Abstract Methods in Partial Differential Equations (Dover Books on Mathematics) - Softcover

Carroll, Robert W.

Softcover

ISBN 10: 0486488357 ISBN 13: 9780486488356

Publisher: Dover Publications, 2012

Synopsis

This self-contained text is directed to graduate students with some previous exposure to classical partial differential equations. Readers can attain a quick familiarity with various abstract points of view in partial differential equations, allowing them to read the literature and begin thesis work. The author's detailed presentation requires no prior knowledge of many mathematical subjects and illustrates the methods' applicability to the solution of interesting differential problems.
The treatment emphasizes existence-uniqueness theory as a topic in functional analysis and examines abstract evolution equations and ordinary differential equations with operator coefficients. A concluding chapter on global analysis develops some basic geometrical ideas essential to index theory, overdetermined systems, and related areas. In addition to exercises for self-study, the text features a thorough bibliography. Appendixes cover topology and fixed-point theory in addition to Banach algebras, analytic functional calculus, fractional powers of operators, and interpolation theory.

About this title

About the Author

Robert W. Carroll is Professor of Mathematics, University of Illinois at Urbana-Champagne, and the author of a dozen books on mathematics and mathematical physics. His recent publications include On the Emergence Theme of Physics (World Scientific, 2010), Fluctuations, Information, Gravity and the Quantum Potential (Springer, 2006), and Calculus Revisited (Kluwer, 2003).

Edition details

• Publisher: Dover Publications
• Publication date: 2012
• Language: English
• ISBN 10: 0486488357
• ISBN 13: 9780486488356
• Binding: Paperback
• Number of pages: 384