• Introduction

Matrix Algebra

• Matrices
• Determinants and Inverses
• Eigenvalues and Eigenvectors
• Linear Systems
• Diagonalization
• Sylvester Formula
• Resolvent Method
• Spectral Decomposition
• Positive Matrices
• Miscellaneous Examples
• References

Systems of ODEs

• Intro
• Phase Portrait
• Linearization
• Variation of Parameters
• Undetermined Coefficients
• Laplace Transform
• Second Order ODEs
• Euler System
• Limit Circles
• Lyapunov Method
• Applications

Fourier Series

• Sturm--Liouville Problems
• Green Functions
• Orthogonal Expansions
• Fourier Series
• Gibbs Phenomenon
• Even and Odd Functions
• Cesaro Approximations
• Applications

PDEs

• Heat Conduction problems
• Other Heat problems
• Wave equation
• Transvers Vibrations
• Laplace Equation
• Laplace in Polar coor--s
• Applications
• Resources