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Equations of mathematical physicsgeneralized functions and historical notes /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Equations of mathematical physicsby A. S. Demidov.
Reminder of title:	generalized functions and historical notes /
Author:	Demidov, A. S.
Published:	Cham :Springer International Publishing :2023.
Description:	xv, 248 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical physics.
Online resource:	https://doi.org/10.1007/978-3-031-30358-6
ISBN:	9783031303586$q(electronic bk.)

Equations of mathematical physicsgeneralized functions and historical notes /
Demidov, A. S.

Equations of mathematical physicsgeneralized functions and historical notes /[electronic resource] :by A. S. Demidov. - Cham :Springer International Publishing :2023. - xv, 248 p. :ill., digital ;24 cm.

This concise volume presents an overview of equations of mathematical physics and generalized functions. While intended for advanced readers, the accessible introduction and text structure allows beginners to study at their own pace as the material gradually increases in difficulty. The text introduces the concept of generalized Sobolev functions and L. Schwartz distributions briefly in the opening section, gradually approaching a more in-depth study of the "generalized" differential equation (also known as integral equality) In contrast to the traditional presentation of generalized Sobolev functions and L. Schwartz distributions, this volume derives the topology from two natural requirements (which are equivalent to it) The text applies the same approach to the theory of the canonical Maslov operator. It also features illustrative drawings and helpful supplementary reading in the footnotes concerning historical and bibliographic information related to the subject of the book. Additionally, the book devotes a special chapter to the application of the theory of pseudodifferential operators and Sobolev spaces to the inverse magneto/electroencephalography problem. Explicit numerically realizable formulas related to the Cauchy problem for elliptic equations (including quasilinear ones) and also to the Poincaré--Steklov operators are presented. The book is completed by three additions, which were written by famous mathematicians Yu. V. Egorov, A. B. Antonevich, and S. N. Samborski.

ISBN: 9783031303586$q(electronic bk.)

Standard No.: 10.1007/978-3-031-30358-6doiSubjects--Topical Terms:

190854
Mathematical physics.

LC Class. No.: QC20 / .D46 2023

Dewey Class. No.: 530.15

Equations of mathematical physicsgeneralized functions and historical notes /
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520 $a This concise volume presents an overview of equations of mathematical physics and generalized functions. While intended for advanced readers, the accessible introduction and text structure allows beginners to study at their own pace as the material gradually increases in difficulty. The text introduces the concept of generalized Sobolev functions and L. Schwartz distributions briefly in the opening section, gradually approaching a more in-depth study of the "generalized" differential equation (also known as integral equality) In contrast to the traditional presentation of generalized Sobolev functions and L. Schwartz distributions, this volume derives the topology from two natural requirements (which are equivalent to it) The text applies the same approach to the theory of the canonical Maslov operator. It also features illustrative drawings and helpful supplementary reading in the footnotes concerning historical and bibliographic information related to the subject of the book. Additionally, the book devotes a special chapter to the application of the theory of pseudodifferential operators and Sobolev spaces to the inverse magneto/electroencephalography problem. Explicit numerically realizable formulas related to the Cauchy problem for elliptic equations (including quasilinear ones) and also to the Poincaré--Steklov operators are presented. The book is completed by three additions, which were written by famous mathematicians Yu. V. Egorov, A. B. Antonevich, and S. N. Samborski.
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