# Texas A&M Aerospace Engineering - AERO 430 - Numerical Simulation
AERO 430 involves the discussion and application of the finite difference method (FDM) and finite element method (FEM) to 
2 types of problems: the stable heat transfer in a beam and the unstable forced vibration of a beam.

## HW1
Compute the numerical solution to the 1 dimensional heat transfer of a uniform beam using first and second order FDM 
and compare to the analytical solution.

[Homework 1 Report](HW1/Judson_Upchurch_HW1.pdf)

## HW2
Compute the numerical solution to the 1 dimensional heat transfer of a uniform beam using second order FDM and linear 
shape function FEM.

[Homework 2 Report](HW2/Judson_Upchurch_HW2.pdf)

## HW3
Compute the numerical solution to the 1 dimensional heat transfer of a non-uniform beam using second order FDM and linear 
shape function FEM.

[Homework 3 Report](HW3/Judson_Upchurch_HW3.pdf)

## HW4
Compute the numerical solution to the 1 dimensional heat transfer of a non-uniform beam using second and fourth order FDM 
and linear and quadratic shape function FEM.

[Homework 4 Report](HW4/Judson_Upchurch_HW4.pdf)

## HW5-6
Compute the numerical solution to the 1 dimensional forced vibration of a uniform beam using second and fourth order FDM 
and linear and quadratic shape function FEM. Also perform a frequency sweep to determine the natural frequencies of the method and the beam.

[Homework 5-6 Report](HW5/Judson_Upchurch_HW5_6.pdf)