Generalized Functions and Partial Differential Equations (Dover Books on Mathema 1.4tics) - Softcover

Friedman, Avner; Krieger, C. Cecilia

Softcover

ISBN 10: 0486446107 ISBN 13: 9780486446103

Publisher: Dover Publications Inc., 2006

Synopsis

This self-contained 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 upper-level 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 end-of-chapter problems, bibliographical remarks, and a bibliography.

About this title

About the Author

Baltazar Aguda is currently associate professor of Genetics & Genomics at the Boston University
School of Medicine. He holds joint appointments in Biomedical Engineering, in the Bioinformatics
& Systems Biology program at Boston University, and a membership in the Center for Biodynamics
in the same university. Recently, he was appointed member of the National Science
Foundation's (NSF, USA) research proposal review panel in molecular & cellular biosciences
(2004-7). He was a visiting faculty at the Mathematical Biosciences Institute at Ohio State University
(2003), at the Weizmann Institute of Science in Israel (2000), and a visiting associate at
the California Institute of Technology (2000-2001). Dr. Aguda obtained his PhD in Chemistry
(Chemical Physics Program) from the University of Alberta in Canada (1986), and was a tenured
faculty member of the Department of Chemistry & Biochemistry at Laurentian University in
Canada (1994-2002) before moving to Boston. Avner Friedman is a Distinguished Professor of Mathematics and Physical Sciences at
the Ohio State University, where he also serves as the Director of the Mathematical Biosciences
Institute. He received his Ph.D. degree in 1956 from the Hebrew University.
He was Professor of Mathematics at Northwestern University (1962-1985), and a Duncan
Distinguished Professor of Mathematics at Purdue University (1985-1987).

Edition details

• Publisher: Dover Publications Inc.
• Publication date: 2006
• Language: English
• ISBN 10: 0486446107
• ISBN 13: 9780486446103
• Binding: Paperback
• Number of pages: 352