. Basic Concepts 15
2. Relationship Between Linear Differential Equations and Volterra Integral Equations 18
3. Resolvent Kernel of Volterra Integral Equation. Solution
of Integral Equation by Resolvent Kernel 21
4. The Method of Successive Approximations 32
5. Convolution-Type Equations 38
6. Solution of Integro-Differential Equations with the
Aid of the Laplace Transformation 43
7. Volterra Integral Equations with Limits (x, + $\infty$) 46
8. Volterra Integral Equations of the First Kind 50
9. Euler Integrals 52
10. Abel’s Problem. Abel’s Integral Equation and Its Generalizations 56
11. Volterra Integral Equations of the First Kind of the
Convolution Type 62

CHAPTER II.
FREDHOLM INTEGRAL EQUATIONS 71

12. Fredholm Equations of the Second Kind. Fundamentals 71
13. The Method of Fredholm Determinants 73
14. Iterated Kernels. Constructing the Resolvent Kernel
with the Aid of Iterated Kernels 78
15. Integral Equations with Degenerate Kernek. Hammerstein
Type Equation 90
16. Characteristic Numbers and Eigenfunctions 99
17. Solution of Homogeneous Integral Equations with
Degenerate Kernel 118
18. Nonhomogeneous Symmetric Equations 119
19. Fredholm Alternative 127
20. Construction of Green’s Function for Ordinary
Differential Equations 134
21. Using Green’s Function in the Solution of Boundary-
Value Problems 144
22. Boundary-Value Problems Containing a Parameter;
Reducing Them to Integral Equations 148
23. Singular Integral Equations 151

CHAPTER III.
APPROXIMATE METHODS 166

24. Approximate Methods of Solving Integral Equations 166
1. Replacing the kernel by a degenerate kernel 166
2. The method of successive approximations 171
3. The Bubnov-Galerkin method 172
25. Approximate Methods for Finding Characteristic Numbers 174
1. Ritz method 174
2. The method of traces 177
3. Kellogg’s method 179

ANSWERS 182
APPENDIX. SURVEY OF BASIC METHODS FOR SOLVING
INTEGRAL EQUATIONS 198
BIBLIOGRAPHY 208
INDEX 210

In this post we will see Problems in Higher Mathematics by V. P. Minorsky.

About the book:

The list of topics covered is quite exhaustive and the book has over 2500 problems and solutions. The topics covered are plane and solid analytic geometry, vector algebra, analysis, derivatives, integrals, series, differential equations etc. A good reference for those looking for many problems to solve.

The book was translated from the Russian by Yuri Ermolyev and was first published by Mir Publishers in 1975.

PDF | OCR | Cover | 600 dpi | Bookmarked | Paginated | 16.4 MB (15.6 MB Zipped) | 408 pages

(Note: IA file parameters maybe different.)

You can get the book here (IA) and here (filecloud).

Password, if needed: mirtitles

See FAQs for password related problems.

Chapter I.
Plane Analytic Geometry 11

1.1. Coordinates of a Point on· a Straight Line and in a Plane. The Distance Between Two Points 11
1.2. Dividing a Line Segment in a Given Ratio. The Area of a Triangle and a Polygon 13
1.3. The Equation of a Line as a Locus of Points 15
1.4. The Equation of a Straight Line: (1) Slope-Intercept Form, (2) General Form, (3) Intercept Form 17
1.5. The Angle Between Two Straight Lines. The Equation of a Pencil of Straight Lines Passing Through a Given Point. The Equation of a Straight Line Passing Through Two Given Points. The Point of Intersection of Two Straight Lines 20
1.6. The Normal Equation of a Straight Line. The Distance of a Point from a Straight Line. Equations of Bisectors. The Equations of a Pencil of Straight Lines Passing Through the Point of Intersection of Two Given Straight Lines 24
1.7. Miscellaneous Problems 26
1.8. The Circle 28
1.9. The Ellipse 30
1.10. The Hyperbola 33
1.11. The Parabola 37
1.12. Directrices, Diameters, and Tangents to Curves of the Second Order 41
1.13. Transformation of Cartesian Coordinates 44
1.14. Miscellaneous Problems on Second-Order Curves 49
1.15. General Equation of a Second-Order Curve 51
1.16. Polar Coordinates 57
1.17. Algebraic Curves of the Third and Higher Orders 61
1.18. Transcendental Curves 63

Chapter 2.
Vector Algebra 64

2.1. Addition of Vectors. Multiplication of a Vector by a Scalar 64
2.2. Rectangular Coordinates of a Point and a Vector in Space 68
2.3. Scalar Product of Two Vectors 71
2.4. Vector Product of Two Vectors 75
2.5. Scalar Triple Product 78

Chapter 3.
Solid Analytic Geometry 81

3.1. The Equation of a Plane 81
3.2. Basic Problems Involving the Equation of a Plane. 83
3.3. Equations of a Straight Line in Space 86
3.4. A Straight Line and a Plane 89
3.5. Spherical and Cylindrical Surfaces 92
3.6. Conical Surfaces and Surfaces of Revolution 95
3.7. The Ellipsoid, Hyperboloids, and Paraboloids 97

Chapter 4.
Higher Algebra 101

4.1. Determinants 101
4.2. Systems of First-Degree Equations 104
4.3. Complex Numbers 108
4.4. Higher-Degree Equations. Approximate Solution of Equations 111

Chapter 5.
Introduction to Mathematical Analysis 116

5.1. Variable Quantities and Functions 116
5.2. Number Sequences. Infinitesimals and Infinities. The Limit of a Variable. The Limit of a Function 120
5.3. Basic Properties of Limits. Evaluating the Indeterminate Forms 0/0 \infty/ infty 126
5.4. The Limit of the Ratio sin(x)/x as x–> \infty a 128
5.5. Indeterminate Expressions of the Form \infty –> \infty 129
5.6. Miscellaneous Problems on Limits 129
5.7. Comparison of Infinitesimals 130
5.8. The Continuity of a Function 132
5.9. Asymptotes 136
5.10. The Number e 137

Chapter 6.
The Derivative and the Differential 139

6.1. The Derivatives of Algebraic and Trigonometric Functions 139
6.2. The Derivative of a Composite Function 141
6.3. The Tangent Line and the Normal to a Plane Curve 142
6.4. Cases of Non-differentiability of a Continuous Function 145
6.5. The Derivatives of Logarithmic and Exponential Functions 147
6.6. The Derivatives of Inverse Trigonometric Functions 149
6.7. The Derivatives of Hyperbolic Functions 150
6.8. Miscellaneous Problems on Differentiation 151
6.9. Higher-Order Derivatives 151
6.10. The Derivative of an Implicit Function 154
6.11. The Differential of a Function 156
6.12. Parametric Equations of a Curve 158

Chapter 7.
Applications of the Derivative 161

7.1. Velocity and Acceleration 161
7.2. Mean-Value Theorems 163
7.3. Evaluating Indeterminate Forms. L’Hospital’s Rule 166
7.4. Increase and Decrease of a Function. Maxima and Minima 168
7.5. Finding Greatest and Least Values of a Function 172
7.6. Direction of Convexity and Points of Inflection of a Curve. Construction of Graphs 174

Chapter 8.
The Indefinite Integral 177

8.1. Indefinite Integral. Integration by Expansion 177
8.2. Integration by Substitution and Direct Integration 179
8.3. Integrals of the form dx and Those Reduced to Them 181
8.4. Integration by Parts 183
8.5. Integration of Some Trigonometric Functions 184
8.6. Integration of Rational Algebraic Functions 186
8.7. Integration of Certain Irrational Algebraic Functions 188
8.8. Integration of Certain Transcendental Functions 190
8.9. Integration of Hyperbolic Functions. Hyperbolic Substitutions 192
8.10. Miscellaneous Problems on Integration 193

Chapter 9.
The Definite Integral 195

9.1. Computing the Definite Integral 195
9.2. Computing Areas 199
9.3. The Volume of a Solid of Revolution 201
9.4. The Arc Length of a Plane Curve 203
9.5. The Area of a Surface of Revolution 205
9.6. Problems in Physics 206
9.7. ImproperIntegrals 209
9.8. The Mean Value of a Function 212
9.9. Trapezoid Rule and Simpson’s Formula 213

Chapter 10.
Curvature of Plane and Space Curves 216

10.1. Curvature of a Plane Curve. The Centre and Radius of Curvature. The Evolute of a Plane Curve 216
10.2.The Arc Length of a Space Curve 218
10.3. The Derivative of a Vector Function of a Scalar Argument and Its Mechanical and Geometrical Interpretations. The Natural Trihedron of a Curve 218
10.4. Curvature and Torsion of a Space Curve 222

Chapter 11.
Partial Derivatives, Total Differentials, and Their Applications 224

11.1. Functions of Two Variables and Their Geometrical Representation 224
11.2. Partial Derivatives of the First Order 227
11.3. Total Differential of the First Order22 8
11.4. The Derivative of a Composite Function 230
11.5. Derivatives of Implicit Functions 232
11.6. Higher-Order Partial Derivatives and Total Differentials 234
11.7. Integration of Total Differentials 237
11.8. Singular Points of a Plane Curve 239
11.9. The Envelope of a Family of Plane Curves 240
11.10. The Tangent Plane and the Normal to a Surface 241
11.11. Scalar Field. Level Lines and Level Surfaces. A Derivative Along a Given Direction. Gradient 243
11.12. The Extremum of a Function of Two Variables 245

Chapter 12.
Differential Equations 248

12.1. Fundamentals 248
12.2. First-Order Differential Equation with Variables Separable. Orthogonal Trajectories 250
12.3. First-Order Differential Equations: (I) Homogeneous, (2) Linear, (3) Bernoulli’s 253
12.4. Differential Equations Containing Differentials of a Product or a Quotient 255
12.5. First-Order Differential Equations in Total Differentials. Integrating Factor 255
12.6. First-Order Differential Equations Not Solved for the Derivative. Lagrange’s and Clairaut’s Equations 257
12.7. Differential Equations of Higher Orders Allowing for Reduction of the Order 259
12.8. Linear Homogeneous Differential Equations with Cons- tant Coefficients 261
12.9. Linear Non-homogeneous Differential Equations with Constant Coefficients 262
12.10. Differential Equations of Various Types 265
12.11. Euler’s Linear Differential Equation 266
12.12. Systems of Linear Differential Equations with Constant Coefficients 266
12.13. Partial Differential Equations of the Second Order (the Method of Characteristics) 267

Chapter 13.
Double, Triple, and Line Integrals 269

13.1. Computing Areas by Means of Double Integrals 269
13.2. The Centre of Gravity and the Moment of Inertia of an Area with Uniformly Distributed Mass (for Density \mu = 1) 271
13.3. Computing Volumes by Means of Double Integrals 273
13.4. Areas of Curved Surfaces 274
13.5. The Triple Integral and Its Applications 275
13.6. The Line Integral. Green’s Formula 277
13.7. Surface Integrals. Ostrogradsky’s and Stokes’ Formulas 281

Chapter 14.
Series 285

14.1. Numerical Series 285
14.2. Uniform Convergence of a Functional Series 288
14.3. Power Series 290
14.4. Taylor’s and Maclaurin’s Series 292
14.5. The Use of Series for Approximate Calculations 295
14.6. Taylor’s Series for a Function of Two Variables 298
14.7. Fourier Series. Fourier Integral 299

Answers 305
Appendices 383

In this post we will see Selected Questions and Problems in Physics  by R. Gladkova and N. Kutylovskaya.

About the book

This collection of questions and problems in physics is in ­ tended for the students of correspondence courses and evening classes in intermediate colleges and is in accord with the existing curriculum .

The purpose of this book is to teach the students how to solve problems in physics. This should stimulate corre­spondence course students to work independently, encourage them to accumulate an adequate theoretical background, and develop in them the requisite aptitude for practical activity in various branches of the economy.

Each section begins with a brief description of the basic theoretical concepts, laws, and formulas. This provides the maxim um possible help to correspondence course students in
solving problems. A large number of problem s are supplied with detailed solutions and an analysis of the results, while in some cases different approaches are used to solve the same
problem so that the student can discover the most rational form of independent study.

The theoretical material is presented in a lucid form, and most problems are of medium complexity. However, each section contains tougher problem s as well. Their solution requires a broader range of theoretical data, and will fa­cilitate a deeper understanding of the physics course.

In keeping with the existing curriculum, problem s in astronomy have also been included in the collection. Their solution requires the use of a star chart, which is printed on the flyleaf.
The book was translated from the Russian by Natalia Wadhwa and was published by Mir in 1989.

All credits to the original uploader.

You can get the book here.

In this post we will see another book in the Problems and Solutions book, namely, General Methods for Solving Physics Problems by B. S. Belikov

About

This book attempts to create systematic use of generalised methods , general methodological principles, and very general concepts in a segment of students instruction of vital importance, the solution of physics problems. The approach is based on the application of the most general concepts of physics to the solution of any problem. I consider the theoretical aspects underlying the general approach to problem solution and methods for solving standard, non-standard, non-specific, and general problems.

The book was translated from the Russian by Eugene Yankovsky and was first published by Mir in 1989.

You can get the book here.

All credits to the original uploader.

Contents

The book has three parts

Part 1: The Theoretical Bases of the General Approach to Solving Any Physics Problem

Chapter 1: The System of Fundamental Concepts of Physics

1 Some General Concepts of Physics

2 Idealization of a Physics Problem

3 Classification of Physics Problems

Chapter 2: Some General Methods for Solving Physics Problems

4 Stages in Solving a Formulated Problem

5 Method of Analysing the Physical Content of a Problem

6 General-Particular Methods. The DI Method

7 The Simplification and Complication Method. The Estimate Method

8 The Problem Statement Method

9 Another Classification of Formulated Problems

Part 2: Solution of Standard Problems

Chapter 3: The motion of a particle

10 Particle Kinematics

11 Particle Dynamics

12 Mechanical Oscillations

13 Conservation Laws

Chapter 4: The motion of a rigid body

14 Rigid Body Dynamics

15 Conservation Laws in rigid body Dynamics

Chapter 5: The Gravitational Field

16 The Basic Problem of Gravitational Theory

17 The Gravitational Field Generated by a system of particles

18 The Gravitational Field Generated by an arbitrary Mass Distribution

Chapter 6: The Electric Field

19 The Electrostatic Field in Vacuum

20 The Electrostatic Field in Insulators

21 Conductors in Electrostatic Field

22 Direct Current

Chapter 7: The Magnetic Field

23 The Magnetic Field in a Vacuum

24 The Magnetic Field in Matter

Chapter 8: The Electromagnetic Field

25 Electromagnetic Induction and Self-Induction

26 Electromagnetic Oscillations

Chapter 9: Electromagnetic Waves

27 Interference of Light

28 Diffraction of Light

Chapter 10: Thermodynamics

29 The First Law of Thermodynamics

30 The Second Law of Theormodynamics

Chapter 11: Kinetic Theory

31 The Maxwell-Boltzmann Distribution

32 The Boltzmann Distribution

Part 3: Solution of Nonstandard, Nonspecified and Arbitrary problems

Chapter 12: Non-standard and Original Problems

33 Non-standard Problems

34 Original Problems

Chapter 13: Nonspecified, Research and Arbitrary Problems

35 Nonspecified Problems

36 Research Problems

37 Arbitrary Problems

Conclusion

In this post we will see another Problem and Solution book:

Selected Problems on Physics by S. P. Myasnikov, T. N. Osanova

About

The main purpose of the book is to help those preparing for entrance examinations to  engineering colleges in revisiing the high-school physics course and in further studies at the college.

The fourth edition of the book came out in 1981.  Amendments to the physics curriculum at the high-school and polytechnic level have been incorporated as well as extra material on other branches of the physics course.  The 6Eth edition was prepared by taking into account the modified style of problems set at the entrance examinations.

Each section begins with a brief description of the basic theory, physical laws, and formulas. This is followed by worked problems and a few descriptive problems. Exercises and questions for revision are givena at the end of each section. The problems are solved according to the unified and optimal approach described in the introduction. By solving the problems, students will acquire a firm theoretical background and knowledge which will help them in their work in whichever sector of the economy they will be employed. The appendices contain tables required for solving problems, SI units of physical quantities. And the rules for approximate calculations.

In addition to the problems composed by the autbors this book also includes a selection  of problems set for the aptitude tests and entrance examination in physics at the N.E. Buaman Higher Technical School and other technical institutios in Moscow.
Intended for students of preparatory courses at engineering colleges, this book can also be used by high-school students, students of intermediate colleges, and those interested in self-education.

The author is indebted to Prof. A.N. Remizov and Asst. Prof. N .V. Tygliyan for their  enormous help in preparing the  manuscript for publication.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1990.

You can get the book here.

All credits to the original uploader.

Comment from Node

Hello,

I have uploaded the following to LibGen.

600 dpi | OCR | Cleaned & Processed [Perfect]
The files are now fully processed & cleaned.

Kiselev’s Geometry / Book I. Planimetry Vol IBy A. P. Kiselev, Alexander Givental
http://gen.lib.rus.ec/book/index.php?md5=1f9f931274c93623a7391f1a75158295

Kiselev’s Geometry / Book II. Stereometry  Vol IIBy A. P. Kiselev, Alexander Givental
http://gen.lib.rus.ec/book/index.php?md5=09ed3a3d2576f80753b3800998d5d00e

Selected Problems and Theorems in Elementary Mathematics By D.O. Shklyarsky, N. N. Chentsov, I. M. Yaglom | MIR 1979
http://gen.lib.rus.ec/book/index.php?md5=494b709112fb7acef897d1cc9b6db6c8
Regards,

Thanks for all the good work!

In this post we will see the book Elementary Physics: Problems and Solutions by I. P. Gurskii

The book is intended for those preparing for university entrance examinations in physics. The contents and sequence of topics are in keeping with the requirements for such examinations. The few sections beyond the entrance examination programme are marked by circles. In view of the introduction of the elements of higher mathematics to the high-school curriculum, some problems have also been illustrated using differential calculus. The author has endeavoured to present the basic principles of school physics in a compact form to help the candidates revise the entire course in the shortest possible time. All sections have been illustrated with problems to give a better understanding of the subject. Each problem and its solution is followed by one or more exercises on the same topic, the exercises corresponding to problems that have been solved in the text are assigned the same number.Those intending to use this book independently are advised to attempt the exercises after going through the theoretical part. The relevant solved problems should be consulted if difficulties are encountered while solving the exercises. After this, the exercise should be tried again, and if there is more than one exercise bearing the same number, another exercise (preferably the last one) should be tackled. In most cases, the last exercises in a series are the most difficult.

The book was translated from Russian by Natalia Wadhwa and was first published in 1987.

PDF | OCR | 13.1 MB

All credits to Siddharth  for scanning and posting this book.

You can get the book here (fc link) or here (IA link)

Contents

Foreword
From the Preface to the Second Russian Edition

INTRODUCTION

1.1. SI System of Units
1.2. Vectors. Some Mathematical Operations on Vectors
1.3. Projections of Points and Vectors onto an Axis
1.4. General Methodical Hints to the Solution of Problems

1. MECHANICS

1.1. Basic Concepts

A. Kinematics

1.2. Kinematics of Translatory Motion
1.3. Uniform Rectilinear Motion. Velocity. Graphs of Velocity and Path Length in Uniform Motion
1.4. Nonuniform Motion. Average and Instantaneous Velocities. Acceleration
1.5. Uniformly Variable Motion. Graphs of Velocity and Path Length in Uniformly Variable Motion

Problems with Solutions
Exercises

B. Dynamics of Translatory Motion

1.6. Force
1.7. Newton’s First Law. Inertial and Noninertial Reference Systems
1.8. Newton’s Second Law. Momentum of a Body
1.9. Newton’s Third Law
1.10. Principle of Independence of Action
1.11. Addition of Forces Acting at an Angle
1.12. Resolution of a Force into Two Components at an Angle to Each Other
1.13. Law of Momentum Conservation
1.14. Idea of Reaction Propulsion
1.15. Friction. Coefficient of Friction
1.16. Elastic Force. Hooke’s Law
1.17. Law of Universal Gravitation
1.18. Force of Gravity. Free Fall of Bodies
1.19. Weight of a Body. Weighing
1.20. Weightlessness

Problems with Solutions
Exercises

1.21. Work and Power
1.22. Energy. Kinetic and Potential Energies
1.23. Law of Energy Conservation

Problems with Solutions
Exercises

C. Kinematics and Dynamics of Rotational Motion of a Rigid Body

1.24. Uniform Rotational Motion. Angular Velocity. Linear Velocity
1.25. Centripetal Acceleration
1.26. Weight of a Body Considering the Rotation of the Earth
1.27. Reasons Behind the Emergence of Weightlessness in Artificial Satellites. Orbital Velocity

Problems with Solutions
Exercises

D. Statics

1.28. Equilibrium of a Nonrotating Body. Equilibrium Conditions for a Body on an Inclined Plane

Problems with Solutions
Exercises

1.29. Moment of Force
1.30. Addition of Parallel Forces. A Couple
1.31. Equilibrium of a Body with a Fixed Rotational Axis (Law of Torques)
1.32. Equilibrium of a Rigid Body in the General Case

Problems with Solutions
Exercises

1.33. Types of Equilibrium
1.34. Centre of Mass of a Body
1.35. Determination of the Centre of Mass for Bodies of Various Shapes

Problems with Solutions
Exercises

2. FLUIDS

2.1. Pressure
2.2. Pascal’s Law
2.3. Hydraulic Press
2.4. Pressure of a Fluid on the Bottom and Walls of a Vessel. Law of Communicating Vessels
2.5. Atmospheric Pressure. Barometers
2.6. Archimedean Principle

Problems with Solutions
Exercises

3. MOLECULAR PHYSICS. THERMAL PHENOMENA

A. Molecular Physics

3.1. Basic Concepts of Molecular-Kinetic Theory
3.2. Brownian Movement. Gas Pressure
3.3. Diffusion in Gases, Liquids, and Solids
3.4. Motion of Molecules in Gases, Liquids, and Solids
3.5. Intermolecular Interaction

B. Thermal Phenomena

3.6. Internal Energy of a Body
3.7. Law of Conservation and Transformation of Energy. First Law of Thermodynamics
3.8. Temperature Gradient. Thermodynamic Temperature Scale. Absolute Zero
3.9. Heat Capacity
3.10. Experimental Determination of Specific Heat of a Substance
3.11. Heat of Combustion of a Fuel
3.12. Efficiency of a Heat Engine
3.13. Phase of a Substance. Fusion. Latent Heat of Fusion
3.14. Evaporation. Condensation. Vaporization and Boiling. Latent Heat of Vaporization

Problems with Solutions
Exercises

3.15. Temperature Coefficients of Linear and Cubic Expansion

Problems with Solutions
Exercises

C. Gas Laws

3.16. Isobaric Process. Charles’ Law
3.17. Isothermal Process. Boyle’s Law. Dalton’s Law
3.18. Isochoric Process. Gay-Lussac’s Law
3.19. Adiabatic Process
3.20. The Boyle-Charles Generalized Law. Equation of State for an Ideal Gas
3.21. The Clapeyron-Mendeleev Equation. Avogadro’s Law
3.22. Ideal Gas. Physical Meaning of Thermodynamic Temperature
3.23. Work Done by a Gas During Expansion

Problems with Solutions
Exercises

3.24. Saturated and Unsaturated Vapours. Temperature Dependence of Saturation Vapour Pressure
3.25. Absolute Humidity. Relative Humidity
3.26. Instruments for Determining Humidity

Problems with Solutions
Exercises

4. FUNDAMENTALS OF ELECTRODYNAMICS

A. Electrostatics

4.1. Law of Electric Charge Conservation. Electric Field. Coulomb’s Law. Effect of Medium on the Force of Interaction of Charges
4.2. Charge Equilibrium in Metals. Electrostatic Induction
4.3. Electroscope
4.4. Electric Field Strength. Electric Field Lines
4.5. Work Done on a Charge by the Forces of Electrostatic Field. Potential
4.6. Relation Between Potential and Field Strength for a Uniform Electric Field
4.7. Capacitance
4.8. Capacitors. Energy of a Charged Capacitor

Problems with Solutions
Exercises

B. Direct Current

4.9. Electric Current. Current Intensity. Electromotive Force
4.10. Ohm’s Law for a Subcircuit. Resistance of Conductors
4.11. Temperature Dependence of Resistance. Semiconductors
4.12. Series Connection of Conductors
4.13. Parallel Connection of Conductors
4.14. Rheostats
4.15. Current Sources. Ohm’s Law for a Closed Circuit
4.16. Parallel and Series Connection of Current Sources
4.17. Direct Current Power. Joule’s Law

Problems with Solutions
Exercises

4.18. Electrolysis
4.19. Faraday’s Laws of Electrolysis

Problems with Solutions
Exercises

4.20. Electric Current in Gases
4.21. Electron and Ion Beams, Their Properties and Application
4.22. Thermionic Emission.’ Electron Work Function

Problems with Solutions
Exercises

C. Magnetic Phenomena

4.23. Interaction of Currents. Magnetic Field. Magnetic Induction. Magnetic Field Lines
4.24. Force Acting on a Current-Carrying Conductor in a Magnetic Field. Magnetic Forces
4.25. Permeability of a Medium. Magnetic Field Strength
4.26. Forces of Interaction Between Parallel Current-Carrying Conductors
4.27. Magnetic Flux
4.28. Ammeter and Voltmeter

D. Electromagnetic Phenomena

4.29. Electromagnetic Induction
4.30. Induced Electromotive Force
4.31. Lenz’s Law
4.32. Self-Induction. Inductance

Problems with Solutions
Exercises

5. OSCILLATIONS AND WAVES

5.1. Oscillatory Motion. Amplitude, Period, and Frequency of Oscillations
5.2. Harmonic Oscillations. Phase of Oscillation
5.3. Pendulum. Period of Oscillations of a Mathematical Pendulum
5.4. Free and Forced Oscillations. Resonance
5.5. Waves. Velocity and Wavelength
5.6. Sonic Waves

Problems with Solutions
Exercises

5.7. Electromagnetic Oscillations and Waves
5.8. Oscillatory Circuit

Problems with Solutions
Exercises

5.9. Alternating Current. A.C. Generator
5.10. Period and Frequency of Alternating Current. Effective Current and Voltage
5.11. Transmission and Distribution of Electric Energy
5.12. Transformer
5.13. D.C. Generator

Problems with Solutions
Exercises

5.14. Electron Tubes (Valves)
5.15. Diode as a Rectifier of Alternating Current
5.16. Cathode-Ray Tube
5.17. Electron Tubes as Generators and Amplifiers
5.18. Open Oscillatory Circuit. Emission and Reception of Electromagnetic Waves
5.19. Scale of Electromagnetic Waves

Problem with Solution
Exercise

6. OPTICS

6.1. Light Sources. Propagation of Light in a Straight Line
6.2. Velocity of Light. Michelson’s Experiment

A. Photometry

6.3. Luminous Flux. Luminous Intensity
6.4. Illuminance (Illumination Intensity)
6.5. Comparison of Luminous Intensity of Different Sources. Photometers

Problems with Solutions
Exercises

B. Geometrical Optics

6.6. Law of Reflection of Light. Construction of Image Formed by a Plane Mirror
6.7. Construction of Image Formed by a Spherical Mirror. Spherical Aberration

Problems with Solutions
Exercises

6.8. Laws of Refraction of Light. Refractive Index
6.9. Total Internal Reflection. Critical Angle
6.10. Ray Path in a Plane-Parallel Plate. Ray Path in a Prism
6.11. Converging and Diverging Lenses
6.12. Lens Formula. Lens Power
6.13. Image Formation by a Lens

Problems with Solutions
Exercises

C. Optical Instruments

6.14. Searchlight. Projection Lantern
6.15. Photographic Camera
6.16. Magnifying Glass. Human Eye as an Optical Instrument
6.17. Accommodation of Eye. Myopia and Hyperopia. Spectacles

Problems with Solutions
Exercises

D. Composition of Light. Invisible Rays

6.18. Dispersion of Light. Spectrum. Spectroscope
6.19. Infrared and Ultraviolet Radiation
6.20. Emission and Absorption Spectra. Fraunhofer Lines. Spectral Analysis
6.21. On the Wave and Quantum Nature of Light
6.22. Interference of Light
6.23. Diffraction of Light
6.24. Photoelectric Effect
6.25. Photocells and Their Application
6.26. Effects of Light

Problems with Solutions
Exercise

7. STRUCTURE OF THE ATOM 492
7.1. Structure of the Atom and Its Energy
7.2. Atomic Nucleus
7.3. Radioactivity
7.4. Uranium Nuclear Fission. Chain Reaction
7.5. Binding Energy of Atomic Nucleus

Problem with Solution
Exercise

Graphical Solutions to Exercises

Appendices