|| MA12110 |
|| BASIC ALGEBRA |
|| 2004/2005 |
|| Dr T McDonough |
|| Semester 1 |
|| A or AS level Mathematics or equivalent. |
|| May not be taken at the same time as, or after, any of MA10020, MA11010 |
| Course delivery
|| Lecture || 22 x 1 hour lectures |
|| Seminars / Tutorials || 6 x 1 hour example classes |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||100%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
On completion of this module, a student should be able to:
manipulate trigonometric functions and use trigonometric identities;
solve certain polynomial equations;
solve a system of linear equations using row reduction of matrices;
find the eigenvalues and corresponding eigenvectors of a matrix;
form inverse functions;
use the binomial theorem and the binomial series.
The purpose of this module is to present some of the basic concepts of algebra at a level suitable for applications in other areas. The syllabus includes the trigonometric functions and identities, roots of polynomial equations, the binomial theorem, simple matrix algebra and solution of linear equations by row reduction of matrices.
To introduce students to algebraic ideas, at a level suitable for application in subjects other than Mathematics.
1. TRIGONOMETRY: Trigonometric functions and identities.
2. POLYNOMIALS: Factors and roots, the Remainder Theorem and the Factor Theorem, relationships between roots and coefficients.
3. MATRICES: Matrix operations, the solution of a system of linear equations, eigenvalues and eigenvectors, determinants, adjoints and inverses, the Cayley-Hamilton theorem.
4. SERIES: The Binomial Theorem and the binomial series.
** Recommended Text
K A Stroud (2001) Engineering Mathematics
5/e. Palgrave 0333919394
** Supplementary Text
M M Nicolson Fundamentals and Techniques of Mathematics for Scientists
P G Andres, H J Miser & H Reingold Basic Mathematics for Engineers
This module is at CQFW Level 4