A Course in Real Analysis

Inspect Bank For A Module in Practical Analysis

1. ISBN-10

   9781482219272
2. ISBN-13

   978-1482219272

3. A Module in Practical Analysis provides a strict treatment of the fundamentals of differential and integral calculus at the advanced undergraduate level. The material in the book has been extensively tested in the author’s two-semester undergraduate course on real analysis at The George Washington University.

   The initial portion of the text presents the calculus of functions of 1 variable. This part covers conventional 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 Stirling’s formula, functions of bounded variation, Riemann–Stieltjes integration, and other topics.

   The second portion focuses on functions of multiple variables. It introduces the topological concepts (such as compact and connected sets) required 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 Rn.

   The third portion includes appendices on set theory and linear algebra as well as solutions to some of the exercises. A complete solutions manual provides full solutions to all exercises for qualifying instructors.

   With clear proofs, detailed examples, and numerous exercises, this textbook offers a thorough treatment of the subject. It progresses from single variable to multivariable functions, providing a logical progression of material that will prepare students for more advanced research-based courses.