School of Computer Science and Mathematics

Faculty of Natural Sciences

For academic year: 2024/25 Last Updated: 17 May 2024

MAT-20004 - Complex Variable I and Vector Calculus

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This module contains a first course on vector calculus and a first course in functions of a complex variable. The topics covered include complex functions, differentiation and integration, Cauchy's Theorems, Taylor and Laurent Series, singularities, the Residue Theorem, differentiation of vectors, differential operators, line, volume and surface integrals, Green's Theorem, the Divergence Theorem and Stokes' Theorem.

Complex variable leads to elegant results in pure mathematics and both complex variable and vector calculus provide a framework for solving physical and geometrical problems.

Complex variable leads to elegant results in pure mathematics and both complex variable and vector calculus provide a framework for solving physical and geometrical problems.

The aim of this module is to introduce the core subjects of vector calculus and complex variable and to provide some of their many and varied applications.

analyse a problem involving vector functions, then select and apply appropriate theoretical material and/or computational methods to solve the problem: 1,3

2,3

1,2,3

combine theoretical results to prove theorems involving vector and complex functions: 3

analyse a problem involving complex functions, then select and apply appropriate theoretical material and/or computational methods to solve the problem: state and/or prove standard theorems involving vector and complex functions:

2,3

1,2,3

combine theoretical results to prove theorems involving vector and complex functions: 3

analyse a problem involving complex functions, then select and apply appropriate theoretical material and/or computational methods to solve the problem: state and/or prove standard theorems involving vector and complex functions:

Lectures: 36 hours

Tutorials: 12 hours

Preparation of coursework assignments: 12 hours

Independent study: 88 hours

Unseen examination: 2 hours

Tutorials: 12 hours

Preparation of coursework assignments: 12 hours

Independent study: 88 hours

Unseen examination: 2 hours

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Take-home assignment on Vector Calculus

An assignment, containing a set of questions on Vector Calculus, with pre-allocated space for written solutions. Students should expect to spend 6 hours on this assignment.¿

Take-home assignment on complex functions

An assignment, containing a set of questions on Complex Variable, with pre-allocated space for written solutions. Students should expect to spend 6 hours on this assignment.¿

2-hour unseen examination

The examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.