School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 30 May 2020

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: 1,2,3

1,2,3

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:

1,2,3

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 and class tests: 24 hours

Independent study: 76 hours

Unseen examination: 2 hours

Tutorials: 12 hours

Preparation of coursework and class tests: 24 hours

Independent study: 76 hours

Unseen examination: 2 hours

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Take-home assignments

Two equally weighted take-home, written assignments. Each assignment consists of a set of questions with pre-allocated space for written solutions. The assignments are set at regular intervals across the semester. Students should expect to spend 12 hours across the semester on their assignments.¿

Two class tests.

Two class tests to assess both theoretical and practical aspects of the module. The class tests are equally weighted. Each class test will last 40 minutes.

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.