Complex Analysis (L7) (975G1)
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Complex Analysis (L7)
Module 975G1
Module details for 2025/26.
15 credits
FHEQ Level 7 (Masters)
Module Outline
The module will explore the extension of mathematical analysis from the real numbers to the larger field of complex numbers, with an appeal to planar geometry for some intuition. The module will focus on complex differentiation and path integrals, including the deep theorem of Cauchy and its consequences such as the fundamental theorem of algebra, analytic continuation and the residue theorem.
Module learning outcomes
Comprehensively understand the key algebraic structures and geometric interpretations of the field of complex numbers including de Moivre’s identity and complex roots of unity
Comprehensively recognize and explain the differences between differentiable real functions and holomorphic complex functions
Demonstrate a comprehensive understanding of the deep theorem of Cauchy and its consequences including applications to standard problems in complex analysis
Evaluate certain real integrals via a rigorous application of the residue theorem for complex path integrals
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 20.00% | |
| Coursework components. Weighted as shown below. | ||
| Problem Set | T2 Week 6 | 15.00% |
| Problem Set | T2 Week 9 | 15.00% |
| Problem Set | T2 Week 11 | 15.00% |
| Portfolio | T2 Week 11 | 40.00% |
| Problem Set | T2 Week 4 | 15.00% |
| Unseen Examination | Semester 2 Assessment | 80.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring Semester | Lecture | 1 hour | 11111111111 |
| Spring Semester | Lecture | 2 hours | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Gabriel Koch
Convenor, Assess convenor
/profiles/284961
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