معادلات دیفرانسیل پاره‌ای فیزیک ریاضی ۲۰۱۴
Partial Differential Equations of Mathematical Physics 2014

1. Front Cover

2. Partial Differential Equations of Mathematical Physics

3. Copyright Page

4. Table of Contents

5. TRANSLATION EDITOR’S PREFACE

6. LECTURE 1. DERIVATION OF THE FUNDAMENTAL EQUATIONS

7. LECTURE 2. THE FORMULATION OF PROBLEMS OF MATHEMATICAL PHYSICS. HADAMARD’S EXAMPLE

8. LECTURE 3. THE CLASSIFICATION OF LINEAR EQUATIONS OF THE SECOND ORDER

9. LECTURE 4. THE EQUATION FOR A VIBRATING STRING AND ITS SOLUTION BY D’ALEMBERT’S METHOD

10. LECTURE 5. RIEMANN’S METHOD

11. LECTURE 6. MULTIPLE INTEGRALS: LEBESGUE INTEGRATION

12. LECTURE 7. INTEGRALS DEPENDENT ON A PARAMETER

13. LECTURE 8. THE EQUATION OF HEAT CONDUCTION

14. LECTURE 9. LAPLACE’S EQUATION AND POISSON’S EQUATION

1. The Theorem of the Maximum

2. The Principal Solution. Green’s Formula

3. The Potential due to a Volume, to a Single Layer, and to a Double Layer

18. LECTURE 10. SOME GENERAL CONSEQUENCES OF GREEN’S FORMULA

19. LECTURE 11. POISSON’S EQUATION IN AN UNBOUNDED MEDIUM. NEWTONIAN POTENTIAL

20. LECTURE 12. THE SOLUTION OF THE DIRICHLET PROBLEM FOR A SPHERE

21. LECTURE 13. THE DIRICHLET PROBLEM AND THE NEUMANN PROBLEM FOR A HALF-SPACE

22. LECTURE 14. THE WAVE EQUATION AND THE RETARDED POTENTIAL

23. LECTURE 15. PROPERTIES OF THE POTENTIALS OF SINGLE AND DOUBLE LAYERS

24. LECTURE 16. REDUCTION OF THE DIRICHLET PROBLEM AND THE NEUMANN PROBLEM TO INTEGRAL EQUATIONS

25. LECTURE 17. LAPLACE’S EQUATION AND POISSON’S EQUATION IN A PLANE

26. LECTURE 18. THE THEORY OF INTEGRAL EQUATIONS

27. LECTURE 19. APPLICATION OF THE THEORY OF FREDHOLM EQUATIONS TO THE SOLUTION OF THE DIRICHLET AND NEUMANN PROBLEMS

28. LECTURE 20. GREEN’S FUNCTION

29. LECTURE 21. GREEN’S FUNCTION FOR THE LAPLACE OPERATOR

30. LECTURE 22. CORRECTNESS OF FORMULATION OF THE BOUNDARY-VALUE PROBLEMS OF MATHEMATICAL PHYSICS

31. LECTURE 23. FOURIER’S METHOD

32. LECTURE 24. INTEGRAL EQUATIONS WITH REAL, SYMMETRIC KERNELS

33. LECTURE 25. THE BILINEAR FORMULA AND THE HILBERTS-CHMIDT THEOREM

34. LECTURE 26. THE INHOMOGENEOUS INTEGRAL EQUATION WITH A SYMMETRIC KERNEL

35. LECTURE 27. VIBRATIONS OF A RECTANGULAR PARALLELEPIPED

36. LECTURE 28. LAPLACE’S EQUATION IN CURVILINEAR COORDINATES. EXAMPLES OF THE USE OF FOURIER’S METHOD

37. LECTURE 29. HARMONIC POLYNOMIALS AND SPHERICAL FUNCTIONS

38. LECTURE 30. SOME ELEMENTARY PROPERTIES OF SPHERICAL FUNCTIONS

39. INDEX