Description
Book SynopsisA Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The bookâs material has been extensively classroom tested in the authorâs two-semester undergraduate course on real analysis at The George Washington University.
The first part of the text presents the calculus of functions of one variable. This part covers traditional topics, such as sequences, continuity, differentiability, Riemann integrability, numerical series, and the convergence of sequences and series of functions. It also includes optional sections on Stirlingâs formula, functions of bounded variation, RiemannâStieltjes integration, and other topics.
The second part focuses on functions of several variables. It introduces the topological ideas (such as compact and connected sets) needed to describe analytical properties of multivariable functions. This part also discusses differentiability and inte
Trade Review
"… intended for a first course in real analysis. … It could also be used to support an advanced calculus course. … The approach is theoretical and the writing rigorously mathematical. There are numerous exercises. … If a library needs to add to its collection in this area, this book would be a good choice. Summing up: Recommended. Upper-division undergraduates and graduate students."
—D. Z. Spicer, University System of Maryland, USA for CHOICE, October 2015
"The book is carefully written, with rigorous proofs and a sufficient number of solved and unsolved problems. It is suitable for most university courses in mathematical analysis."
—Zentralblatt MATH 1317
Table of ContentsFunctions of One Variable: The Real Number System. Numerical Sequences. Limits and Continuity on R. Differentiation on R. Riemann Integration on R. Numerical Infinite Series. Sequences and Series of Functions. Functions of Several Variables: Metric Spaces. Differentiation on Rn. Lebesgue Measure on Rn. Lebesgue Integration on Rn. Curves and Surfaces in Rn. Integration on Surfaces. Appendices. Bibliography. Index.
