Module Identifier MA11010  
Academic Year 2001/2002  
Co-ordinator Dr T McDonough  
Semester Semester 2  
Other staff Dr Jane Pearson  
Pre-Requisite MA10020  
Course delivery Lecture   20 x 1 hour lectures  
  Seminars / Tutorials   5 x 1 hour tutorials  
  Workshop   2 x 1 hour workshops (including test)  
Assessment Continuous assessment     25%  
  Exam   2 Hours (written examination)   75%  
  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, symmetric, skew-symmetric, orthogonal). Row equivalence.
2. LINEAR EQUATIONS: Systems of linear equations. Coefficient matrix, augmented matrix. Elementary row operations. Gaussian and Gauss-Jordan elimination.
3. DETERMINANTS: Properties of determinants. Computation of determinants.
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. Addison-Wesley 0201549778
H Anton & C Rorres. (2000) Elementary Linear Algebra: Applications Version. 8th. J Wiley 0471170526
** Supplementary Text
T S Blyth & E F Robertson. Basic Linear Algebra. Springer 3540761225
D.W.Jordan & P.Smith. (1994) Mathematical Techniques: an introduction for the engineering, physical and mathematical sciences. Oxford University Press 0198562683