2005;
197 pp;
Hardcover

MSC: Primary 26; 49; 42; 83;

**Print ISBN: 978-0-8218-3841-9
Product Code: REALAPP**

List Price: $49.00

AMS Member Price: $39.20

MAA Member Price: $44.10

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#### Supplemental Materials

# Real Analysis and Applications: Including Fourier Series and the Calculus of Variations

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*Frank Morgan*

Real Analysis and Applications starts with a
streamlined, but complete, approach to real analysis. It finishes with
a wide variety of applications in Fourier series and the calculus of
variations, including minimal surfaces, physics, economics, Riemannian
geometry, and general relativity. The basic theory includes all the
standard topics: limits of sequences, topology, compactness, the
Cantor set and fractals, calculus with the Riemann integral, a chapter
on the Lebesgue theory, sequences of functions, infinite series, and
the exponential and Gamma functions. The applications conclude with a
computation of the relativistic precession of Mercury's orbit, which
Einstein called "convincing proof of the correctness of the theory [of
General Relativity]."

The text not only provides clear, logical proofs, but also shows
the student how to derive them. The excellent exercises come with
select solutions in the back. This is a text that makes it possible to
do the full theory and significant applications in one semester.

Frank Morgan is the author of six books and over one hundred articles
on mathematics. He is an inaugural recipient of the Mathematical Association of
America's national Haimo award for excellence in teaching. With this applied
version of his Real
Analysis text, Morgan brings his famous direct style to the growing
numbers of potential mathematics majors who want to see applications along with
the theory.

The book is suitable for undergraduates interested in real
analysis.

#### Readership

Undergraduate students interested in real analysis and its applications.