First Order Partial Differential Equations
2 partial differential equations Second order partial derivatives could be written in the forms ¶2u ¶x2,uxx,¶xxu, D2xu. ¶2u ¶x¶y = ¶2u ¶y¶x,uxy,¶xyu, DyDxu. Note, we are assuming that u(x,y,. . .) has continuous partial derivatives. Then, according to Clairaut’s Theorem (Alexis Claude Clairaut, 1713-1765) , mixed partial derivatives ...
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