A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's twosemester 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 Stirling's formula, functions of bounded variation, RiemannStieltjes 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 integrability of multivariable functions and develops the theory of differential forms on surfaces in Rn. The third part consists of appendices on set theory and linear algebra as well as solutions to some of the exercises. A full solutions manual offers complete solutions to all exercises for qualifying instructors. With clear proofs, detailed examples, and numerous exercises, this textbook gives a thorough treatment of the subject. It progresses from single variable to multivariable functions, providing a logical development of material that will prepare students for more advanced analysisbased courses.
About Hugo D. Junghenn
Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics. His research interests include functional analysis, semigroups, and probability.Details Book
Author  :  Hugo D. Junghenn 
Publisher  :  Apple Academic Press Inc. 
Data Published  :  01 April 2015 
ISBN  :  1482219271 
EAN  :  9781482219272 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  613 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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