A First Look at Numerical Functional Analysis

by W.W. Sawyer

Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis.
Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence of an iteration, and Rall's ideas of polynomial and quadratic operators. Numerous examples appear throughout the text.

Genres: Mathematics

208 pages, Paperback

First published July 13, 1978

About the author

Walter Warwick Sawyer (or W.W. Sawyer) was a mathematician, mathematics educator and author, who taught on several continents.
https://en.wikipedia.org/wiki/Walter_...

Reviews

[Kyle · Rating 5 out of 5]

This is a wonderful book for getting you to understand why functional analysis is extremely useful for numerical calculations. It is also just well written, with good exercises that will teach you how to think about solving these types of problems. Sawyer does an excellent job of introducing and explaining concepts, esp. by using analogies with lower dimensions to the harder-to-visualize large or infinite dimension cases.

If you have an interest in functional analysis, this book is a great introduction. I especially like the Newton-Raphson explanation for finding functions that solve differential (or integral) equations.