Mathematics

Partial Differential Equations

Module code: G1114
Level 6
15 credits in autumn teaching
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

Topics include: 

  • second-order partial differential equations (wave equation, heat equation, Laplace equation)
  • D'Alembert's solution
  • separation of variables
  • Duhamel's principle
  • energy method
  • Maximum principle
  • Green's identities.

Module learning outcomes

  • Know the classification of second-order partial differential equations;
  • Be able to solve model problems involving second-order partial differential equations;
  • Be able to formulate the standard boundary-value, initial-value and boundary-initial-value problems for the Laplace, heat and wave equations;
  • Be able to state and prove the uniqueness and existence theorems for the above equations using the energy method and the Maximum principle.