Author(s): N. S. Koshlyakov, M. M. Smirnov, E. B. Gliner
Edition: 1
Publisher: Mir Publishers, North Holland Publishing Company
Year: 1964
Language: English
Pages: 701
City: Moscow
Front Cover
Title Page
PREFACE
CONTENTS
INTRODUCTION
PART I DIFFERENTIAL EQUATIONSOF THE HYPERBOLIC TYPE
1. METHODS OF FINDING THE GENERAL SOLUTION TO EQUATIONS OF THE HYPERBOLIC TYPE
2. THE CAUCHY PROBLEM ON A PLANE
3. THE APPLICATION OF THE METHOD OF CHARACTERISTICS TO THE STUDY OF LOW-AMPLITUDE VIBRATIONS OF A STRING
4. LONGITUDINAL VIBRATIONS OF A ROD
5. APPLICATION OF THE METHOD OF CHARACTERISTICS TO THE STUDY OF ELECTRICAL VIBRATIONS IN CONDUCTORS
6. THE WAVE EQUATION
7. FUNCTIONALLY INVARIANT SOLUTIONS
7. APPLICATION OF THE FOURIER METHOD TO THE STUDY OF FREE VIBRATIONS OF STRINGS AND RODS
9. FORCED VIBRATIONS OF STRINGS AND RODS
10. TORSIONAL VIBRATIONS OF A HOMOGENEOUS ROD
11. ELECTRIC OSCILLATIONS IN LINES
12. BESSEL FUNCTIONS
13. SMALL-AMPLITUDE VIBRATIONS OF A THREAD SUSPENDED FROM ONE END
15. LEGENDRE POLYNOMIALS
16. THE APPLICATION OF THE FOURIER METHOD TO THE STUDY OF SMALL - AMPLITUDE VIBRATIONS OF RECTANGULAR AND CIRCULAR MEMBRANES
17. INTEGRAL FORMULAE THAT ARE APPLICABLE TO THE THEORY OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE
PART II DIFFERENTIAL EQUATIONSOF THE ELLIPTIC TYPE
18. LAPLACE AND POISSON EQUATIONS
19. POTENTIAL THEORY
20 .ELEMENTS OF THE THEORY OF LOGARITHMIC POTENTIAL
21. SPHERICAL FUNCTIONS
22. SEVERAL QUESTIONS ON GRAVIMETRY AND THE THEORY OF THE SHAPE OF THE EARTH
23. APPLICATION OF THE THEORY OF SPHERICAL FUNCTIONS TO THE SOLUTION OF PROBLEMS IN MATHEMATICAL PHYSICS
24. GRAVITY WAVES ON THE SURFACE OF A LIQUID
25. THE HELMHOLTZ EQUATION
26. THE EMISSION AND SCATTERING OF SOUND
27. COMMENTS ON EQUATIONS OF THE ELLIPTIC TYPE IN THE GENERAL FORM
PART III EQUATIONS OF THE PARABOLIC TYPE
28. THE SIMPLEST PROBLEMS LEADING TO THE HEAT-FLOW EQUATION. SOME GENERAL THEOREMS
29. HEAT-FLOW IN AN INFINITE ROD
30. THE APPLICATION OF THE FOURIER METHOD TO THE SOLUTION OF BOUNDARY- VALUE PROBLEMS
PART IV SUPPLEMENTARY MATERIAL
31. THE USE OF INTEGRAL OPERATORS IN SOLVING PROBLEMS IN MATHEMATICAL PHYSICS
32. EXAMPLES OF THE APPLICATION OF FINITE INTEGRAL TRANSFORMATIONS
33. EXAMPLES OF THE APPLICATION OF INTEGRAL TRANSFORMATIONS WITH INFINITE LIMITS
34. MAXWELL'S EQUATIONS
35. EMISSION OF ELECTROMAGNETIC WAVES
36. DIRECTED ELECTROMAGNETIC WAVES
37. ELECTROMAGNETIC HORNS AND RESONATORS
38. MOTION OF A VISCOUS FLUID
38. GENERALIZED FUNCTIONS +
REFERENCES
