A First Course in the Calculus of Variations

A First Course in the Calculus of Variations

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This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields.

The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics.

Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.
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Product details

  • Paperback | 298 pages
  • 140 x 216 x 12.7mm | 385.55g
  • Providence, United States
  • English
  • 1470414953
  • 9781470414955
  • 983,320

Table of contents

The first variation
Cases and examples
Basic generalizations
The second variation
Review and preview
The homogeneous problem
Variable-endpoint conditions
Broken extremals
Strong variations
Sufficient conditions
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Review quote

"This introductory text follows the historical development of the subject and offers the reader a mixture of theory, techniques and applications. The book is aimed at advanced undergraduates and beginning graduate students in mathematics, physics and engineering. The author integrates theory and applications quite deftly with the historical background and gives us a very attractive book."
-- MAA
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About Mark Kot

Mark Kot, University of Washington, Seattle, WA, USA.
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