Module Identifier MA11010  
Academic Year 2000/2001  
Co-ordinator Dr T P McDonough  
Semester Semester 2  
Other staff Dr R J Douglas, Dr V C Mavron, Dr J M Pearson  
Pre-Requisite MA10020  
Course delivery Lecture   20 x 1 hour lectures  
  Seminars / Tutorials   6 x 1 hour tutorials  
  Workshop   2 x 1 hour workshops (including test)  
Assessment Exam   2 Hours (written examination)   75%  
  Continuous assessment     25%  
  Resit assessment   2 Hours (written examination)   100%  

General description
The aim of this module is to study situations in which functions of several variables arise naturally in Mathematics. Linear functions lead to techniques for the solution of linear equations and elementary matrix theory. Non-linear functions lead to a study of partial derivatives and multiple integrals.

To establish a clear understanding of the techniques for studying functions of several variables and a facility for recognising when these techniques may be profitably employed.

Learning outcomes
On completion of this module, a student should be able to:

1. MATRIX ALGEBRA: Matrix operations (addition, scalar multiplication, matrix multiplication, transposition, inversion). Special types of matrices (zero, identity, diagonal, triangular, unimodular, symmetric, skew-symmetric, orthogonal). Row equivalence. LU factorisation.
2. LINEAR EQUATIONS: Systems of linear equations. Coefficient matrix, augmented matrix. Elementary row operations. Gaussian and Gauss-Jordan elimination.
3. DETERMINANTS: Properties of determinants. Matrix cofactors, adjoints and inverses.
4. PARTIAL DERIVATIVES: Functions of several variables. Partial Derivatives. Differentiability and linearisation. The chain rule. Critical points. Change of variables - the Jacobian.
5. MULTIPLE INTEGRALS: Riemann sums and definite integrals. Double and triple integrals in rectangular coordinates. Areas and volumes. Substitution in multiple integrals.

Reading Lists
** Recommended Text
R L Finney & G B Thomas. (1994) Calculus. 2nd edition. Addison-Wesley
H Anton & C Rorres. (2000) Elementary Linear Algebra: Applications Version. 8th edition. J Wiley
** Supplementary Text
T S Blyth & E F Robertson. Basic Linear Algebra. Springer
D.W.Jordan & P.Smith. Mathematical Techniques: an introduction for the enginee ring, physical and mathematical sciences. Oxford University Press