The Way of Analysis

by Robert S. Strichartz

The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.

Genres: Mathematics, Textbooks, Science, Computers, Calculus

739 pages, Paperback

First published April 1, 1995

About the author

Received his Ph.D. (1966) from Princeton University and is currently teaches mathematics at Cornell University. Research interests cover a wide range of topics in analysis, including harmonic analysis, partial differential equations, analysis on Lie groups and manifolds, integral geometry, wavelets and fractals. Robert's early work using methods of harmonic analysis to obtain fundamental estimates for linear wave equations has played an important role in recent developments in the theory of nonlinear wave equations. His work on fractals began with the study of self-similar measures and their Fourier transforms. More recently his have been concentrating on a theory of differential equations on fractals created by Jun Kigami. Much of this work has been done in collaboration with undergraduate students through a summer Research Experiences for Undergraduates (REU) program at Cornell that he directs. Robert wrote an expository article Analysis On Fractals, Notices of the AMS 46 (1999), 1199 - 1208 explaining the basic ideas in this subject area and the connections with other areas of mathematics.

Reviews

[Deniz Yuret · Rating 4 out of 5]

http://denizyuret.blogspot.com/2005/0...

[dead letter office · Rating 2 out of 5]

this book is a decent read and a horrible reference. i had the feeling i was being taught analysis by someone's weird hippie uncle (remember dharma's father from dharma and greg?)

[Joe Cole · Rating 5 out of 5]

I liked the development of Reals as equivalence classes of sequences of rationals it makes so much sense to do it that way. Rudin in his infinite wisdom chose to develop the real numbers as a field/dedikind cuts, go figure.

[Mathilda · Rating 1 out of 5]

This is an absolutely horrible introductory book to real analysis. It reads like a novel with no clear separation between motivation, proofs and explanations. It makes learning analysis a pain in the ass especially when you try to learn it through Zoom University during COVID from a professor whose handwriting is scribbles. 0 out of 10 recommend