Mark KotA First Course in the Calculus of Variations (Student Mathematical Library) (Student Mathematical Library, 72)

This is a great book for self study! It gives a organized and enjoyable historical rundown alongside the development of calculus of variations. If you happen to be in Seattle while Mark Kot is teaching the course at UW, it's worthwhile to try and sit in on the class.

In the preface the author states that this book is a set of notes intended to augment a course in the Calculus of Variables implying that the course has its own reference text. I found that statement to be very true. Let me emphasize that this book is not that reference text. There are mathematical flaws of omission in both the analysis and the notation. The material is there but it is not presented in the clear manner typical of a mathematical treatise. Instead a lot of time is spent with historical anecdotes. Looking through the books listed by the author, evidently his primary interest was historical not mathematical. Thus, a college student or self-study individual has to find the reference book that does fill in the gaps. I am not sure if that even exists. Most authors find the anecdotes more interesting than the subject. With the rise of digital methods, Bellman's approach has largely eclipsed this material in engineering optimization problems. Even so, the Calculus of Variations is not just a bag of tricks for control systems. Combined with Noether's Theorem it contributes to the fundamental understanding of Mechanics, Physics, and in particular Particle Dynamics. Thus, neither the anecdotes nor the samples convey the whole scope of the material. But, if you do know some of that "extra" baggage, then this book is a valuable second source of discussion. I recommend it for your library.

The instructor expresses it clearly

I am a graduate of math, but I can't understand its context. Maybe the theory is quite difficult to follow and there are many symbols that are for further advanced study.