Items tagged with partial-differentiation partial-differentiation Tagged Items Feed

Hello,

I need to verify some terms in an equation which would involve the application of chain rule. I have A:=f(x,y), x:=g(t,s) and y:=h(t,s). Now I want to find the terms that will be present in the expression after application of Chain rule for the term d^4(A)/dt^4. The exact definition of A is not know. It is just known that it is function of x & y. I just need the expression for d^4(A)/dt^4 in terms of dA/dt*dt/dx and so on. Could anyone please suggest a way of doing this in Maple?

This is just a programmatic twist on Robert Lopez's very nice original post on this topic.

I'd rather be able to control such declarations with code, than to have to manipulate the palettes or context menus in order to get what are -- in essence -- additional programming and authoring tools. Such code can be dynamic and flexible, and could be inserted in Code- or Startup regions.

Download atomicpartials.mw

Hello,

I’m just toying around with diff(), dsolve(), and, as it happens, also with pdsolve(). Let’s say I have an equation as the following:

DF := (diff(f(x, y, t), `$`(x, 2)))*omega+(diff(f(x, y, t), `$`(y, 2)))^2+diff(f(x(t), y(t), t), t) = 5;

A function f, depending on x, y and t where x and y also depend on t. I multiply the second partial derivative of f by x with ω, add it to the square of the second partial derivative of f by...

I have always preferred the notation  for the derivative of

Hi All,

Given the partial differential equation of a plate on an elastic foundation, how do I solve the analytical solution for the deflection given the boundary conditions.

This is what I have:

partial differential equation of a plate on an elastic foundation:
> pde := E*(diff(w(r, phi), r, r, r, r)+2*(diff(w(r, phi), r, r, phi, phi))+diff(w(r, phi), phi, phi, phi, phi))+k*w(r, phi) = 0

The solution for w(r, phi) of this is:

I'm taking a calculus of variations class and checking some answers with Maples VariationalCalculus package and the EulerLagrange command in particular.

I've done an exercise by hand for which I don't get the same results from Maple and I'm trying to see why.

Can anyone help me construct the EL equation "manually", in partcular how do I get the partial derivartive of an expression containing x, y(x) and diff(y(x),x) with respect to diff(y(x),x) ? That...