## Problems of Mathematical Physics – Lebedev, Skalsyaka, Uflyand

In this post, we will see the book Problems of Mathematical Physics by N. N. Lebedev; I. P. Skalsyaka; Y. S. Uflyand. The aim of the present book is to help the reader ac­quire the proficiency needed to successfully apply the methods of mathematical physics to a variety of prob­lems drawn from mechanics, the theory of heat conduc­tion, and the theory of electric and magnetic phenomena. A wide range of topics is covered, including not only problems of the simpler sort, but also problems of a more complicated nature involving such things as curvilinear coordinates, integral transforms, certain kinds of integral equations, etc. The book is intended both for students concomitantly studying the cor­ responding topics in courses of mathematical physics, and for research scientists who in their work find it necessary to carry out calculations using the methods described here. We also think that quite apart from its value as a tool for acquiring technique, the book can also serve as a handbook, especially in view of the fact that answers to the problems are included.

The book was translated from the Russian by Richard Silverman and was published in 1965.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles
Write to us: mirtitles@gmail.com
Fork us at GitLab: https://gitlab.com/mirtitles/

Contents

PROBLEMS, Page 1.

1. DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS, Page 3.

1. Mechanics, 3.
2. Heat Conduction, 9.
3. Electricity and Magnetism, 11.

2. SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS, Page 20.

1. Hyperbolic Equations, 20.
2. Elliptic Equations: The Green’s Function Method, 27.
3. Elliptic Equations: The Method of Conformal Mapping, 33.

3. STEADY-STATE HARMONIC OSCILLATIONS, Page 42.

1. Elastic Bodies: Free Oscillations, 43.
2. Elastic Bodies: Forced Oscillations, 46.
3. Electromagnetic Oscillations, 49.

4. THE FOURIER METHOD, Page 55.

1. Mechanics: Vibrating Systems, Acoustics, 60.
2. Mechanics: Statics of Deformable Media, Fluid Dynamics, 73.
3. Heat Conduction: Nonstationary Problems, 77.
4. Heat Conduction: Stationary Problems, 83.
5. Electricity and Magnetism, 91.

5. THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS, Page 103.

1. Mechanics: Vibrating Systems, 107.
2. Mechanics: Statics of Deformable Media, 114.
3. Heat Conduction: Nonstationary Problems, 119.
4. Heat Conduction: Stationary Problems, 124.
5. Electricity and Magnetism, 131.

6. INTEGRAL TRANSFORMS, Page 143.

1. The Fourier Transform, 146.
2. The Hankel Transform, 160.
3. The Laplace Transform, 169.
4. The Mellin Transform, 189.
5. Integral Transforms Involving Cylinder Functions of Imaginary Order, 194.

7. CURVILINEAR COORDINATES, Page 203.

1. Elliptic Coordinates, 204.
2. Parabolic Coordinates, 210.
3. Two-Dimensional Bipolar Coordinates, 212.
4. Spheroidal Coordinates, 219.
5. Paraboloidal Coordinates, 231.
6. Toroidal Coordinates, 233.
7. Three-Dimensional Bipolar Coordinates, 242.
8. Some General Problems on Separation of Variables, 247.

8. INTEGRAL EQUATIONS, Page 253.

1. Diffraction Theory, 254.
2. Electrostatics, 259.

PART 2 SOLUTIONS, Page 273.

MATHEMATICAL APPENDIX, Page 381.

1. Special Functions Appearing in the Text, 381.
2. Expansions in Series of Orthogonal Functions, 384.
3. Some Definite Integrals Frequently Encountered in the Applications, 386.
4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates, 388.

Supplement. VARIATIONAL AND RELATED METHODS, Page 391.

1. Variational Methods, 392.
1.1. Formulation of Variational Problems, 392.
1.2. The Ritz Method, 396.
1.3. Kantorovich’s Method, 401.

2. Related Methods, 404.
2.1. Galerkin’s Method, 404.
2.2. Collocation, 407.
2.3. Least Squares, 411.

3. References, 412.

BIBLIOGRAPHY, Page 415.
NAME INDEX, Page 423.
SUBJECT INDEX, Page 427. 