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Euler equation is often associated to Euler-Lagrange equation but I got an impression during the lecture that Euler equation is not the same as Euler-Lagrange. Please help me to understand their difference.

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Which "Euler equation" are you talking about? –  Rahul Mar 5 '13 at 23:20
@RahulNarain something related to Lagrange-Euler, I don't know which one. I am not sure whether my lecture material use the term "Euler Equation" and "Lagrange-Euler" as synonyms...I still got an impression that they are somehow different but could not understand the difference. –  hhh Mar 5 '13 at 23:22
Does this look relevant? "By calculating the first-order conditions associated with the Bellman equation, and then using the envelope theorem to eliminate the derivatives of the value function, it is possible to obtain a system of difference equations or differential equations called the 'Euler equations'. Standard techniques for the solution of difference or differential equations can then be used to calculate the dynamics of the state variables and the control variables of the optimization problem." –  user53153 Mar 6 '13 at 0:20
@5pm yes, thank you. This is something very important but very hard-written, implicitly, on my lecture slides, trying to dig into it... –  hhh Mar 6 '13 at 4:52
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