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I would appreciate any suggestions for "cheat sheets" (summary sheets) on the calculus of variations/ variational calculus in particular on the Euler -Lagrange equation, Lagrange multipliers, Legendre transform etc. Any suggestions? Thanks.

I know I could make one myself by laboriously pawing through a textbook, but I am just looking for a nice concise summary.

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On the cheat sheet level, the only thing you need is that "under reasonable assumptions, you can do calculus on infinite dimensional spaces just like on finite dimensional ones". If you need more, you should probably say what this sheet is for. (For example, if you are taking a course and are preparing for an exam, it may be more worthwhile to know the counterexamples: situations where the "reasonable assumptions" are violated and the finite dimensional intuition doesn't carry over to the infinite dimensional case.) –  Willie Wong Nov 8 '11 at 12:12
    
@WillieWong: Thanks, I'm learning about the Euler-Lagrange equations, Lagrange multipliers etc. And would like a consice summary on the "important formulae"... –  Refplz Nov 8 '11 at 12:18
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Please edit that clarification into your question text. The more precise you are about what you are looking for, the more likely you will get an answer suited to your needs. –  Willie Wong Nov 8 '11 at 12:24
    
@WillieWong: Edited. Thanks. –  Refplz Nov 8 '11 at 12:45
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2 Answers 2

One possible resource is Schaum's Outlines. While there are no Schaum's Outlines for Calculus of Variations (as far as I know), there are chapters on calculus of variations in

  • Schaum's Outlines of Advanced Mathematics for Engineers and Scientists
  • Schaum's Outline Introduction to Mathematical Economics

which may suffice for your purpose.

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You may find something similar on Lagrange Multipiers here.

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