Techniques of Functional Analysis for Differential and Integral Equations

ISBN-13: 9780128114261 / Angielski / Miękka / 2017 / 320 str.

Paul Sacks

Opis

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature.

• Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas
• Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations
• Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

Recenzje

"Globally, the reviewer very much likes the spirit and the scope of the book. The writing is lively, the material is diverse and maintains a strong unity." --Zentralblatt MATH 1375

"For readers with interest in the theory or application of differential equations, integral equations, optimization, or numerical analysis, Techniques of Functional Analysis for Differential and Integral Equations is a very valuable resource. I highly recommend this book to any such person. I also believe that the book can serve as a nice supplement to more abstract texts on functional analysis, helping one to see how the abstract theory influences thinking about other areas of mathematics."--MAA Reviews

Spis treści

1. Introduction2. Preliminaries3. Vector spaces4. Metric spaces5. Normed linear spaces and Banach spaces6. Inner product spaces and Hilbert spaces7. Distributions8. Fourier analysis and distributions9. Distributions and Differential Equations10. Linear operators11. Unbounded operators12. Spectrum of an operator13. Compact Operators14. Spectra and Green's functions for differential operators15. Further study of integral equations16. Variational methods17. Weak solutions of partial differential equations18. Appendices

O autorze

Professor Paul Sacks received his B.S. degree from Syracuse University and M.S. and Ph.D. degrees from the University of Wisconsin-Madison, all in Mathematics. Since 1981 he has been in the Mathematics department at Iowa State University, as Full Professor since 1990. He is particularly interested in partial differential equations and inverse problems. He is the author or co-author of more than 60 scientific articles and conference proceedings. For thirty years he has regularly taught courses in analysis, differential equations and methods of applied mathematics for mathematics graduate students.