Introductory description

This module covers the essential ideas and techniques that underpin university-level study mathematical subjects such as physics and engineering. It covers a range of fundamental topics – including calculus, vectors, matrices and complex numbers.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Functions and their graphs to include simple graph transformations.
Algebra to include polynomials, rational functions, partial fractions.
Exponentials and logarithms to include basic properties and modelling.
Statistics to include presenting and summarising data, probability, correlation and regression.
Sequences, series and the binomial expansion
Trigonometry to include geometrical problems, identities and solving trigonometric equations.
Calculus. Differentiation and Integration to include basic functions, rules and applications to real world contexts. Solving first order ordinary differential equations.
Numerical methods to include solution of equations and areas beneath curves.
Matrices to include basic operations (2x2 and 3x3), inverse matrices (2x2 only) and applications.
Vectors to include fundamental properties, vector addition, scalar product and applications to lines and planes in 3D space.
Complex numbers to include basic arithmetic, algebraic, polar and exponential form, Argand diagram, De Moivre’s theorem and its applications.

Learning outcomes

By the end of the module, students should be able to:

• From a range of mathematical principles and processes choose and apply appropriate mathematical tools and techniques to solve problems set in a variety of contexts.
• Analyse and interpret results obtained from an application of mathematics to the solution of a real-world problem in the sciences and engineering.
• Construct and present mathematical arguments through appropriate use of logical deduction and precise statements involving correct use of symbols and appropriate mathematical language.

Indicative reading list

• Stewart, J. et al. (2016). Precalculus: mathematics for calculus. Boston: Cengage Learning.
• Sadler, A.J. and Thorning, D.W.S. (1987). Understanding pure mathematics. Oxford: Oxford University Press
• Stroud K. A. and Booth D. J. (2013). Engineering Mathematics. Basingstoke: Palgrave Macmillan.
• Jordan, S., Ross, S. and Murphy, P. (2012). Mathematics for Science. Oxford University Press.
• Stewart, J. (2012). Calculus. Belmont: Brooks/Cole Pub Co

View reading list on Talis Aspire

Subject specific skills

• construct and present mathematical and logical arguments;
• develop advanced numeracy skills;
• understand, interpret and extract information from data presented in various forms;
• convert real-world problems into mathematical problems;
• state a problem, break it down into sub-problems and clearly present solutions using appropriate symbols and terms.

Transferable skills

• use of appropriate technology to help in the solution of mathematical, scientific and engineering problems.