Volume: 72; 2014; 298 pp; Softcover
MSC: Primary 49;
Print ISBN: 978-1-4704-1495-5
Product Code: STML/72
List Price: $53.00
Individual Price: $42.40
Electronic ISBN: 978-1-4704-1961-5
Product Code: STML/72.E
List Price: $50.00
Individual Price: $40.00
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Supplemental Materials
A First Course in the Calculus of Variations
Share this pageMark Kot
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.
Readership
Undergraduate students interested in the calculus of variations.
Reviews & Endorsements
The author addresses several subtle aspects of the subject that are traditionally not covered in texts that are geared to the interests of applied mathematicians, physicists, and engineers ... What distinguishes this book from others is the author's style of introducing each topic with a practical example that serves to motivate the subsequent theory. Rather than presenting a prosaic collection of lemmas and theorems, the author demonstrates the practical need for addressing the more subtle aspects of the theory, which is well suited for an applications-oriented audience. The text also includes historical notes that are fascinating to read.
-- Joel Storch, IEEE Control Systems Magazine
The text follows the historical development of the subject and offers the reader a mixture of theory, techniques, and applications. This nice book is likely to be especially successful. [The] author has managed admirably to bring to light both the beauty and the usefulness of the calculus of variations in many problems arising in applied sciences, thus creating a beautiful introduction to this field. All the details are included in a way that is both attractive and easy for students to follow.
-- Zentralblatt Math
This text follows the historical development of the subject and offers the reader a mixture of theory, techniques and applications. ...The author integrates theory and applications quite deftly with the historical background and gives us a very attractive book. ...The introductory chapter gives a good indication of what's to come: clear writing, a carefully laid out development, well-chosen line drawings, and a thoughtful selection of recommended reading. ...This would serve admirably as the text for a course or as a tool for self-study. The exercises are first rate...
-- MAA Reviews
Kot displays more than a pedagogical sensitivity to notation (a traditional pitfall!); he inculcates the appreciation of notational nuance in his readers. Everyone who wants to learn this subject should start by investing the few hours necessary to read this book.
-- CHOICE
Table of Contents
Table of Contents
A First Course in the Calculus of Variations
- Cover Cover11 free
- Title page iii4 free
- Table of contents v6 free
- Preface ix10 free
- 1. Introduction 112 free
- 2. The First Variation 2738 free
- 3. Cases and Examples 4758
- 4. Basic Generalizations 6980
- 5. Constraints 107118
- 6. The Second Variation 139150
- 7. Review and Preview 171182
- 8. The Homogeneous Problem 177188
- 9. Variable-Endpoint Conditions 191202
- 10. Broken Extremals 215226
- 11. Strong Variations 235246
- 12. Sufficient Conditions 255266
- Bibliography 277288
- Index 295306 free
- Back Cover Back Cover1311