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Six Themes on Variation

Edited by: Robert Hardt Rice University, Houston, TX
Steven J. Cox Rice University, Houston, TX
Robin Forman Rice University, Houston, TX
Frank Jones Rice University, Houston, TX
Barbara Lee Keyfitz The Fields Institute, Toronto, ON, Canada
Frank Morgan Williams College, Williamstown, MA
Michael Wolf Rice University, Houston, TX
Available Formats:
Softcover ISBN: 978-0-8218-3720-7
Product Code: STML/26
List Price: $37.00 Individual Price:$29.60
Electronic ISBN: 978-1-4704-2138-0
Product Code: STML/26.E
List Price: $34.00 Individual Price:$27.20
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List Price: $55.50 Click above image for expanded view Six Themes on Variation Edited by: Robert Hardt Rice University, Houston, TX Steven J. Cox Rice University, Houston, TX Robin Forman Rice University, Houston, TX Frank Jones Rice University, Houston, TX Barbara Lee Keyfitz The Fields Institute, Toronto, ON, Canada Frank Morgan Williams College, Williamstown, MA Michael Wolf Rice University, Houston, TX Available Formats:  Softcover ISBN: 978-0-8218-3720-7 Product Code: STML/26  List Price:$37.00 Individual Price: $29.60  Electronic ISBN: 978-1-4704-2138-0 Product Code: STML/26.E  List Price:$34.00 Individual Price: $27.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$55.50
• Book Details

Student Mathematical Library
Volume: 262004; 153 pp
MSC: Primary 49;

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.

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

• Articles
• Frank Jones - 1. Calculus of variations: What does “variations” mean?
• Robin Forman - 2. How many equilibria are there? An introduction to Morse theory
• Steven J. Cox - 3. Aye, there’s the rub. An inquiry into why a plucked string comes to rest
• Frank Morgan - 4. Proof of the double bubble conjecture
• Michael Wolf - 5. Minimal surfaces, flat cone spheres and moduli spaces of staircases
• Barbara Lee Keyfitz - 6. Hold that light! Modeling of traffic flow by differential equations

• 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.

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 262004; 153 pp
MSC: Primary 49;

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.

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

• Articles
• Frank Jones - 1. Calculus of variations: What does “variations” mean?
• Robin Forman - 2. How many equilibria are there? An introduction to Morse theory
• Steven J. Cox - 3. Aye, there’s the rub. An inquiry into why a plucked string comes to rest
• Frank Morgan - 4. Proof of the double bubble conjecture
• Michael Wolf - 5. Minimal surfaces, flat cone spheres and moduli spaces of staircases
• Barbara Lee Keyfitz - 6. Hold that light! Modeling of traffic flow by differential equations
• 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.