A first course in the calculus of variations (Q2921242)

This book is an introduction to the calculus of variations and it is suitable for undergraduate students and beginning graduate students. 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.NEWLINENEWLINEThe book under review covers everything one expects in a first course in this field, such as the first variation of a function (Euler's and Lagrange's approaches), the brachistochrone problem, higher-order derivatives applied to Hamiltonian mechanics and the spherical pendulum, Dido's problem and isoperimetric constraints. But the volume under review also covers more challenging topics that might be used in a second course, such as Jacobi's and Legendre's conditions, Euler-Lagrange equations, broken extremals, Newton's problem, and Hilbert's invariant integral.NEWLINENEWLINEThe exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes and exercises, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in the calculus of variations to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the used techniques of analysis. No background in analysis beyond rigorous calculus and knowledge in the theory of functions of several variables is assumed.NEWLINENEWLINEThe 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 reviewer feels that 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.