Calculus of Variations

by Lev D. Elsgolc

This concise text offers an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, its subjects include practical direct methods for solution of variational problems. Each chapter features numerous illustrative problems, with solutions. 1961 edition.

192 pages, Paperback

First published January 15, 2007

Reviews

[Joe Richardson · Rating 2 out of 5]

Not pedagogically clear. The author does not introduce the principle of least action, which is the main motivation for calculus of variations, so unless you are familiar with that from elsewhere, the choice of topics will seem arbitrary. The text is neither sufficiently formal nor intuitive. For example, the first definition given is that of "functionals" which are defined as "variable values which depend on a variable running through a set of functions, or on a finite number of such variables, and which are completely determined by a definite choice of these variable functions." To me, this definition raises several questions many of which are not addressed. How is the "variable value" different from a function? What does it mean to "run through" in mathematical context? Does that refer to just elements of a set or specifically something parametric? If it's a variable value that depends on a variable, is it allowed to depend on itself or would that be recursive and break the definition? Maybe I'm wrong and these terms are rigidly defined somewhere else in some text that I should know as a prerequisite, but to me it just seems like the author is mixing set theory formalities with metaphors to gesture at a concept that isn't itself fully defined for the reader. Maybe there's some topic in graduate level functional analysis that I've missed, but that seems awfully formal for a text that claims it's aimed at engineers. I also don't care for how the first set of examples deal with solving something called the "Euler equation" and the way this is shown is just be showing the integral and then skipping to the answer without any derivation. No, I could not follow along, partially because the F subscript symbols are never actually defined in the text and the first three guesses I had for what they were that I threw at the problem yielded a different equation than what was shown. It's entirely possible I'm just stupid and that other readers of this review find these issues trivial and they may get value out of this text, but I'm going to try learning this material elsewhere.