Module code: G5110
15 credits in spring teaching
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination
In this module, the topics you will cover will include:
- holomorphic functions, Cauchy's theorem and its consequences
- power series, integration, differentiation and analysis of convergence
- Taylor expansions and circle of convergence
- Laurent expansions and classification of isolated singularities
- residue theorem and evaluation of integrals
- Rouche's theorem and the fundamental theorem of algebra.
Module learning outcomes
- Substantially increased strength in analysis and analytical rigor, including analytic proofs and constructions from first principles;
- an algebraic and geometric understanding of complex numbers and complex multiplication including finding explicit roots of simple polynomials;
- an appreciation for how holomorphic functions refine the notion of real differentiability and the strong consequences of being differentiable in the complex sense;
- a working knowledge of power series, Laurent series, the residue theorem and the evaluation of real integrals via complex singularities and residues.