Lecture Notes for Math 4233
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Lecture 1: Linear Algebra and Matrices
Lecture 2: Systems of Homogeneous Linear ODEs
Lecture 3: Systems of Non-Homogeneous Linear ODEs
Lecture 4: Numerical Methods for ODEs, I (Euler Method)
Lecture 5: Numerical Differentiation
Lecture 6: Numerical Methods for ODEs, II (Runge-Kutta Methods)
Lecture 7: Numerical Methods for ODEs, III (Multi-Step Methods)
Lecture 8: Autonomous Systems and Stability
Lecture 9: Interacting Species
Lecture 10: Liapunov's Second Method
Lecture 11: Fourier Series
Lecture 12: The Heat Equation and Separation of Variables
Lecture 13: The Wave Equation
Lecture 14: Laplace's Equation
Lecture 15: Sturm-Liouville Theory
Lecture 16: Sturm-Liouville Theory and Nonhomogeneous Boundary Value Problems
Lecture 17: Sturm-Liouville Theory and Special Functions
Lecture 18: Power Series Solutions
Lecture 19: Regular Singular Points and Generalized Power Series
Lecture 20: A Vibrating Membrane Problem
