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A First Course in the Calculus of Variations.
・ISBN 978-1-4704-1495-5 paper US$ 50.00
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| 著者・編者 | Kot, Mark, |
|---|---|
| シリーズ | Student Mathematical Library |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2014 |
| ページ数 | 298 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-15595＞ |
解説
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.
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.