Mathematics

Differential Equations

Module code: G5097
Level 5
15 credits in spring teaching
Teaching method: Class, Lecture, Workshop
Assessment modes: Unseen examination, Coursework

In this module, the topics you will cover will include:

Ordinary differential equations:

  • solution methods; variation of the constant formula, separation of variables
  • solution of linear ODE with constant coefficients
  • Lipschitz continuity
  • existence and uniqueness (Picard-Lindeloef), maximal solutions, Gronwall
  • higher order equations into system of first order
  • boundary value problems.

Partial differential equations:

  • partial and total derivatives
  • first order PDEs; method of characteristics for semilinear and quasilinear equations, initial boundary value problems.

Module learning outcomes

  • At the end of the course the successful student will be able to: explain Picard-Lindeloef existence and uniqueness result for ordinary differential equations; formulate and solve some initial and boundary value problems for ordinary differential equations, and partial differential equations of first order