My Math Forum Partial differential:Presentation function

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 August 26th, 2010, 01:03 PM #1 Member   Joined: Feb 2009 Posts: 76 Thanks: 0 Partial differential:Presentation function My prof talked about "presentation functions". According to his definition, *edit (His definition is "The function F") He gave an example: $\ u_{t}=u_{xx}+2u_{x}+u\$ If we take $\ F(x,t,P_{0},P_{1}, P_{2},P_{11},P_{12},P_{22})\equiv \\ =P_{11}+2P_{1}-P_{2}+P_{0}\$ Then the presentation function is $\ P_{0}+2P_{1}-P_{2}+P_{11}=0\$ I understand that problem but I am not sure how to write the presentation function for this problem: $\ u_{t}=u_{xx}+4e^{-t}+ sin \: t\$ Not sure how the exponent and the trigonometric function would look like. I am not sure about the trigonometric function. I do have some thought about the exponent sign. I think if it was for a different situation, say $\ 4e^{-t}u_{xx}\$, then it would be $\ 4e^{-t}P_{11}\$. So for the problem above, it would be just be $\ 4e^{-t}$ because it's like a coefficient or a a constant or a given function of t. I don't know if that make sense. Can someone please clarify this for me. Thanks in advance.

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### presentation for math about partial differentiation

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