A Course in Real Analysis

ISBN-13: 9781482219272 / Angielski / Twarda / 2015 / 616 str.

Hugo D. Junghenn

Opis

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 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 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 (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 analysis-based courses."

Spis treści

Functions 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 R_n. Lebesgue Measure on R_n. Lebesgue Integration on R_n. Curves and Surfaces in R_n. Integration on Surfaces. Appendices. Bibliography. Index.

O autorze

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.