Functional Analysis for the Applied Sciences

This advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications. Special attention is paid to creating appropriate frameworks towards solving significant problems involving differential and integral equations. Exercises at the end of each chapter help the reader to understand the richness of ideas and methods offered by Functional Analysis. Some of the exercises supplement theoretical material, while others relate to the real world. This textbook, with its friendly exposition, focuses on different problems in physics and other applied sciences and uniquely provides solutions to most of the exercises. The text is aimed toward graduate students and researchers in applied mathematics, physics, and neighboring fields of science.

1. Introduction.- 2. Metric Spaces.- 3. The Lebesgue Integral and Lp Spaces.- 4. Continuous Linear Operators and Functionals.- 5. Distributions, Sobolev Spaces.- 6. Hilbert Spaces.- 7. Adjoint, Symmetric and Self-adjoint Linear Operators.- 8. Eigenvalues and Eigenvectors.- 9. Semigroups of Linear Operators.- 10. Solving Linear Evolution Equations by the Fourier Method.- 11. Integral Equations.- 12. Answers to Exercises.- Bibliography.