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Real Analysis

ISBN-10: 0821836706

ISBN-13: 9780821836705

Edition: 2005

Authors: Frank Morgan

List price: $46.00
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Intended for undergraduates studying real analysis, this text builds the theory behind calculus directly from the basic concepts of real numbers and limits.
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Book details

List price: $46.00
Copyright year: 2005
Publisher: American Mathematical Society
Publication date: 7/19/2005
Binding: Hardcover
Pages: 151
Size: 7.25" wide x 10.00" long x 0.50" tall
Weight: 1.210
Language: English

Frank Morgan is the Dennis Meenan '54 Third Century Professor of Mathematics at Williams College. He obtained his B.S. from MIT and his M.S. and Ph.D. from Princeton University. His research interest lies in minimal surfaces, studying the behavior and structure of minimizers in various settings. He has also written Riemannian Geometry: A Beginner's Guide, Calculus Lite, and most recently The Math Chat Book, based on his television program and column on the Mathematical Association of America Web site.

Real numbers and limits: Numbers and logic
Infinity Sequences Functions and limits
Topology: Open and closed sets
Continuous functions Composition of functions
Subsequences Compactness Existence of maximum
Uniform continuity
Connected sets and the intermediate value theorem
The Cantor set and fractals
Calculus: The derivative and the mean value theorem
The Riemann integral
The fundamental theorem of calculus
Sequences of functions
The Lebesgue theory
Infinite series $\sum a_n$
Absolute convergence
Power series
Fourier series
Strings and springs
Convergence of Fourier series
The exponential function
Volumes of $n$-balls and the gamma function
Metric spaces: Metric spaces Analysis on metric spaces
Compactness in metric spaces
Ascoli's theorem
Partial solutions to exercises
Greek letters