The Way of Analysis, Revised Edition

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.
Robert S. Strichartz, Cornell UniversityReceived 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 recentlyhis have been concentrating on a theory of differential equationson 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 thathe 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.