Techniques of Functional Analysis for Differential and Integral Equations

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.

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