**Student Mathematical Library**

Volume: 26;
2004;
153 pp;
Softcover

MSC: Primary 49;

Print ISBN: 978-0-8218-3720-7

Product Code: STML/26

List Price: $34.00

Individual Price: $27.20

**Electronic ISBN: 978-1-4704-2138-0
Product Code: STML/26.E**

List Price: $34.00

Individual Price: $27.20

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#### Supplemental Materials

# Six Themes on Variation

Share this page *Editors and Authors: *
*Robert Hardt; Steven J. Cox; Robin Forman; Frank Jones; Barbara Lee Keyfitz; Frank Morgan; Michael Wolf*

The calculus of variations is a beautiful subject with a rich
history and with origins in the minimization problems of calculus. Although
it is now at the core of many modern mathematical fields, it does not
have a well-defined place in most undergraduate mathematics
curricula. This volume should nevertheless give the undergraduate
reader a sense of its great character and importance.

Interesting functionals, such as area or energy, often give rise to problems
for which the most natural solution occurs by differentiating a one-parameter family of
variations of some function. The critical points of the functional are related
to the solutions of the associated Euler-Lagrange equation. These differential
equations are at the heart of the calculus of variations and its applications
to other subjects. Some of the topics addressed in this book are Morse theory,
wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All
are readily accessible to advanced undergraduates.

This book is derived from a workshop sponsored by Rice University. It
is suitable for advanced undergraduates, graduate students and
research mathematicians interested in the calculus of variations and
its applications to other subjects.

#### Table of Contents

# Table of Contents

## Six Themes on Variation

- Cover Cover11 free
- Title i2 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- List of Contributors xi12 free
- Calculus of Variations: What Does "Variations" Mean? 114 free
- How Many Equilibria Are There? An Introduction to MorseTheory 1326
- Aye, There's the Rub. An Inquiry into Why a Plucked String Comes to Rest 3750
- Proof of the Double Bubble Conjecture 5972
- Minimal Surfaces, Flat Cone Spheres and Moduli Spaces of Staircases 7992
- Hold That Light! Modeling of Traffic Flow by Differential Equations 127140
- Back Cover Back Cover1169

#### Readership

Undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

#### Reviews

This is a nice little book on many levels. The exposition is entertaining, the interplay between the mathematics and the applications is interesting, and the idea of 'advertising' higher mathematics to undergraduates and graduate students seems exciting and productive.

-- MAA Reviews

The book is recommended to an audience of undergraduate students as well as to teachers looking for inspiration for their own lectures.

-- EMS Newsletter

This work is a beautiful collection of six papers written by well known specialists in the Calculus of Variations. ... All these papers are very well written and they illustrate the fruitful interplay between pure and applied mathematics.

-- Zentralblatt MATH