Introduction to the Calculus of Variations (Dover Books on Mathematics)
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The last three chapters examine variable end points and strong variations, including an account of Weierstrass's theory of strong variations, based upon the work of Hilbert.
Ideal as a text, this volume offers an exceptionally clear presentation of the mathematics involved, with many illustrative examples, while numerous references cite additional source readings for those interested in pursuing a topic further. Students are assumed to have a knowledge of partial differentiation and differential equations.
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Reviewer: a e b - favorite favorite favorite favorite favorite - July 26, Subject: An Amazing Book Forsyth's Calculus of Variations was published in , and is a marvelous example of solid early twentieth century mathematics. The book looks at half-a-dozen different types of problems dealing with different numbers of independent and dependent variables. It looks at weak and strong variations.
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This book covers several times more material than many modern books on Calculus of Variations. The down-side, of course, is that the proofs move quickly it can take the reader a few hours to fill in the missing steps in order to verify Forsyth's calculations in a proof and do not worry about truely bizarre behavior such as encountered in nonlinear dynamics. But the proofs are complete given the understanding of derivatives of functions and quite solid again, by standards.
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I reccomend this book to anyone who wishes to explore the wild, wild world of Calculus of Variations.