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- 000 02381cam a2200265 a 4500
- 008 111205s2012 riua b 001 0 eng
- 020 __ |a 9780821869321 (alk. paper)
- 020 __ |a 0821869329 (alk. paper)
- 040 __ |a DLC |b eng |c DLC |d YDX |d YDXCP |d BTCTA |d OCLCO |d BWX |d DLC
- 050 00 |a QA320 |b .D87 2012
- 100 1_ |a Duren, Peter L., |d 1935-
- 245 10 |a Invitation to classical analysis / |c Peter Duren.
- 260 __ |a Providence, R.I. : |b American Mathematical Society, |c 2012.
- 300 __ |a xiii, 392 p. : |b ill. ; |c 26 cm.
- 490 1_ |a Pure and applied undergraduate texts ; |v v. 17
- 490 1_ |a The Sally series
- 504 __ |a Includes bibliographical references and index.
- 520 __ |a 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 second-semester 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. --Publisher description.
- 650 _0 |a Functional analysis |v Textbooks.