Important Dates
Exams
Exam 1: Wednesday, October 24
Final: Tuesday, December 11, 2:30-4:20 pm
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