README.md

# Computational Mechanics 5 - Boundary Value Problems


# [01_Revisiting_derivatives](./notebooks/01_Revisiting_derivatives.ipynb)

* How to approximate error in approximate derivatives
* How to approximate derivatives using forward difference methods
* How to approximate derivatives using backward difference methods
* How to approximate derivatives using central difference methods
* How to approximate higher order derivatives with forward, backward, and
* central differences

# [02_Keep_it_steady](notebooks/02_Keep_it_steady.ipynb)

* The difference between a _PDE_ and an _ODE_
* How to approximate differential equations with boundary conditions
* Solve steady-state heat transfer problem
* Solve static deflection of elastic beam
* Demonstrate convergence of finite difference solutions


# [03_Good_Vibrations](./notebooks/03_Good_Vibrations.ipynb)
* How to set up and solve an eigenvalue problem
* How eigenvalues and eigenvectors relate to natural frequencies and mode shapes
* How to turn a _PDE_ into a finite difference _ODE_
* How to use eigenvalues to calculate natural frequencies of a vibrating string
* How to solve a coupled set of _ODEs_ 
* Visualize solutions to finite difference equations with 3D plots and
* animations
* How to _listen_ to vibration solutions