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Partial differential equations for mathematical physicists

Author: Bijan Kumar Bagchi
Publisher: Boca Raton, FL : CRC Press, [2020] ©2020
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Partial Differential Equations for Mathematical Physicistsis intended for graduate students, researchers of theoretical physics and applied mathematics, and professionals who want to take a course in partial differential equations. This book offers the essentials of the subject with theprerequisite being only an elementary knowledge of introductory calculus, ordinary differential equations, and certain aspects of  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bagchi, Bijan Kumar.
Partial differential equations for mathematical physicists.
Boca Raton, FL : CRC Press, [2020]
(OCoLC)1091239302
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Bijan Kumar Bagchi
ISBN: 9780429276477 0429276478 9781000300819 1000300811 9781000264876 1000264874 9781000228939 1000228932
OCLC Number: 1107493769
Notes: "A Chapman & Hall book."
Description: 1 online resource (xiii, 224 pages) : illustrations
Contents: Preliminary concepts and background material --
Basic properties of second order linear PDEs --
PDE: elliptic form --
PDE: hyperbolic form --
PDE: parabolic form --
Solving PDEs by integral transform method
Responsibility: Bijan Kumar Bagchi

Abstract:

Partial Differential Equations for Mathematical Physicistsis intended for graduate students, researchers of theoretical physics and applied mathematics, and professionals who want to take a course in partial differential equations. This book offers the essentials of the subject with theprerequisite being only an elementary knowledge of introductory calculus, ordinary differential equations, and certain aspects of classical mechanics. We have stressed more the methodologies of partial differential equations and how they can be implemented as tools for extracting their solutions rather thandwelling on the foundational aspects. After covering some basic material, the book proceeds to focus mostly on the three main types of second order linear equations, namely those belonging to the elliptic, hyperbolic, and parabolic classes. For such equations a detailed treatment is given of the derivation of Green's functions, and of the roles of characteristics and techniques required in handling the solutions with the expected amount of rigor. In this regard we have discussed at length the method of separation variables, application of Green's function technique, and employment of Fourier and Laplace's transforms. Also collected in the appendices are some useful results from the Dirac delta function, Fourier transform, and Laplace transform meant to be used as supplementary materials to the text. A good number of problems is worked out andan equallylarge number of exercises has been appended at the end of each chapter keeping in mind the needs of the students. It is expected that this book will provide a systematic and unitary coverage of the basics of partial differential equations. Key Features An adequate and substantive exposition of the subject. Covers a wide range of important topics. Maintainsmathematical rigor throughout. Organizes materials in a self-contained way with each chapter ending with a summary. Contains a large number of worked out problems

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