Partial Differential Equations through Examples and Exercises by E. PapPartial Differential Equations through Examples and Exercises by E. Pap

Partial Differential Equations through Examples and Exercises

byE. Pap, Arpad Takaci, Djurdjica Takaci

Paperback | October 11, 2012

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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.
Title:Partial Differential Equations through Examples and ExercisesFormat:PaperbackDimensions:404 pagesPublished:October 11, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401063494

ISBN - 13:9789401063494


Table of Contents

Preface. List of Symbols. 1. Introduction. 2. First Order PDEs. 3. Classification of the Second Order PDEs. 4. Hyperbolic Equations. 5. Elliptic Equations. 6. Parabolic Equations. 7. Numerical Methods. 8. Lebesgue's Integral, Fourier Transform. 9. Generalized Derivative and Sobolev Spaces. 10. Some Elements from Functional Analysis. 11. Functional Analysis Methods in PDEs. 12. Distributions in the Theory of PDEs. Bibliography. Index.