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I did not understand two transitional stages in the red rectangulars. (Please look question marks) Could you help me? enter image description here enter image description here enter image description here

HD239
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    The first rectangle is simple Taylor expansion. And the second rectangle is just a definition for the "first variation" – Andrei Sep 08 '17 at 23:41
  • Thank you for interest. Can you explain some more details about how to get that equality from Taylor expansion? I know Taylor expansion for multivariable functions but I don't understand this. – HD239 Sep 08 '17 at 23:48
  • But the first box is exactly the first order expansion of the function $f(x,y+\epsilon \eta, y'+\epsilon \eta')$. What part do you not understand? – Cyclone Sep 08 '17 at 23:57
  • I don't understand the first order expansion of the function , unfortunately :/ – HD239 Sep 09 '17 at 00:18
  • The last few lines on this website might help.Take a=x ; b=$\eta\epsilon$ ; c=$\eta'\epsilon'$ – Rohan Marwah Apr 29 '19 at 07:40

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