I continued with the ideas from this book to then study Analytic Mechanics which after studying the Calculus of Variations was a much easier task. A whole historical timeline of ideas was presented to me, ' why didn't anyone tell me this when I was studying Electromagnetics at University ?' I also started to see how the Cov lead via the extension to 2 independent variables to the idea of capping surfaces and how this in turn applied to vector fields lead eventually to Maxwell's equations. In fact I actually started DOING mathematics, by filling in the gaps, rewriting the proofs in my own 'style' and adding simulation into matlab and DESMOS. In the process I learned a WHOLE lot more mathematics than is in this book. I worked through line per line equation to equation and filled in all the missing mathematics in between. When I started on the Fox book I dedicated myself to it. I originally tried the Fomin book but found the initial introduction via vector space as an unnecessarily cumbersome (maybe if you are introducing Fourier Analysis then this may be a good idea but I thought it over the top for an introduction to CoV) addition. After which the rest of calculus of variations became accessible to me. Having struggled with Calculus of Variations I went back to Euler's original work which explained the derivation of the Euler Lagrange equation in a purely simple geometric manner. Students are assumed to have a knowledge of partial differentiation and differential equations. ![]() ![]() 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. 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. Applied mathematics are discussed in Chapters V, VI, and VII, including studies of least action, a proof of Hamilton's principle and its use in dealing with dynamical problems in the special theory of relativity, and such methods of approximation as the Rayleigh-Ritz method, illustrated by applications to the theory of elasticity. Chapters III and IV delve into pure mathematics, exploring generalizations and isoperimetrical problems. The first two chapters deal with the first and second variation of an integral in the simplest case, illustrated by applications of the principle of least action to dynamical problems. In this highly regarded text, aimed at advanced undergraduate and graduate students in mathematics, the author develops the calculus of variations both for its own intrinsic interest and because of its wide and powerful applications to modern mathematical physics. An understanding of variational methods, the source of such fundamental theorems as the principle of least action and its various generalizations, is essential to the study of mathematical physics and applied mathematics.
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