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Curricular information is subject to change
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. Prove key results such as Bessel’s inequality, Parseval’s equality and its relationship to completeness
Student Effort Type | Hours |
---|---|
Lectures | 36 |
Specified Learning Activities | 24 |
Autonomous Student Learning | 40 |
Total | 100 |
Not applicable to this module.
Description | Timing | Component Scale | % of Final Grade | ||
---|---|---|---|---|---|
Assignment(Including Essay): In-depth assignment linking lecture notes to key skills such as solving mathematical problems, proving theorems, writing up results clearly, etc. | n/a | Standard conversion grade scale 40% | No | 20 |
|
Exam (In-person): Final exam to assess all the learning outcomes of the module | n/a | Standard conversion grade scale 40% | No | 80 |
Resit In | Terminal Exam |
---|---|
Autumn | Yes - 2 Hour |
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
Not yet recorded.