Learning Outcomes:
On completion of this module students should be able to:
1. Understand conditions guaranteeing existence and uniqueness results for ordinary differential equations and recognize examples where those conditions do not hold;
2. State and prove Picard’s theorem;
3. Transform between an initial value problem and the corresponding Volterra integral equation;
4. Transform between a boundary value problem and the corresponding Fredholm integral equation;
5. State the axiomatic properties of the Green function for a second order initial value problem and boundary value problem;
6. Understand the concept of the adjoint differential operator;
7. Recognise a Sturm-Liouville eigenvalue problem and prove the basic properties of eigenvalues and eigenfunctions;
8. Understand the fundamental properties of infinite-dimensional vectors spaces;
9. Understand the application of these techniques to standard problems in Applied Mathematics.