Week 1: Sections 7.1-7.4

• June 20: Introduction and start in depth linear algebra review
• June 22: Review of Linear Algebra
• June 24: Introduction to Systems of First Order Linear Equations

Week 2: Sections 7.5-7.7

• June 27: Analysis of Systems with Distinct Real Roots
• June 29: Analysis of Systems with Complex Eigenvalues
• July 1: Fundamental Matrices and the Exponential

Week 3: Sections 7.8-7.9

• July 4: No class
• July 6: Repeated Real Eigenvalues and Generalized Eigenvectors
• July 8: Nonhomogeneous systems

Week 4: Sections 7.9, 9.1, 9.2

• July 11: Finish nonhomogeneous techniques, stability of critical points
• July 13: Trace, determinant plane and placing 2x2 systems in a broader context
• July 15: Review day

Week 5: Sections 10.1 and 10.5

• July 18: Midterm
• July 20: Intro to PDEs and review of specific second order ODEs
• July 22: The Method of Separation of Variables

Week 6:Sections 10.2, 10.3, 10.4

• July 25: Deriving the Euler-Fourier Formulas
• July 27: Computing Fourier Series and Convergence Issues
• July 29: Sine and Cosine Series

Week 7: Sections 10.6 and 10.7

• Aug 1: Variations on the Heat Equation
• Aug 3: Derivation and Separation of Variables of the Wave Equation
• Aug 5: Wave Equation Examples and General Analysis of the Solution

Week 8: Section 10.8 and Harmonic Functions

• Aug 8: Introduction to Laplace's equation and Harmonic Functions
• Aug 10: Solving the Dirichlet Problem
• Aug 12: Properties of Harmonic Functions

Week 9: Review and Final

• Aug 15: Alternative methods for PDEs
• Aug 17: Review Day
• Aug 19: Final Exam