# Gwybodaeth Modiwlau

Module Identifier
MA03610
Module Title
Foundations of Mathematics 2
2019/2020
Co-ordinator
Semester
Semester 2
Pre-Requisite
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (Written Examination)  100%
Supplementary Exam 2 Hours   (Written Examination)  100%

### Learning Outcomes

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.

### Brief description

This module continues the thread of MA02610 with optimization of functions of several variables and Lagrange multipliers. It also includes basic matrix techniques.

### Aims

To introduce further fundamental techniques required in later courses.

### Content

1. FURTHER OPTIMISATION. Constrained optimization in functions of one variable, the interpretation of Lagrange multipliers, unconstrained optimization in functions of more than one variable, constrained optimization in functions of more than one variable.
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.

### Module Skills

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.
Research skills N/A
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.

### Notes

This module is at CQFW Level 3