Textbooks in Mathematics Functional Analysis for the Applied Mathematician

This self-contained volume provides a rigorous introduction to functional analysis and its applications. It is accessible to graduate and advanced undergraduate students with a solid background in undergraduate mathematics and an appreciation of mathematical rigor. 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