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Full Description
Functional Analysis for the Applied Mathematician is a self-contained volume providing a rigorous introduction to functional analysis and its applications. Students from mathematics, science, engineering, and certain social science and interdisciplinary programs will benefit from the material. It is accessible to graduate and advanced undergraduate students with a solid background in undergraduate mathematics and an appreciation of mathematical rigor. Students are called upon to actively engage with the material, to the point of proving some of the basic results or their straightforward generalizations, both within the text and within the generous set of exercises.
Features:
Replete with exercises and examples
Suitable for graduate students and advanced undergraduates
Develops the basics of functional analysis, exploring the interplay between algebraic linear space theory and topology
Presents a variety of applications, often dealing with partial differential equations and their numerical approximation
Doubles as a reference book with an extensive index listing the concepts and results
Contents
1. Preliminaries. 2. Normed Linear Spaces and Banach Spaces. 3. Hilbert Spaces. 4. Spectral Theory and Compact Operators. 5. Distributions. 6. The Fourier Transform. 7. Sobolev Spaces. 8. Boundary Value Problems. 9. Differential Calculus in Banach Spaces. 10. The Calculus of Variations.
