MAT-20004: Complex Variable I and Vector Calculus

School of Computing and Mathematics

MAT-20004

Complex Variable I and Vector Calculus

Co-ordinator:

Dr Maria Heckl Room: MAC2.23, Tel:33423

Teaching Team:

Level:

Credits:

Study Hours:

150

School Office:

Tel: 01782 733075

Programme/Approved Electives for

None

Available as a Free Standing Elective

Prerequisites

Level 1 Mathematics or equivalent

Barred Combinations

None

Description

This module contains a first course on vector calculus and a first course in functions of a complex variable. 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 topics covered include: complex functions, analytic functions, Cauchy&©s theorems, complex power series, singularities, the residue theorem, contour integration, differentiation of vectors, differential operators, integration of vectors, the divergence theorem and Stokes&© theorem.

Aims

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.

Intended Learning Outcomes

Differentiate vector functions of real variable and apply results to find arc lengths, tangents and normals to curves (1, 2).
Calculate the divergence and curl of a vector function and derive their properties (1, 2).
Apply knowledge of the divergence and curl to find tangent planes, normals to surfaces and surface area (1, 2).
Calculate line, volume and surface integrals (1, 2).
Derive and apply Green&©s Theorem, the Divergence Theorem and Stokes&©s Theorem (1, 2).
Derive elementary properties of functions of a complex variable (1, 2).
Derive and apply the Cauchy-Riemann equations related to differentiation (1, 2).
Calculate definite integrals of a function of a complex variable (1. 2).
Derive and apply the Fundamental Theorem of Calculus, Cauchy&©s Theorem and Cauchy&©s Integral Formula (1, 2).
Derive and apply the Residue Theorem to calculate complex definite integrals, with application to the calculation of real integrals of certain types (1, 2).

Study hours

Lectures: 36 hours
Examples Classes: 12 hours
Preparation of coursework: 24 hours
Independent study: 78 hours

Description of Module Assessment

1: Exercise weighted 20%

PROBLEM SOLVING
Approximately 10 assignments set at weekly intervals

2: 2 Hour Unseen Exam weighted 80%

2 HOUR UNSEEN EXAM
Two hour unseen examination, answer 4 questions from 6

Version: (1.04S) Created: 04/Jun/2010

This document is the definitive current source of information about this module and supersedes any other information.