Methods of Mathematical Physics

Classical and Modern

Alexey N. Karapetyants, Vladislav V. Kravchenko (Autoren)

Buch | Hardcover

XI, 405 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-17844-3 (ISBN)

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This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses.
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
Themenwelt	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