Courses :: Module, INTRODUCTION TO COMPLEX ANALYSIS

	Overview
	Complex numbers, regions in the complex plane. Complex functions, the derivative of a complex function, holomorphic functions, harmonic functions. The Cauchy-Riemann equations, Cauchy's Theorem, Cauchy's Integral Formula. Taylor series and examples, Laurent series. The residue theorem. Computation using mathematical/statistical software.

Overview

Complex numbers, regions in the complex plane. Complex functions, the derivative of a complex function, holomorphic functions, harmonic functions. The Cauchy-Riemann equations, Cauchy's Theorem, Cauchy's Integral Formula. Taylor series and examples, Laurent series. The residue theorem. Computation using mathematical/statistical software.

	Learning Outcomes
	On successful completion of the module, students should be able to: Differentiate and integrate functions of a complex variable. Define the exponential, logarithmic and trigonometric functions. Test for the analyticity of a given function. Use the methods from the course to solve problems. State definitions and theorems covered in the course. Prove simple results in complex analysis using rigorous arguments.

Learning Outcomes

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes Is Supplemental Continuous Assessment registration permitted? No Is Supplemental Continuous Assessment capped? No

Autumn Supplementals/Resits

	Pre-Requisites
	MT201S/MT201A and MT202S/MT202A, or equivalent.

Pre-Requisites

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Courses / Module

INTRODUCTION TO COMPLEX ANALYSIS

Semester 1

Semester 2