Topic outline

  • General

  • Week 1: Introductions to PDEs

  • Week 2: First order PDEs

  • Week 3: Classification of second order PDEs

  • Week 4: D' Alembert's formula for wave equations on the real line

  • Week 5: Separation of variables and wave equations on the intervals

  • Week 6: Duhamel's principle and inhomogenous wave equations

  • Week 7: Reading week

  • Week 8: Harmonic functions and Laplace equations on symmetric domains

  • Week 9: Properties of harmonic functions

  • Week 10: Heat equation on intervals and energy monotonicity

  • Week 11: Heat kernels and heat equations on the real line

  • Week 12: Further properties of heat equations

  • Assessment information

    • Assessment patterns: 80% final exam + 20% coursework