Real Analysis And Applications: Including Fourier Series And the Calculus of Variations - Hardcover

Morgan, Frank

Hardcover

ISBN 10: 0821838415 ISBN 13: 9780821838419

Publisher: Amer Mathematical Society, 2005

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)

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2005
• Language: English
• ISBN 10: 0821838415
• ISBN 13: 9780821838419
• Binding: Hardcover
• Number of pages: 197