# The 1D heat equation

It is given that that a Fourier Cosine series of teh function f(x) is given by (see file)

A PDE is given by:

u_t = u_xx 0<x>Pi t>0

With boundary conditions:

u_x(0,t) = u_x(pi, t)=0

1. Determine all the solutions of the PDE that satisfy these boundary conditions.

2. find teh solution that satisfies in addition the initial condition u(x,0) = f(x)

https://brainmass.com/math/algebra/heat-equation-243279

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in ...

#### Solution Summary

Included is an 8 pages file that contains a full derivation general solution to the 1D heat equation and then shows how to apply it to the specific problem.

$2.19