Lecture Notes

• First order ODEs (PDF)
• Linear systems (theory) (PDF)
• Solving LCC systems/ODEs (PDF)
• Inhomogeneous ODEs (PDF)
• LCC systems in n-d (PDF)
• Dynamics in 1d (autonomous) (PDF)
• Phase planes; planar LCC systems (PDF)
• Dynamics in 2d; nonlinear (PDF)
• Conservative systems; Lyapunov functions (PDF)
• Fourier series (PDF)
• PDEs: preliminaries (PDF)
• BVPs and eigenfunctions (PDF)
• The heat and wave equations (PDF)
• Time-independent problems; Laplace's equation (PDF)
• Laplace's equation in a disk (PDF)
• Sturm-Liouville theory; inhomgoeneous BCs (PDF)
• Eigenvalue estimates; graphical approach (PDF)
• Phase portraits (summary) (PDF)

Homework

• Homework 1 (PDF)
• Homework 2 (PDF)
• Homework 3 (PDF)
• Homework 4 (PDF)
• [pre-midterm HW] (PDF)
• Homework 5 (PDF)
• Homework 6 (PDF)
• Homework 7 (PDF)
• Homework 8 (PDF)
• Homework 9 (PDF)

Examples/Review

• Midterm Exam I (PDF)
• Midterm Exam II (PDF)
• Midterm I Review problems (PDF)
• Final Review problems (PDF)
• Midterm I Study Guide (PDF)
• Midterm II Study Guide (PDF)
• Formula sheet (PDF)