Course Details in 2027/28 Session

Module Title	LH Multivariable and Vector Analysis
School	Mathematics
Department	Mathematics
Module Code	06 35172
Module Lead	Michael Grove
Level	Honours Level
Credits	20
Semester	Semester 1
Pre-requisites	LC Real Analysis - (06 34051)
Co-requisites
Restrictions	None
Contact Hours	Lecture-46 hours Tutorial-10 hours Guided independent study-144 hours Total: 200 hours
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, including situations involving novel and real-world applications. Evaluate line and multiple (surface and volume) integrals and 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 and recognise conservative vector fields and their properties. Demonstrate an understanding of the applications of vector calculus to a range of real-world problems in (for example) physics and engineering, and be able to independently apply the knowledge and mathematical techniques developed in this module to model and solve problems drawn from diverse areas and contexts.
Assessment	35172-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	3 hour Written Unseen Examination (80%); In-course Assessment (20%).
Other
Reading List