First Course in the Calculus of Variations

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

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

• IntroductionThe first variationCases and examplesBasic generalizationsConstraintsThe second variationReview and previewThe homogeneous problemVariable-endpoint conditionsBroken extremalsStrong variationsSufficient conditionsBibliographyIndex