SYLLABUS AND NOTES

• Syllabus
• Useful ODE facts
• Useful calculus facts
• 1. Some definitions
• 2. Separation of variables
• 3. Method of characteristics
• 4. Second-order linear equations
• 5. Wave equation: initial value problem
• 6. Wave equation: boundary value problems
• 7. Wave equation: remaining facts
• 8. Heat equation: initial value problem
• 9. Heat equation: boundary value problems
• 10. Laplace equation: general facts
• 11. Laplace equation: Poisson formulas
• 12. Burgers' equation

EXAM-RELATED MATERIAL

• Solutions for the 2007 exam. You may ignore questions 7 and 9.
• Solutions for the 2009 exam. You may ignore questions 3 and 6.
• You should know how to prove these results. You will find their proofs here.