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- Lecture 1: Linear Algebra and Matrices
- Lecture 2: Homogeneous Linear Systems of ODEs
- Lecture 3: Nonhomogeneous Linear Systems of ODEs
- Lecture 4: Stability of Autonomous Systems
- Lecture 5: Interacting Species
- Lecture 6: Liapunov's Second Method
- Lecture 7: Fourier Series
- Lecture 8: The Heat Equation
- Lecture 9: The Wave Equation
- Lecture 10: Laplace's Equation
- Lecture 11: Sturm-Liouville Theory
- Lecture 12: Sturm-Liouville Theory and Nonhomogeneous Boundary Value Problems
- Lecture 13: Sturm-Liouville Theory and Special Functions
- Lecture 14: Green's Functions
- Lecture 15: The Delta Function
- Lecture 16: Numerical Methods
- Lecture 17: Numerical Differentiation
- Lecture 18: Runge-Kutta Methods
- Lecture 19: Multi-Step Methods