Week 1: Sections 7.1-7.4

• Sept 24: Introduction to the class and overview of topics
• Sept 26: Linear Algebra Review
• Sept 28: Linear Algebra and Intro to systems of ODEs

Week 2: Sections 7.4-7.6

• Oct 1: How to solve a system, Begin analysis of two distinct real eigenvalues
• Oct 3: Distinct real eignevalues
• Oct 5: Begin analysis of complex eigenvalues

Week 3: Sections 7.6-7.8

• Oct 8: Analysis of systems with complex eigenvalues
• Oct 10: Fundamental Matrices and the Matrix Exponential
• Oct 12: Repeated Real Eigenvalues and Generalized Eigenvectors

Week 4: Sections 7.8, 7.9, 9.1, 9.2

• Oct 15: Finish repeated eigenvalues
• Oct 17: Nonhomogeneous Systems
• Oct 19: Stability, trace-determinant plane, selected topics (time permitting)

Week 5: Midterm week

• Oct 22: Review Day (no quiz)
• Oct 24: Midterm
• Oct 26: Introduction to PDEs

Week 6: Sections 10.1, 10.5, 10.2, 10.3

• Oct 29: The eigenvalue problem, separation of variables
• Oct 31: Introduction to Fourier series
• Nov 2: Euler-Fourier formulas and Fourier convergence

Week 7: Sections 10.4, 10.5, 10.6

• Nov 5: Sine and Cosine series
• Nov 7: Applications of Fourier series
• Nov 9: Returning to the heat equation

Week 8: Section 10.7

• Nov 12: No class
• Nov 14: Introduction to the wave equation
• Nov 16: Wave equation variations and properties

Week 9: Section 10.8

• Nov 19: Comparison of wave and heat equation, Introduction to Laplace's equation
• Nov 21: Laplace's equation
• Nov 23: No class

Week 10: Harmonic Function Notes 2-3.1

• Nov 26: Finish Dirichlet Problem on Rectangle, Start DP on Disk
• Nov 28: Poisson Integral Formula
• Nov 30: Properties of Harmonic Functions

Week 11: Harmonic Function Notes Chapter 3

• Dec 3: Applications of Mean Value Property and Maximal Principle
• Dec 5: Finish remaining harmonic functions, Generalities on PDEs
• Dec 7: Review Day