## MATHEMATICS FOR TECHNOLOGY

 SHE Level 1 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M1G112791 Module Leader Charlotte Craig School INTO Subject INTO Trimester B (January start)

### Pre-Requisite Knowledge

Foundation Programme Entry Requirements

### Summary of Content

This module provides a grounding in a range of mathematical topics including algebraic manipulation, trigonometry, matrices, vectors, complex numbers, differential and integral calculus, elementary differential equations, as well as an introduction to basic statistical techniques. Applications of the mathematics are considered whenever appropriate.

### Syllabus

Algebra: Manipulation of formulae and solution of equations Co-ordinate Geometry: Straight line, circle, polar co-ordinates Trigonometry: Solution of simple trigonometric equations; graphs of sinusoidal functions Matrices: Matrix arithmetic, determinants and inverses; solution of simultaneous algebraic equations; matrix multiplication as a geometrical transformation. Vectors: Vector arithmetic in 2 and 3 dimensions, dot and cross products Complex Numbers: Complex arithmetic in Cartesian and polar forms Statistics: Mean and standard deviation; confidence limits for a population mean; linear regression and correlation Differential Calculus: Definition of derivative; chain, product and quotient rules Integral Calculus: Indefinite integration, integration by substitution; analytical and numerical evaluation of definite integrals. Ordinary Differential Equations: Analytical solution of linear ODE's with constant coefficients up to 2nd order; numerical methods for solving 1st order ODE's.

### Learning Outcomes

On completion of this module the student should be able to: Algebraically manipulate mathematical expressions Solve linear, quadratic and trigonometric equations Describe Cartesian and polar co-ordinate systems, and use them to represent lines and curves Model sinusoidal behaviour Perform complex arithmetic Perform vector arithmetic Perform matrix arithmetic Solve simultaneous linear equations by matrix methods Organise experimental data and calculate means, standard deviations and confidence limits Determine the sample regression line and correlation coefficient from experimental data Differentiate functions using the chain, product and quotient rules Obtain indefinite and definite integrals of basic functions using analytical methods or, where appropriate, numerical methods Solve linear, constant coefficient ordinary differential equations (up to 2nd order) analytically Solve 1st order differential equations numerically

### Teaching / Learning Strategy

This module will be based on lectures, tutorials and self learning. Lectures will demonstrate techniques and indicate approaches to analytical and numerical problem solving. Techniques will be practiced under directed learning and tutorials. Formative assessments will be adminstered on a topic by topic basis to provide diagnostic feedback on progress.

### Indicative Reading

Croft A and Davison R (2008) "Mathematics for Engineers - A Modern Interactive Approach" (3rd ed.) Prentice Hall "Mathcentre" web site: http://www.mathcentre.ac.uk/

### Transferrable Skills

Numeracy Skills Critical thinking and problem solving; Cognitive/intellectual skills; Knowledge and understanding in the context of the subject; Independent working; IT Skills Communication skills, written, oral and listening

### Module Structure

Activity Total Hours
Tutorials (FT) 56.00
Assessment (FT) 20.00
Lectures (FT) 42.00
Independent Learning (FT) 82.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) n/a 25.00 35% CLASS TEST
Exam (School) n/a 25.00 35% CLASS TEST
Exam (School) n/a 50.00 35% school exam