Invitation to Classical Analysis

Portada
American Mathematical Soc., 2012 - 392 pàgines
1 Ressenya
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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.
 

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Continguts

Special Sequences
51
Power Series and Related Topics
73
Inequalities
109
5
131
Approximation by Polynomials
145
Tauberian Theorems
179
Fourier Series
197
The Gamma Function
247
Bernoulli Numbers
291
12
309
18
320
Differential Equations
327
22
336
33
358
Elliptic Integrals
369
39
387

Two Topics in Number Theory
269

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