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Synopsis
Morgan, recipient of the Haimo award for excellence in mathematics teaching, here provides a one-semester introduction to real analysis, starting with basic theory and ending in a wide variety of applications. He starts with real numbers and limits, including descriptions of numbers and logic, infinity, sequences, subsequences, functions and limits and composition of functions, then moves to a complete description of topology, including the Cantor set and fractals, then covers interrelated issues of calculus including the Riemann Integral, the Lebesque Theory and power series. He then moves to applications in Fourier series, including strings and springs, and devotes the rest of the text to the calculus of variations, including Euler's Equation, harmonic functions, Hamilton's Action and Lagranges' Equation, finishing with nonEuclidean geometry and some fun with relativity. The exercises here are especially well done, and Morgan provides partial solutions. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)
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- PublisherAmer Mathematical Society
- Publication date2005
- ISBN 10 0821838415
- ISBN 13 9780821838419
- BindingHardcover
- LanguageEnglish
- Number of pages197
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Real Analysis And Applications: Including Fourier Series And the Calculus of Variations
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Amer Mathematical Society (edition ), 2005
ISBN 10: 0821838415
ISBN 13: 9780821838419
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Real Analysis And Applications: Including Fourier Series And the Calculus of Variations
Published by
Amer Mathematical Society, 2005
ISBN 10: 0821838415
ISBN 13: 9780821838419
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Real Analysis And Applications: Including Fourier Series And the Calculus of Variations
Published by
Amer Mathematical Society, 2005
ISBN 10: 0821838415
ISBN 13: 9780821838419
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Real Analysis And Applications: Including Fourier Series And the Calculus of Variations
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Amer Mathematical Society, 2005
ISBN 10: 0821838415
ISBN 13: 9780821838419
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