- Department: Mathematics
- Credit value: 10 credits
- Credit level: I
- Academic year of delivery: 2022-23
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Occurrence | Teaching period |
---|---|
A | Spring Term 2022-23 |
The Core modules in the second year of mathematics programmes cover material which is essential for accessing a wide range of topics later on. Such material underpins the development of mathematics across all three of the major streams we offer through our single-subject degrees, and it is also very important for many combined programmes. As well as covering fundamental material, these modules address applications and techniques which all students will subsequently be able to draw on in various contexts.
As part of the broad aims outlined above, this module considers two important developments in calculus and analysis. First, differentiable functions of a complex variable have very many properties beyond those of the differentiable functions of real variables that were studied previously. This has applications to the expansion of functions in power series and also to the important techniques of contour integration. Second, a powerful tool both in applied mathematics and analysis is the Fourier transform, which has applications in many areas.
Academic and graduate skills
Academic Skills: our second year Core modules continue to develop themes which start in the first year, such as the application of rigorous mathematical techniques and ideas to the development of mathematics; the power of abstraction as a way of solving many similar problems at the same time; the development and consolidation of essential skills which a mathematician needs in their toolkit and needs to be able to use without pausing for thought.
Graduate skills: The techniques of Fourier analysis developed in this course are widely used in real-world applications (some of which the students will encounter during the module). These techniques are used by many graduates in their day-to-day work.
This module will extend the ideas developed about real functions to complex functions, develop the theory of holomorphic functions, and apply this theory to understand problems arising in real analysis or calculus and describe the idea and basic properties of the Fourier transform, indicating their applications in fields such as digital signal processing and differential equations.
Subject content
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
H A Priestley "Introduction to Complex Analysis" (2 ed) OUP 2003, JBM S7
A Pinkus and S Zafrany, Fourier Series and Integral Transforms (S 7.39 PIN)