MA22033: Analysis 2B
[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: | |
| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA22032
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| Learning Outcomes: |
After taking this unit, you should be able to:
- demonstrate a good knowledge and understanding of the topology of Euclidean spaces, differentiation of functions of several variables, and the inverse and implicit function theorems;
- find derivatives of functions of several variables and draw conclusions about the properties of these functions;
- analyse surfaces and submanifolds defined by equations;
- apply the theory to simple examples.
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| Synopsis: | Continuing from Analysis 2A, you will extend the key ideas and methods from mathematical analysis to study functions of several variables.
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| Content: | Topology of Euclidean spaces: Bolzano-Weierstrass, Heine-Borel, and Weierstrass theorems. Decreasing sets.
Differentiation of functions of several variables: Frechet derivative, partial derivatives, Jacobian matrix and directional derivatives. Chain rule. Symmetry of the second derivative. Higher order partial derivatives and the Hessian matrix. Stationary points and second derivative test. Taylor's theorem.
Inverse and implicit function theorems for continuously differentiable maps, surfaces (submanifolds) defined by equations.
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| Course availability: |
MA22033 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-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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