Invitation to classical analysis
 Author/Creator
 Duren, Peter L., 1935
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xiii, 392 p. : ill ; 26 cm.
 Series

Pure and applied undergraduate texts ; 17.
Sally series (Providence, R.I.)
Access
Available online

Stacks

Unknown
QA320 .D87 2012

Unknown
QA320 .D87 2012
More options
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for secondsemester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics..
(source: Nielsen Book Data)
Subjects
 Subject
 Functional analysis > Textbooks.
 Real functions  Instructional exposition (textbooks, tutorial papers, etc.)
 Special functions (33XX deals with the properties of functions as functions)  Instructional exposition (textbooks, tutorial papers, etc.)
 Ordinary differential equations  Instructional exposition (textbooks, tutorial papers, etc.)
 Sequences, series, summability  Instructional exposition (textbooks, tutorial papers, etc.)
 Approximations and expansions  Instructional exposition (textbooks, tutorial papers, etc.)
 Harmonic analysis on Euclidean spaces  Instructional exposition (textbooks, tutorial papers, etc.)
 Number theory  Instructional exposition (textbooks, tutorial papers, etc.)
 Number theory  Sequences and sets  Bernoulli and Euler numbers and polynomials.
 Sequences, series, summability  Inversion theorems  Tauberian theorems, general.
Bibliographic information
 Publication date
 2012
 Responsibility
 Peter Duren.
 Series
 Pure and applied undergraduate texts ; v. 17
 The Sally series
 ISBN
 9780821869321 (alk. paper)
 0821869329 (alk. paper)