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|All Authors / Contributors:||
Peter L Duren
|Description:||xiii, 392 p. : ill. ; 26 cm.|
|Contents:||1. Basic principles --
2. Special sequences --
3. Power series and related topics --
4. Inequalities --
5. Infinite products --
6. Approximation by polynomials --
7. Tauberian theorems --
8. Fourier series --
9. The gamma function --
10. Two topics in number theory --
11. Bernoulli numbers --
12. The Cantor set --
13. Differential equations --
14. Elliptic integrals.
|Series Title:||Pure and applied undergraduate texts, 17.; Sally series (Providence, R.I.)|
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.
Retrieving notes about this item
- Functional analysis -- Textbooks.
- Real functions -- Instructional exposition (textbooks, tutorial papers, etc.).
- Special functions (33-XX 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.
- Functional analysis.