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

**Electronic ISBN: 978-1-4704-1214-2
Product Code: REALAPP.E**

List Price: $46.00

AMS Member Price: $36.80

MAA Member Price: $41.40

#### You may also like

#### Supplemental Materials

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

Share this page
*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.

#### Table of Contents

# Table of Contents

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

- Front Cover 11
- Contents 66
- Preface 1010
- Part I: Real Numbers and Limits 1212
- Part II: Topology 4444
- Part III: Calculus 7070
- Chapter 13: The Derivative and the Mean Value Theorem 7272
- Chapter 14: The Riemann Integral 7676
- Chapter 15: The Fundamental Theorem of Calculus 8282
- Chapter 16: Sequences of Functions 8686
- Chapter 17: The Lebesgue Theory 9292
- Chapter 18: Infinite Series Σ∞n=1 an 9696
- Chapter 19: Absolute Convergence 100100
- Chapter 20: Power Series 104104
- Chapter 21: The Exponential Function 110110
- Chapter 22: Volumes of n-Balls and the Gamma Function 114114

- Part IV: Fourier Series 118118
- Part V: The Calculus of Variations 132132
- Chapter 26: Euler’s Equation 134134
- Chapter 27: First Integrals and the Brachistochrone Problem 140140
- Chapter 28: Geodesics and Great Circles 146146
- Chapter 29: Variational Notation, Higher Order Equations 150150
- Chapter 30: Harmonic Functions 156156
- Chapter 31: Minimal Surfaces 160160
- Chapter 32: Hamilton’s Action and Lagrange’s Equations 164164
- Chapter 33: Optimal Economic Strategies 168168
- Chapter 34: Utility of Consumption 172172
- Chapter 35: Riemannian Geometry 176176
- Chapter 36: NonEuclidean Geometry 180180
- Chapter 37: General Relativity 184184

- Partial Solutions toExercises 192192
- Greek Letters 204204
- Index 206206
- Back Cover 209209