Generalized Functions And Partial Differential Equations (Dover Books On Mathematics)

Generalized Functions And Partial Differential Equations (Dover Books On Mathematics)

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This Selfcontained Treatment Develops The Theory Of Generalized Functions And The Theory Of Distributions, And It Systematically Applies Them To Solving A Variety Of Problems In Partial Differential Equations. A Major Portion Of The Text Is Based On Material Included In The Books Of L. Schwartz, Who Developed The Theory Of Distributions, And In The Books Of Gelfand And Shilov, Who Deal With Generalized Functions Of Any Class And Their Use In Solving The Cauchy Problem. In Addition, The Author Provides Applications Developed Through His Own Research.Geared Toward Upperlevel Undergraduates And Graduate Students, The Text Assumes A Sound Knowledge Of Both Real And Complex Variables. Familiarity With The Basic Theory Of Functional Analysis, Especially Normed Spaces, Is Helpful But Not Necessary. An Introductory Chapter Features Helpful Background On Topological Spaces. Applications To Partial Differential Equations Include A Treatment Of The Cauchy Problem, The Goursat Problem, Fundamental Solutions, Existence And Differentiality Of Solutions Of Equations With Constants, Coefficients, And Related Topics. Supplementary Materials Include Endofchapter Problems, Bibliographical Remarks, And A Bibliography.

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Frequently Asked Questions

  • Q: What topics are covered in 'Generalized Functions and Partial Differential Equations'? A: The book covers the theory of generalized functions, distributions, applications in solving partial differential equations, the Cauchy problem, the Goursat problem, fundamental solutions, and existence and differentiality of solutions.
  • Q: Who is the author of this book? A: The author of 'Generalized Functions and Partial Differential Equations' is Avner Friedman.
  • Q: What is the intended audience for this book? A: This book is geared toward upper-level undergraduates and graduate students with a sound knowledge of real and complex variables.
  • Q: Does this book include end-of-chapter problems? A: Yes, the book includes end-of-chapter problems, bibliographical remarks, and a bibliography for further reading.
  • Q: What is the binding type of this book? A: The book is available in paperback binding.
  • Q: When was this book published? A: The book was published on December 10, 2005.
  • Q: Is there a specific background needed to understand this book? A: While familiarity with functional analysis and normed spaces is helpful, it is not necessary. An introductory chapter provides background on topological spaces.
  • Q: How many pages does this book contain? A: The book contains a total of 368 pages.
  • Q: What edition of the book is available? A: This book is an illustrated edition.
  • Q: Are there applications based on research in this book? A: Yes, the author includes applications developed through his own research in the field.