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Partial Differential Equations through Examples and Exercises : Texts in the Mathematical Sciences - E. Pap

Partial Differential Equations through Examples and Exercises

Texts in the Mathematical Sciences

Hardcover

Published: 31st October 1997
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The book Partial Differential Equations through Examples and Exercises has evolved from the lectures and exercises that the authors have given for more than fifteen years, mostly for mathematics, computer science, physics and chemistry students. By our best knowledge, the book is a first attempt to present the rather complex subject of partial differential equations (PDEs for short) through active reader-participation. Thus this book is a combination of theory and examples. In the theory of PDEs, on one hand, one has an interplay of several mathematical disciplines, including the theories of analytical functions, harmonic analysis, ODEs, topology and last, but not least, functional analysis, while on the other hand there are various methods, tools and approaches. In view of that, the exposition of new notions and methods in our book is "step by step". A minimal amount of expository theory is included at the beginning of each section Preliminaries with maximum emphasis placed on well selected examples and exercises capturing the essence of the material. Actually, we have divided the problems into two classes termed Examples and Exercises (often containing proofs of the statements from Preliminaries). The examples contain complete solutions, and also serve as a model for solving similar problems, given in the exercises. The readers are left to find the solution in the exercises; the answers, and occasionally, some hints, are still given. The book is implicitly divided in two parts, classical and abstract.

Preface
List of symbols
Introductionp. 1
First Order PDEsp. 17
Classification of the Second Order PDEsp. 49
Hyperbolic Equationsp. 71
Elliptic Equationsp. 143
Parabolic Equationsp. 183
Numerical Methodsp. 227
Lebesgue's Integral, Fourier Transformp. 249
Generalized Derivative and Sobolev Spacesp. 279
Some Elements from Functional Analysisp. 303
Functional Analysis Methods in PDEsp. 329
Distributions in the theory of PDEsp. 373
Bibliographyp. 397
Indexp. 401
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792347248
ISBN-10: 0792347242
Series: Texts in the Mathematical Sciences
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 404
Published: 31st October 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.69