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Module Title
LI Multivariable & Vector Analysis
School
Mathematics
Department
Mathematics
Module Code
06 25667
Module Lead
Dr Chris Good
Level
Intermediate Level
Credits
20
Semester
Semester 1
Pre-requisites
Co-requisites
Restrictions
None
Exclusions
Description
Most models of real world situations depend on more than one variable and the techniques of calculus can be extended to solve problems arising in such situations. Typically these are problems whose solutions are functions of position, describing, for example, heat distribution or velocity potential, and involve the partial differentiation or multiple integration of functions of more than one variable. The theory and classification of stationary points of functions of two or more variables is developed allowing maxima and minima, including those subject to constraints, to be identified. The differential operators div, grad, curl and the Laplacian are introduced. These are used in particular in the integral theorems (the Divergence theorem and the theorems of Green and Stokes) that relate line, surface and volume integrals and are used in the mathematical formulation of physical conservation laws. This module develops fundamental ideas that are used both in applied mathematics and in the development of analysis.
Learning Outcomes
By the end of the module students should be able to:
use the notation and basic manipulative techniques of the calculus of functions of several real variables
apply a variety of analytic and numerical techniques to solve problems in the calculus of several real variables, e.g. to find and analyse the stationary points of functions of more than one variable
evaluate line and multiple (surface and volume) integrals
evaluate grad, div, curl and the Laplacian in Cartesian and orthogonal curvilinear coordinates
State and apply the integral theorems of vector analysis, namely Stokes' and Green’s theorems and the divergence theorem
recognise conservative vector fields and their properties
Assessment
25667-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions
3 hour Written Unseen Examination (80%); In-course Assessment (20%).
