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Question on Calculus of variations formalism
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[QUOTE="ogg, post: 5487098, member: 514770"] When I was in college, a half a century ago, the word "functional" never came up. Now, it's standard fare. The thing is that the "universe of discourse" of differential calculus is NOT the real numbers; it is the space of all functions (continuous, well-behaved, smooth, etc.). So, logically you move from considering maps "from numbers to numbers" to maps "from functions to functions". Usually CoV is presented after differential calculus of 1 variable, multvariate differentiation, integral calculus of 1 variable, and ordinary differential equations. Generally, partial differential equations (multivariate by definition) is taught along with or prior to CoV because they go hand in hand. Anyway, I learned CoV without any need for the concept of "functional" although once I heard about it I saw how it allowed a more rigorous development of the subject. So, you're not wrong. [/QUOTE]
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