Perfect Form (Paperback)

by Don S. Lemons (Author) "THE PRINCIPLE OF LEAST TIME relates the length and orientation of a light ray to the time required for light to propagate along the ray..." (more)
Key Phrases: Hamilton's Principle, Principle of Least Action, Principle of Least Potential Energy (more...)

Editorial Reviews

Review
[The] ability of variational methods to derive fundamental results in physics hints at their being a kind of short cut towards truly fundamental insights into the design of the cosmos. . . . Don Lemon's short book is aimed at bringing these techniques within reach of the average undergraduate physics student. -- Review

Review
[The] ability of variational methods to derive fundamental results in physics hints at their being a kind of short cut towards truly fundamental insights into the design of the cosmos. . . . Don Lemon's short book is aimed at bringing these techniques within reach of the average undergraduate physics student.
(Robert Matthews New Scientist )

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Product Details

• Paperback: 144 pages
• Publisher: Princeton University Press (March 3, 1997)
• Language: English
• ISBN-10: 0691026637
• ISBN-13: 978-0691026633
• Product Dimensions: 9.1 x 6.1 x 0.4 inches
• Shipping Weight: 7 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #1,127,729 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars Very readable introduction to calculus of variations., January 29, 2000

By	Carey Allen (California) - See all my reviews

This is an engaging book, written on a fairly basic level. Any junior with some calculus should be able to handle it. The author has done a great job of introducing the calculus of variations, Lagrange multipliers, etc, and applying them to clear examples from physics (Fermat's principle, Lagrangians and Hamiltonians). I only wish he had expanded the topics somewhat to introduce a few more topics to whet the appetite, such as phase spaces, Liouville's theorem, Noether's theorem.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Fascinating Look at Variational Methods and Applications, March 6, 2004

By	Michael Wischmeyer (Houston, Texas) - See all my reviews (TOP 500 REVIEWER)    (REAL NAME)

For a third or fourth year student in physics this short book, Perfect Form, would be near perfect as either a short overview of variational methods, or as a supplementary text for an advanced classical physics course.

I have occasionally encountered variational methods, but until reading Perfect Form I had not appreciated the significance and scope and even fascination of this topic. In a little more than one hundred pages Dr. Don Lemons does a credible job of introducing a wide range of physics problems amenable to variational methods.

He begins with optics and Fermat's Principle of Least Time and thereby motivates the derivation of the Euler-Lagrange equation. In later chapters he examines the principle of least potential energy, Lagrange multipliers, the principle of least action, and Hamilton's principle, in both a restricted and more general form. The supplementary problems at the end of each chapter are few in number, but are carefully defined and are more like tutorials than standalone problems.

In my experience textbooks dedicated to this topic - like Calculus of Variations by Robert Weinstock and Introduction to the Calculus of Variations by Hans Sagan - are difficult and require considerable mathematical maturity. Other texts - like Advanced Calculus of Several Variables (C. H. Edwards) and Advanced Mathematical Methods for Engineering and Science Students (Stephenson and Radmore) and Mathematics Applied to Continuum Mechanics (L. A. Segel) - often relegate this subject to a single (and often final) chapter.

Most undergraduates are unlikely to have time for a formal course in calculus of variations. With this book Don Lemons has convinced me that this topic is too important and too interesting to ignore. I recommend that you acquire a copy of Perfect Form for self-study or as supplementary text.

5.0 out of 5 stars A nice short readable introduction, November 25, 2003

By	Kevin Roberge "homology" (Old Town, Maine United States) - See all my reviews (REAL NAME)

I just took an independent study in the calculus of variations out of Gelfand's classic text. I covered the first four chapters which is a nice introduction. However the text is pretty technical and so Perfect Form (PF) was a great companion. Its laid back, accessible to a sophomore physics student and fine for self study. It has a range of physical problems from calculations to nice little problems to think about.

Moreover, it motivates the material well. This is one of those books that keeps driving home a few, just a few points and avoids too many topics. For instance, I was never knew why the lagrangian should be the difference of kinetic and potential energies, this book will motivate this form.

Finally, its a realistic book. I found no great effort in reading the entire book and working about 3/4 of the problems (some I just didn't find interesting) on my own in a busy semester. This is just a fun little book that shows you some variational methods!