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A Course in Real Analysis provides a rigorous treatment of the foundations of differ- ential and integral calculus at the advanced undergraduate level. The rst part of the text presents the calculus of functions of one variable. This part covers traditional topics, such as sequences, continuity, differentiability, Riemann inte- grability, numerical series, and the convergence of sequences and series of functions. It also includes optional sections on Stirling"s formula, functions of bounded variation,

Riemann-Stieltjes integration, and other topics.

The second part focuses on functions of several variables. It introduces the topological ideas needed (such as compact and connected sets) to describe analytical properties of multivariable functions. This part also discusses differentiability and integrability of multivariable functions and develops the theory of differential forms on surfaces in The third part consists of appendices on set theory and linear algebra as well as solu- tions to some of the exercises.

Features

Provides a detailed axiomatic account of the real number system

Develops the Lebesgue integral on

from the beginning Gives an in-depth description of the algebra and calculus of differential forms on surfaces in Offers an easy transition to the more advanced setting of differentiable manifolds by covering proofs of Stokes"s theorem and the divergence theorem at the concrete level of compact surfaces in Summarizes relevant results from elementary set theory and linear algebra Contains over 90 gures that illustrate the essential ideas behind a concept or proof Includes more than 1,600 exercises throughout the text, with selected solutions in an appendix With clear proofs, detailed examples, and numerous exercises, this book gives a thor- ough treatment of the subject. It progresses from single variable to multivariable func- tions, providing a logical development of material that will prepare readers for more advanced analysis-based studies. www.crcpress.com A

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HUGO D. JUNGHENN

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