How can I force Mathematica to calculate symbolically the partial derivative of a function
u[x,y] with respect to a variable
z = f(x, y), where f(x, y) is known?
u is a function, defined on reals, taking real values. Same thing holds for
I want to try different changes of variables in PDEs. An example of what I'm trying to achieve and why it's failing:
z = 2*x + y
2 x + y
D[u[x, y], z]
General::ivar: 2 x+y is not a valid variable. >>
D[u[x, y], 2*x + y]
EDIT: It appears I have failed to convey the essence of the question.
I am not asking how to solve a PDE with Mathematica. I am asking how, given a transformation of the original variables, to calculate the partial derivatives with respect to the new variables. The PDE part is merely some context as to why I want to do this.