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Invitation to Classical Analysis
Peter Duren
Price : ₹ 1140.00  
ISBN : 9781470425784
Language : English
Pages : 408
Binding : Paperback
Book Size : 180 x 240 mm
Year : 2016
Series :
Territorial Rights : Restricted
Imprint : No Image

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About the Book

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.

Table of Contents

Chapter 1. Basic Principles  
Chapter 2. Special Sequences 
Chapter 3. Power Series and Related Topics 
Chapter 4. Inequalities 
Chapter 5. Infinite Products 
Chapter 6. Approximation by Polynomials 
Chapter 7. Tauberian Theorems 
Chapter 8. Fourier Series 
Chapter 9. The Gamma Function 
Chapter 10. Two Topics in Number Theory 
Chapter 11. Bernoulli Numbers 
Chapter 12. The Cantor Set 
Chapter 13. Differential Equations 
Chapter 14. Elliptic Integrals 
Index of Names 
Subject Index

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

Peter Duren is Professor at the Department of Mathematics, University of Michigan, Ann Arbor, USA.