calculus of variations dover books on mathematics

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Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.

In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.

Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.

This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.

First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.

This text offers an introduction to the fundamentals and standard methods of the calculus of variations, covering fixed and movable boundaries, plus solutions of variational problems. 1961 edition.

Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers. Suitable for advanced undergraduate and graduate students as a primary or supplementary text. 1969 edition.

Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.

Pioneering modern treatise studies the development of the subject from Euler to Hilbert, addressing basic problems with sufficient generality and rigor to provide a sound introduction for serious study. 1904 edition.

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