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A First Course in the Calculus of Variations
 
Mark Kot University of Washington, Seattle, WA
Front Cover for A First Course in the Calculus of Variations
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Softcover ISBN: 978-1-4704-1495-5
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Electronic ISBN: 978-1-4704-1961-5
Product Code: STML/72.E
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Individual Price: $40.00
Sale Price: $32.50
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Front Cover for A First Course in the Calculus of Variations
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  • Front Cover for A First Course in the Calculus of Variations
  • Back Cover for A First Course in the Calculus of Variations
A First Course in the Calculus of Variations
Mark Kot University of Washington, Seattle, WA
Available Formats:
Softcover ISBN:  978-1-4704-1495-5
Product Code:  STML/72
List Price: $53.00
Individual Price: $42.40
Sale Price: $34.45
Electronic ISBN:  978-1-4704-1961-5
Product Code:  STML/72.E
List Price: $50.00
Individual Price: $40.00
Sale Price: $32.50
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $79.50
Sale Price: $51.68
  • Book Details
     
     
    Student Mathematical Library
    Volume: 722014; 298 pp
    MSC: Primary 49;

    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.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. The first variation
    • Chapter 3. Cases and examples
    • Chapter 4. Basic generalizations
    • Chapter 5. Constraints
    • Chapter 6. The second variation
    • Chapter 7. Review and preview
    • Chapter 8. The homogeneous problem
    • Chapter 9. Variable-endpoint conditions
    • Chapter 10. Broken extremals
    • Chapter 11. Strong variations
    • Chapter 12. Sufficient conditions
  • Reviews
     
     
    • 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
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Volume: 722014; 298 pp
MSC: Primary 49;

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.

  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. The first variation
  • Chapter 3. Cases and examples
  • Chapter 4. Basic generalizations
  • Chapter 5. Constraints
  • Chapter 6. The second variation
  • Chapter 7. Review and preview
  • Chapter 8. The homogeneous problem
  • Chapter 9. Variable-endpoint conditions
  • Chapter 10. Broken extremals
  • Chapter 11. Strong variations
  • Chapter 12. Sufficient conditions
  • 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
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