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A short introduction to partial differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A short introduction to partial differential equations/ by Arian Novruzi.
作者:	Novruzi, Arian.
出版者:	Cham :Springer Nature Switzerland : : 2023.,
面頁冊數:	xi, 219 p. :ill. (some col.), digital ;24 cm.
內容註:	1 Notations and review -- 2 Partial differential equations -- 3 First order PDEs. Classical and weak solutions -- 4 Second-order linear elliptic PDEs. maximum principle and classical solutions - 5 Distributions -- 6 Sobolev spaces -- 7 Second order linear elliptic PDEs. Weak solutions -- 8 Second order parabolic and hyperbolic PDEs -- 9 Annex.
Contained By:	Springer Nature eBook
標題:	Differential equations, Partial. -
電子資源:	https://doi.org/10.1007/978-3-031-39524-6
ISBN:	9783031395246

A short introduction to partial differential equations
Novruzi, Arian.

A short introduction to partial differential equations[electronic resource] /by Arian Novruzi. - Cham :Springer Nature Switzerland :2023. - xi, 219 p. :ill. (some col.), digital ;24 cm. - CMS/CAIMS books in mathematics,v. 112730-6518 ;. - CMS/CAIMS books in mathematics ;v. 11..

1 Notations and review -- 2 Partial differential equations -- 3 First order PDEs. Classical and weak solutions -- 4 Second-order linear elliptic PDEs. maximum principle and classical solutions - 5 Distributions -- 6 Sobolev spaces -- 7 Second order linear elliptic PDEs. Weak solutions -- 8 Second order parabolic and hyperbolic PDEs -- 9 Annex.

This book provides a short introduction to partial differential equations (PDEs) It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods. The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces. The book ends with an appendix chapter, which complements the previous chapters with proofs, examples and remarks. This book can be used for an intense one-semester, or normal two-semester, PDE course. The reader is expected to have knowledge of linear algebra and of differential equations, a good background in real and complex calculus and a modest background in analysis and topology. The book has many examples, which help to better understand the concepts, highlight the key ideas and emphasize the sharpness of results, as well as a section of problems at the end of each chapter.

ISBN: 9783031395246

Standard No.: 10.1007/978-3-031-39524-6doiSubjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

A short introduction to partial differential equations
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520 $a This book provides a short introduction to partial differential equations (PDEs) It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods. The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces. The book ends with an appendix chapter, which complements the previous chapters with proofs, examples and remarks. This book can be used for an intense one-semester, or normal two-semester, PDE course. The reader is expected to have knowledge of linear algebra and of differential equations, a good background in real and complex calculus and a modest background in analysis and topology. The book has many examples, which help to better understand the concepts, highlight the key ideas and emphasize the sharpness of results, as well as a section of problems at the end of each chapter.
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