In this video, we solve the 1D wave equation. We utilize the separation of variables method to solve this 2nd order, linear, homogeneous, partial differential equation. Topics discussed in this lesson include but are not limited to:

The separation of variables method (AKA the product method) for PDEs.
Eigenvalues and eigenfunctions of the problem.
Composition of a complete solution via Fourier analysis.
Animation of the solution for a PDE.

This video focuses on the solution of the governing PDE only, other videos in this series discuss how to derive this PDE.

A sample Mathematica notebook that accompanies this tutorial is located at
http://faculty.washington.edu/lum/Edu....

Additional videos in this series:
Introduction to Partial Differential Equations (   • Introduction to Partial Differential ...  )
Standing Waves Demonstration (   • Standing Waves Demonstration  )
Derivation of the 1D Wave Equation (   • Derivation of the 1D Wave Equation  )
Solving the 1D Wave Equation (   • Solving the 1D Wave Equation  )
Heat Transfer Demonstration (   • Heat Transfer Demonstration  )
Derivation of the Heat Equation (   • Derivation of the Heat Equation  )
Solving the 1D Heat Equation (   • Solving the 1D Heat Equation  )
Derivation and Solution of Laplace’s Equation (   • Derivation and Solution of Laplace’s ...  )
Derivation of the 2D Wave Equation (   • Derivation of the 2D Wave Equation  )
Solving the 2D Wave Equation (   • Solving the 2D Wave Equation  )

Associated videos on software tools relevant to PDEs include:
Creating Movies and Animations in Mathematica (   • Creating Movies and Animations in Mat...  )
Creating Movies and Animations in Matlab (   • Creating Movies and Animations in Matlab  )