MA22021: Partial differential equations
[Page last updated: 03 June 2024]
| Academic Year: | 2024/25 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Intermediate (FHEQ level 5) |
| Period: |
- Semester 2
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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 MA22016
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| Learning Outcomes: |
* Discuss and apply the basic concepts of Fourier series.
* Discuss the Laplace, heat, and wave equations and their applications.
* Solve the Laplace, heat, and wave equations in simple domains using separation of variables.
* Discuss and apply basic conservation laws for PDEs.
* Write relevant mathematical arguments in a precise and lucid fashion.
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| Synopsis: | In this unit you will develop your understanding of partial differential equations. You will review the three basic classes of linear PDE. You will study techniques for solving and analysing this type of equation. This unit will provide you with a foundation for further study in many important areas of applied maths including fluid dynamics, mathematical physics and mathematical biology.
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| Content: | Fourier series: formal introduction; convergence theorem; Fourier sine and cosine series. Partial differential equations: classification of linear second order PDEs; solution by separation of variables for Laplace's equation in two dimensions, heat and wave equations in one dimension; d'Alembert's formula for wave equation; elementary potential theory and conservation laws.
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| Course availability: |
MA22021 is Compulsory on the following courses:
Department of Physics
- USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 2)
- USPH-AKB26 : BSc(Hons) Mathematics and Physics with professional placement (Year 2)
- USPH-AKB26 : BSc(Hons) Mathematics and Physics with study abroad (Year 2)
- USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 2)
- USPH-AKM26 : MSci(Hons) Mathematics and Physics with professional placement (Year 2)
- USPH-AKM26 : MSci(Hons) Mathematics and Physics with study abroad (Year 2)
MA22021 is Optional on the following courses:
Department of Mathematical Sciences
- USMA-AFB30 : BSc(Hons) Mathematics (Year 2)
- USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 2)
- USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 2)
- USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 2)
- USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 2)
- USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 2)
- USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 2)
- USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 2)
- USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 2)
- USMA-AFM30 : MMath(Hons) Mathematics (Year 2)
- USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 2)
- USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 2)
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Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- Courses 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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