|| MA11010 |
|| FURTHER ALGEBRA AND CALCULUS |
|| 2003/2004 |
|| Dr T McDonough |
|| Semester 2 |
|| MA10020 |
| Course delivery
|| Lecture || 20 x 1 hour lectures |
|| Seminars / Tutorials || 5 x 1 hour tutorials |
|| Other || Workshop. 2 x 1 hour workshops (including test) |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||75%|
|Semester Assessment|| Continuous Assessment: ||25%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
On completion of this module, a student should be able to:
solve systems of linear equations,
manipulate matrices according to the laws of matrix algebra,
evaluate determinants of square matrices,
determine partial derivatives of functions of several variables and establish identities involving them,
obtain the critical points of functions of several variables,
evaluate multiple integrals in rectangular coordinates,
evaluate multiple integrals using change of variables.
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.
** Recommended Text
J Stewart (2001) Calculus : concepts and contexts
2/e. Brooks/Cole 0534377181
H Anton & C Rorres (2000) Elementary Linear Algebra: Applications Version
8th. J Wiley 0471170526
** Supplementary Text
R L Finney & G B Thomas (1994) Calculus
2nd. Addison-Wesley 0201549778
T S Blyth & E F Robertson Basic Linear Algebra
D.W.Jordan & P.Smith (1994) Mathematical Techniques: an introduction for the engineering, physical and mathematical sciences
Oxford University Press 0198562683
This module is at CQFW Level 4