Methods of Mathematical Physics
Springer International Publishing (Verlag)
978-3-031-17844-3 (ISBN)
The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series.
Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.
Alexey N. Karapetyants is professor of the Institute of Mathematics, Mechanics and Computer Sciences and director of Regional Mathematical Center at the Southern Federal University, Rostov-on-Don, Russia. His research interests include operator theory, mathematical physics, harmonic analysis: real and complex variable methods, and functional analysis. Vladislav V. Kravchenko is a researcher in the Department of Mathematics of Center for Research and Advanced Studies of the National Polytechnic Institute, Campus Queretaro, Mexico. His research interests include mathematical physics, differential equations, complex and hypercomplex analysis, spectral theory, and inverse problems.
Introduction.- Classification of PDEs.- Models of mathematical physics.- Boundary value problems.- Cauchy problem for hyperbolic equations.- Fourier method for the wave equation.- Sturm-Liouville problems.- Boundary value problems for the heat equation.- Harmonic functions and their properties.- Boundary value problems for the Laplace equation.- Potential theory.- Elements of theory of integral equations.- Solution of boundary value problems for the Laplace equation.- Helmholtz equation.- Method of non-orthogonal series.- Bergman kernel approach.- Bibliography.- Index.
| Erscheinungsdatum | 19.11.2022 |
|---|---|
| Zusatzinfo | XI, 405 p. 51 illus., 17 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 748 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | Bergman kernel approach • boundary value problems • Elliptic PDEs • Fourier method wave equation • Fundamental solutions math physics • Harmonic Functions • Helmholtz equation • Integral equations • Mathematical Physics • Mathematical physics equations • Mathematical physics models • PDEs mathematical physics • Quantum PDEs • Sturm-Liouville problems |
| ISBN-10 | 3-031-17844-0 / 3031178440 |
| ISBN-13 | 978-3-031-17844-3 / 9783031178443 |
| Zustand | Neuware |
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