The purpose of this module is to ensure the learner can visualise or describe physical systems using the basic elements of mathematics. The leaner must then be able to adapt these constructs as needed using the fundamental skills of algebra and manipulation of equations. The learner will then use expressions from differing areas of mathematics to describe Engineering systems, solve the resulting mathematical problems and interpret the results. These skills and concepts will enable the learner to use mathematics fluently during their career as an engineer.
Algebra
The basics of algebra and the grammar of number – The laws of indices, the distributive law, basic algebraic operations, transposition of equations. The concept of functions and the common notation for the argument of a function. The basic functions: the logarithm and the exponential functions and their connection. The sine and cosine as functions, their angular frequency, phase, amplitude, time displacement and other parameters.
Co-ordinate Geometry
The x-y plane. The behaviour of common functions and their illustration by graphs in the plane, including simple linear functions, power functions, the exponential, logarithm, sine and cosine and other trigonometric functions. The use of the common functions to model the behaviour of physical systems such as the discharge of a capacitor, the voltage and current from a dynamo, waves and other examples.
Trigonometry
The Trigonometric Functions as geometric ideas. The Unit Circle and polar coordinates. The sine and cosine rule and the resolution of triangles. Complex numbers in Cartesian, Polar and exponential forms, their representation as Phasors, and the use of trigonometric knowledge to carry out arithmetic operations on complex numbers. De Moivre’s theorem, the Euler equations and the roots of unity.
Equations
The idea of an equation and the solutions of an equation. The solution of equations as geometric problems in the x-y plane. Simultaneous equations, Quadratic equations and Cubic equations and the remainder theorem.
Delivery will be via in-person lectures, labs and workshops. Learning resources include online practice quizzes, demonstration videos, recorded lectures and worked examples. Students will use resources provided to build their independent learning skills. Peer learning will form part of weekly labs using methods such as 'think-pair-share'. Opportunities for formative assessment will be incorporated into module.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 50 |
| Other Assessment(s) | 50 |