MATH3000

MATH3000: Complex Analysis

Science and Engineering

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About this Unit

This unit broadly covers topics in Complex Analysis, which is the theory of functions of a complex variable. It has applications in a plethora of areas of science and engineering. Examples include theoretical and applied mathematics (and in particular number theory, statistics and combinatorics), physics (for example quantum mechanics, but also thermodynamics), and mechanical and electrical engineering (signal processing and control theory just to mention two). First, we discover that the set of complex numbers is a natural completion of the set of real numbers. Then, we proceed with the introduction of the fundamental complex elementary functions which generalise well-known functions over subsets of the real line: the complex exponential function, the complex sine/cosine and hyperbolic sine/cosine functions, the principal logarithm, power and exponent functions to name a few. We then introduce the notion of complex analytic function, which plays a central role in Complex Analysis: we will discover new regularity properties of complex analytic functions that have no counterpart in the real case.This unit culminates with the so-called Residue Theory, which gives us exciting new methods of integration which enable us to tackle the calculation of integrals that cannot be handled using the standard techniques developed in other units. A further mathematical tool developed in this unit is the Laplace transform, which has countless applications in all areas involving the solution of linear differential equations. Its role is to reduce a linear differential equation, or a system of linear differential equations, to an algebraic problem.

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Unit Details

Credits25

Contact Hours4 Weekly

Result TypeGrade/Mark

AreaSchool of Electrical Engineering, Computing and Mathematical Sciences (EECMS) (1153)

Field of Education010101 Mathematics

Handbook View Official Handbook Page →

Tuition Pattern

Lecture1 x 2 hours weekly
Workshop1 x 2 hours weekly

Prerequisites

PrerequisitesSelect One

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