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Student Mathematical Library
2004; 153 pp; softcover
List Price: US$34
Institutional Members: US$27.20
All Individuals: US$27.20
Order Code: STML/26
A Primer on the Calculus of Variations and Optimal Control Theory - Mike Mesterton-Gibbons
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.
"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
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