MA32043: Analysis of ordinary differential equations
[Page last updated: 22 May 2025]
| Academic Year: | 2025/26 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Honours (FHEQ level 6) |
| Period: |
- Semester 1
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| Assessment Summary: | EXCB 100% |
| Assessment Detail: |
- Closed-book written examination (EXCB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA22032 OR take MA20218
In taking this module you cannot take MA30062
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| Learning Outcomes: |
After taking this unit, students should be able to:
- Demonstrate understanding of and prove basic results in the theory of ordinary differential equations including: existence and uniqueness for the initial value problem, basic properties of flows and basic properties of limit sets.
- Apply the theory to analyse the behaviour of simple examples.
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| Synopsis: | Ordinary differential equations (ODEs) are found across mathematics, as well as natural and social sciences and engineering. In this unit, you will develop your understanding of the qualitative and quantitative properties of their solutions.
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| Content: | Topics will be chosen from the following:
General definition of an ODE. Examples from diverse areas. Solutions of linear ODEs. Explicit solutions for specific nonlinear ODEs. Estimates of solutions using Gronwall's lemma. Proof of existence and uniqueness for solutions for ODEs with sufficiently regular coefficients, maximal solutions, continuous dependence on initial conditions. Autonomous ODEs: introduction to flows, periodic flows, geometric flows, orbits, limit sets, application to examples. Lyapunov functions, La Salle's invariance principle, dynamical approaches to states of equilibria and their associated stability, geometric approaches to states of equilibria, linearisation theory.
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| Course availability: |
MA32043 is Optional on the following courses:
Department of Mathematical Sciences
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB30 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFM30 : MMath(Hons) Mathematics (Year 3)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
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Notes: - This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
- 好色tv and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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