Partial Differential Equations of Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

S. L. Sobolev, I. N. Sneddon, S. Ulam, M. Stark

• Publisher: Pergamon
• Year: 2016
• Print ISBN:
  9780080137209
• eBook ISBN:
  9781483181363
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Pure and Applied Mathematics, Volume 56: Partial Differential Equations of Mathematical Physics provides a collection of lectures related to the partial differentiation of mathematical physics. This book covers a variety of topics, including waves, heat conduction, hydrodynamics, and other physical problems. Comprised of 30 lectures, this book begins with an overview of the theory of the equations of mathematical physics that has its object the study of the integral, differential, and functional equations describing various natural phenomena. This text then examines the linear equations of the second order with real coefficients. Other lectures consider the Lebesgue–Fubini theorem on the possibility of changing the order of integration in a multiple integral. This book discusses as well the Dirichlet problem and the Neumann problem for domains other than a sphere or half-space. The final lecture deals with the properties of spherical functions. This book is a valuable resource for mathematicians.

Table of contents

• Front Cover
• Partial Differential Equations of Mathematical Physics
• Copyright Page
• Table of Contents
• TRANSLATON EDITOR'S PREFACE
• AUTHOR'S PREFACES TO THE FIRST AND THIRD EDITIONS
• LECTURE 1. DERTVATON OF THE FUNDAMENTAL EQUATONS
• LECTURE 2. THE FORMULATION OF PROBLEMS OF MATHEMATICAL PHYSICS HADAMARD'S EXAMPLE
• LECTURE 3. THE CLASSIFICATION OF LINEAR EQUATIONS OF THE SECOND ORDER
• LECTURE 4. THE EQUATION FOR A VIBRATING STRING AND ITS SOLUTION BY D'ALEMBERT'S METHOD
• LECTURE 5. RIEMANN'S METHOD
• LECTURE 6. MULTIPLE INTEGRALS: LEBESGUE INTEGRATION
• LECTURE 7. INTEGRALS DEPENDENT ON A PARAMETER
• LECTURE 8. THE EQUATION OF HEAT CONDUCTION
• LECTURE 9. LAPLACE'S EQUATION AND POISSON'S EQUATION
• LECTURE 10. SOME GENERAL CONSEQUENCES OF GREEN'S FORMULA
• LECTURE 11. POISSON'S EQUATION IN AN UNBOUNDED MEDIUM. NEWTONIAN POTENTIAL
• LECTURE 12. THE SOLUTION OF THE DIRICHLET PROBLEM FOR A SPHERE
• LECTURE 13. THE DIRICHLET PROBLEM AND THE NEUMANN PROBLEM FOR A HALF-SPACE
• LECTURE 14. THE WAVE EQUATION AND THE RETARDED POTENTIAL
• LECTURE 15. PROPERTIES OF THE POTENTIALS OF SINGLE AND DOUBLE LAYERS
• LECTURE 16. REDUCTION OF THE DIRICHLET PROBLEM AND THE NEUMANN PROBLEM TO INTEGRAL EQUATIONS
• LECTURE 17. LAPLACE'S EQUATON AND POISSON'S EQUATION IN A PLANE
• LECTURE 18. THE THEORY OF INTEGRAL EQUATIONS
• LECTURE 19. APPLICATION OF THE THEORY OF FREDHOLM EQUATIONS TO THE SOLUTION OF THE DIRICHLET AND NEUMANN PROBLEMS
• LECTURE 20. GREEN'S FUNCTION
• LECTURE 21. GREEN'S FUNCTION FOR THE LAPLACE OPERATOR
• LECTURE 22. CORRECTNESS OF FORMULATION OF THE BOUNDARY-VALUE PROBLEMS OF MATHEMATICAL PHYSICS
• LECTURE 23. FOURIER'S METHOD
• LECTURE 24. INTEGRAL EQUATONS WTIH REAL, SYMMETRIC KERNELS
• LECTURE 25. THE BILINEAR FORMULA AND THE HILBERT–SCHMIDT THEOREM
• LECTURE 26. THE INHOMOGENEOUS INTEGRAL EQUATION WTTH A SYMMETRIC KERNEL
• LECTURE 27. VIBRATIONS OF A RECTANGULAR PARALLELEPIPED
• LECTURE 28. LAPLACE'S EQUATON IN CURVILINEAR COORDINATES. EXAMPLES OF THE USE OF FOURIER'S METHOD
• LECTURE 29. HARMONIC POLYNOMIALS AND SPHERICAL FUNCTIONS
• LECTURE 30. SOME ELEMENTARY PROPERTIES OF SPHERICAL FUNCTIONS
• INDEX
• OTHER VOLUMES IN THIS SERIES