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Methods of mathematical physics = cl...

Karapetyants, Alexey N.

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Methods of mathematical physics = classical and modern /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Methods of mathematical physics/ by Alexey N. Karapetyants, Vladislav V. Kravchenko.
其他題名:	classical and modern /
作者:	Karapetyants, Alexey N.
其他作者:	Kravchenko, Vladislav V.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xi, 405 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Mathematical physics. -
電子資源:	https://doi.org/10.1007/978-3-031-17845-0
ISBN:	9783031178450

Methods of mathematical physics = classical and modern /
Karapetyants, Alexey N.

Methods of mathematical physicsclassical and modern /[electronic resource] :by Alexey N. Karapetyants, Vladislav V. Kravchenko. - Cham :Springer International Publishing :2022. - xi, 405 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783031178450

Standard No.: 10.1007/978-3-031-17845-0doiSubjects--Topical Terms:

516853
Mathematical physics.

LC Class. No.: QC20

Dewey Class. No.: 530.15

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505 0 $a 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.
520 $a 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.
650 0 $a Mathematical physics. $3 516853
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