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Techniques of Functional Analysis for Differential and Integral Equations
An accessible introduction to the functional analysis techniques increasingly used across modeling, analysis and scientific computation applications
Paul Sacks (Author)
9780128114261
Paperback / softback, published 25 April 2017
320 pages
22.9 x 15.1 x 2.1 cm, 0.54 kg
"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
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.
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
Subject Areas: Applied mathematics [PBW]
