The heat equation
Solve the following PDE:
du/dt = d^2u / dx^2 (note: partial derivatives),
u(x, 0) = sin^2(x),
u(0, t) = 0, u(Pi, t) = 0,
0 < x < Pi
Repeat for the below initial condition:
du/dt (x, 0) = sin^2(x) (note:partial derivatives),0 < x < Pi
Provide step by step calculations.