|Assessment Type||Assessment length / details||Proportion|
|Semester Assessment||Problem sheets||20%|
|Semester Exam||2 Hours Open Book Written Examination||80%|
|Supplementary Exam||2 Hours Open Book Written Examination||100%|
On completion of this module, students should be able to:
1. find the first and second order partial derivatives of a function of 2 or 3 variables;
2. optimize a function of 2 variables using either the substitution method or Lagrange multipliers;
3. perform basic matrix algebra, find the inverse of 2 by 2 or 3 by 3 matrices and use the inverses to solve equations;
4. evaluate 2 by 2 and 3 by 3 determinants and apply Cramer’s Rule to solve equations;
5. reduce a matrix to echelon form, find its rank and solve associated systems of equations;
6. integrate simple polynomial, rational and exponential functions;
7. calculate the area under a curve, apply the technique to examples in modelling.
This module continues the thread of MA02610 with optimization of functions of several variables and Lagrange multipliers. It also includes basic matrix techniques.
To introduce further fundamental techniques required in later courses.
2. MATRIX ALGEBRA. Simultaneous linear equations, Gaussian elimination, laws of matrix algebra, identity and null matrices, matrix addition and subtraction, scalar multiplication, matrix multiplication, matrix inversion, determinants, relation between determinant value and matrix non-singularity, higher-order determinants, matrix inversion using determinants, Cramer’s Rule, matrix rank.
3. INTEGRATION. The notion of an integral. Area under a curve. Integration of simple power and exponential functions.
|Skills Type||Skills details|
|Application of Number||Required throughout the course.|
|Communication||Written answers to exercises must be clear and well structured.|
|Improving own Learning and Performance||Students are expected to develop their own approach to time-management regarding the completion of assignments on time and preparation between lectures.|
|Information Technology||Use of Blackboard.|
|Personal Development and Career planning||Completion of task (assignments) to set deadlines will aid personal development.|
|Problem solving||The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.|
|Subject Specific Skills||Broadens exposure of students to topics in mathematics|
|Team work||Students will be encouraged to work together on questions during problem classes.|
This module is at CQFW Level 3