Next: MC226 Numerical Linear Algebra
Up: Year 2
Previous: MC223 Relativity
MC224 Vector Calculus
Credits: 10 
Convenor: Dr. M. Walmsley 
Semester: 1 (weeks 1 to 6) 
Prerequisites: 
essential: MC125, MC126 
desirable: MC144, MC145, MC146, MC147 
Assessment: 
Coursework: 20% 
One and a half hour exam: 80% 
Lectures: 
18 
Classes: 
5 
Tutorials: 
none 
Private Study: 
52 
Labs: 
none 
Seminars: 
none 
Project: 
none 
Other: 
none 
Total: 
75 


Explanation of Prerequisites
The work on vectors, curves, partial differentiation and multiple
integrals, which was covered in MC126, will form a basis for this
module. A general mathematical knowledge
from other modules is also required.
Course Description
This module will extend the vector algebra of the first year to the calculus
of three dimensional vectors. This is an essential module for those wishing
to take certain later modules in Applied Mathematics, for example
Fluids and Waves, General Relativity, Electromagnetic Theory etc.
Aims
The use of vectors simplifies and condenses the
mathematical discussion of many problems which arise in applied mathematics
and so this module forms a basis for many later modules. However, vector
calculus may be studied in its own right and here links with multivariable
analysis will be apparent.
Objectives
To be familiar with scalar, vector and triple products and their use in
the description of lines and planes.
To be familiar with the use of the summation convention including the
Kronecker delta and the alternating tensor .
To know the definitions of, and to be able to use, the vector differential
operators grad, div and curl, and the Laplacian.
To be able to work with line, surface and volume integrals.
To be able to state and use in simple cases Green's theorem in the plane,
the divergence theorem and Stokes' theorem.
Transferable Skills
This module provides essential mathematics for any practising applied
mathematician.
Syllabus
Introduction to vector algebra.
Introduction of suffix notation and the summation convention including
and .
The vector differential operators grad, div and curl.
Line, surface and volume integrals with particular application to the
divergence theorem and Stokes' theorem.
Reading list
Background:
M. R. Spiegel,
Vector Analysis,
Schaum Outline Series.
H. P. Hsu,
Applied Vector Calculus,
Harcourt Brace Jovanovich College Outline Series.
E. A. Maxwell,
Coordinate Geometry with Vectors and Tensors,
CUP? Probably out of print..
J. Gilbert,
Guide to Mathematical Methods,
MacMillan.
P.C. Matthews,
Vector Calculus,
Springer
There are in addition a number of Vector Analysis texts located at 515.63 in
the Library.
Details of Assessment
There will be four pieces of work of equal weight set for assessment and
these together count for 20% of the final mark. The examination paper
contains four questions. Any number of questions may be attempted but
only the best three answers will be taken into account. Full marks may
be obtained for answers to three questions, and all questions carry
equal weight.
Next: MC226 Numerical Linear Algebra
Up: Year 2
Previous: MC223 Relativity
S. J. Ambler
11/20/1999