Computational Mechanics 5 - Boundary Value Problems

01_Revisiting_derivatives

• 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

• 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

• 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