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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
Six Themes on Variation
Softcover ISBN:  978-0-8218-3720-7
Product Code:  STML/26
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2138-0
Product Code:  STML/26.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-3720-7
eBook: ISBN:  978-1-4704-2138-0
Product Code:  STML/26.B
List Price: $108.00 $83.50
Six Themes on Variation
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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
Softcover ISBN:  978-0-8218-3720-7
Product Code:  STML/26
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2138-0
Product Code:  STML/26.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-3720-7
eBook ISBN:  978-1-4704-2138-0
Product Code:  STML/26.B
List Price: $108.00 $83.50
  • 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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    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.

Readership

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.

    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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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