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Cover: 9783031178474 | Methods of Mathematical Physics | Classical and Modern | Taschenbuch
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Methods of Mathematical Physics
Classical and Modern
Taschenbuch von Vladislav V. Kravchenko (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Theoretische Physik
Genre: Mathematik, Medizin, Naturwissenschaften, Physik, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xi
405 S.
34 s/w Illustr.
17 farbige Illustr.
405 p. 51 illus.
17 illus. in color.
ISBN-13: 9783031178474
ISBN-10: 3031178475
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Kravchenko, Vladislav V.
Karapetyants, Alexey N.
Auflage: 1st edition 2022
Hersteller: Springer Nature Switzerland
Springer International Publishing
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 235 x 155 x 23 mm
Von/Mit: Vladislav V. Kravchenko (u. a.)
Erscheinungsdatum: 18.11.2023
Gewicht: 0,633 kg
Artikel-ID: 127901602
Über den Autor

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Theoretische Physik
Genre: Mathematik, Medizin, Naturwissenschaften, Physik, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xi
405 S.
34 s/w Illustr.
17 farbige Illustr.
405 p. 51 illus.
17 illus. in color.
ISBN-13: 9783031178474
ISBN-10: 3031178475
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Kravchenko, Vladislav V.
Karapetyants, Alexey N.
Auflage: 1st edition 2022
Hersteller: Springer Nature Switzerland
Springer International Publishing
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 235 x 155 x 23 mm
Von/Mit: Vladislav V. Kravchenko (u. a.)
Erscheinungsdatum: 18.11.2023
Gewicht: 0,633 kg
Artikel-ID: 127901602
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