Module Information

Module Identifier
Module Title
Further Algebra and Calculus
Academic Year
Semester 2
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 22 Hours. (22 x 1 hour lectures)
Seminars / Tutorials 5 Hours. (5 x 1 hour tutorials)


Assessment Type Assessment length / details Proportion
Semester Assessment Continuous assessment component is made up from a combination of attendance at lectures (6%), attendance at tutorials (6%) and marks gained from assessed assignments (8%).  20%
Semester Exam 2 Hours   (written examination)  80%
Supplementary Assessment 2 Hours   (written examination)  100%

Learning Outcomes

On successful completion of this module students should be able to:

1. solve systems of linear equations,
2. manipulate matrices according to the laws of matrix algebra,
3. evaluate determinants of square matrices,
4. determine partial derivatives of functions of several variables and establish identities involving them,
5. obtain the critical points of functions of several variables,
6. evaluate multiple integrals in rectangular coordinates,
7. evaluate multiple integrals using change of variables.

Brief 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.


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 integrals in rectangular coordinates; areas. Substitution in multiple integrals.

Reading List

Recommended Text
H Anton & C Rorres (2000) Elementary Linear Algebra: Applications Version 8th J Wiley Primo search Weir, M D, Haas, J and Giordano, F R (2005) Thomas' Calculus 11/e Addison Wesley Primo search
Supplementary Text
D.W.Jordan & P.Smith (1994) Mathematical Techniques: an introduction for the engineering, physical and mathematical sciences Oxford University Press Primo search J Stewart (2001) Calculus : concepts and contexts 2/e Brooks/Cole Primo search Lay, David C. (Nov. 2002) Linear Algebra and Its Applications 3/e Addison-Wesley Primo search R L Finney & G B Thomas (1994) Calculus 2nd Addison-Wesley Primo search T S Blyth & E F Robertson Basic Linear Algebra Springer Primo search


This module is at CQFW Level 4