Calculus of Variations text my Mark Kot

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I've been going around Stackexchange for reviews on Calculus of Variation texts, I've been looking at Mark Kots "A first course in the calculus of variations" and there's no review on this text. My question is whether this text fits alongside an intermediate course in Classical Mechanics that covers lagrangians and hamilton systems.

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I am currently studying Classical mechanics, so naturally, I felt the need to refer to the Calculus of Variations, and unexpectedly I came across this book. So far, I can say this book has been the best because Chapter 1 builds up the need for calculus of variations through examples and history, and the most important chapter for Classical Mechanics, Chapter 2, derives the Euler-Lagrange equation and deals with all cases leading up to Euler-Lagrange, Chapter 3 again dives into applications and in Chapter 4 you are generalizing the Euler-Lagrange equation and officially starting Lagrangian Mechanics. All in all, I feel that up to chapter 5 this book can go along with Classical Mechanics after that it is upon the reader to continue with the mathematical nitty-gritty.