Techniques of Functional Analysis for Differential and Integral Equations

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 areasEstablishes the advanced background needed for sophisticated literature review and research in differential equations and integral equationsSuitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

1. Introduction 2. Preliminaries 3. Vector spaces 4. Metric spaces 5. Normed linear spaces and Banach spaces 6. Inner product spaces and Hilbert spaces 7. Distributions 8. Fourier analysis and distributions 9. Distributions and Differential Equations 10. Linear operators 11. Unbounded operators 12. Spectrum of an operator 13. Compact Operators 14. Spectra and Green's functions for differential operators 15. Further study of integral equations 16. Variational methods 17. Weak solutions of partial differential equations 18. Appendices