Last modified: 28 Jun 2018 10:27
Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on MX3035 Analysis III, continuing the development of multivariable calculus, with a focus on multivariable integration. Hilbert spaces (infinite dimensional Euclidean spaces) are also introduced.
Students will see the benefit of having acquired the formal reasoning skills developed in Analysis I, II, and III, as it enables them to work with increasingly abstract concepts and deep results. Techniques of rigourous argumentation continue to be a prominent part of the course.
| Study Type | Undergraduate | Level | 3 |
|---|---|---|---|
| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Old Aberdeen | Sustained Study | No |
| Co-ordinators |
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Course Aims
To provide students with the basic knowledge of the modern mathematical analysis.
Main Learning Outcomes
* Understanding definitions of the basic concepts of mathematical analysis (real number, limit, continuity, differential, integral etc).
* Fluency in computing limits, differentials and integrals and in manipulating with elementary functions.
* Understanding basic scientific applications of the mathematical concepts discussed in the course.
Course Content
- Multivariable Riemann integration; volume of subsets of Euclidean space
- Fubini and Tonelli Theorems
- Stokes's and Green's Theorems
- Introduction to Hilbert spaces
Information on contact teaching time is available from the course guide.
1st attempt - 1 two-hour written examination (80%); in-course assessment (20%).
Resit – 1 two-hour written examination paper. Maximum of written exam (100%) or written exam (80%) with carried forward in-course assessment (20%).
Informal assessment of weekly homework through discussions in tutorials.
In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.
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