eBook - PDF
Partial Differential Equations of Mathematical Physics
Adiwes International Series in Mathematics
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- 438 pages
- English
- PDF
- Only available on web
eBook - PDF
Partial Differential Equations of Mathematical Physics
Adiwes International Series in Mathematics
Book details
Table of contents
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About This Book
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied mathematics, and researchers will benefit greatly from this book.
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Table of contents
- Front Cover
- Partial Differential Equations of Mathematical Physics
- Copyright Page
- Table of Contents
- TRANSLATION EDITOR'S PREFACE
- LECTURE 1. DERIVATION OF THE FUNDAMENTAL EQUATIONS
- 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
- 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
- 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 EQUATION 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 EQUATIONS WITH REAL, SYMMETRIC KERNELS
- LECTURE 25. THE BILINEAR FORMULA AND THE HILBERTS-CHMIDT THEOREM
- LECTURE 26. THE INHOMOGENEOUS INTEGRAL EQUATION WITH A SYMMETRIC KERNEL
- LECTURE 27. VIBRATIONS OF A RECTANGULAR PARALLELEPIPED
- LECTURE 28. LAPLACE'S EQUATION 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