Preface | |
Introduction | |
Some examples of equations of mathematical physics | |
Classification of second-order partial differential equations | |
Formulation of problems of mathematical physics | |
Hyperbolic partial differential equations | |
The Cauchy problem for the equation of the vibrating string | |
The mixed problem for the equation of the vibrating string | |
The Goursat problem | |
The Riemann method | |
The Cauchy problem for the wave equation | |
An inverse problem for the wave equation | |
Inverse spectral problems | |
Inverse scattering on the line | |
The Cauchy problem for the Korteweg-de Vries equation | |
Parabolic partial differential equations | |
The mixed problem for the heat equation | |
The Cauchy problem for the heat equation | |
Elliptic partial differential equations | |
Harmonic functions and their properties | |
Dirichlet and Neumann problems | |
The Green's function method | |
The method of upper and lower functions | |
The Dirichlet problem for the Poisson equation | |
The method of integral equations | |
The variational method | |
The Cauchy-Kowalevsky theorem | |
Exercises | |
Classification of second-order partial differential equations | |
Hyperbolic partial differential equations | |
Parabolic partial differential equations | |
Elliptic partial differential equations | |
Answers and hints | |
References | |
Index | |
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