# Engineering Mathematics 1

## Module summary

Module code: MATH1143
Level: 4
Credits: 30
School: Engineering and Science
Department: Engineering
Module Coordinator(s): Jan Krabicka

## Specification

None.

### Aims

This module aims to provide students with an understanding of, and competence in the use of, mathematical techniques that are relevant to the solution of engineering problems. It will also give students a firm foundation from which to develop solutions to a wider and deeper range of engineering problems that they will encounter throughout their undergraduate engineering programme of study.

### Learning outcomes

On successful completion of this module a student will be able to:
1 Demonstrate an understanding of relevant mathematical concepts
2 Manipulate mathematical expressions and equations appropriate to the level and context
3 Carry out relevant mathematical calculations in the solutions to engineering problems
4 Apply appropriate mathematical software tools in the solutions to engineering problems

### Indicative content

The topics listed under the indicative content below are the underpinning areas of knowledge and understanding that will be obtained from successful completion of the module. The mathematical topics are illustrated in the context of relevant engineering scenarios.

• Arithmetic: types of numbers, fractions, decimal numbers, powers, number systems, review of basic algebra, trigonometry, and logarithms;
• Introduction to algebra: algebraic expressions, powers as related to logarithms, rules of logarithms, multiplication/ division / factorisation of algebraic expressions;
• Expressions and equations: evaluating expressions, independent variables, transposition of formulas, polynomial equations;
• Functions, graphs, data presentation: Cartesian and polar co-ordinates / axes, use of software tools for plotting graphs and charts;
• Simultaneous linear equations: solution of simultaneous linear equations with two unknowns (by substitution and by equating coefficients);
• Differentiation: small increments and rates of change, critical values, partial differentiation;
• Integration: calculation of areas and volumes, multiple integration;
• Complex numbers: Cartesian, polar and exponential forms, Argand diagrams, complex arithmetic;
• Matrices and determinants: matrix algebra, determinants, solving a stet of linear equations using matrices and determinants;
• Vectors: vectors in two and three dimensions, vector algebra;
• Differential equations: solution of first-order differential equations by separation of variables, and by the use of an integrating factor, solution of homogenous and non-homogenous second-order differential equations with constant coefficients;
• Numerical methods: roots of nonlinear equations, Newton - Raphson method, Simpson's rule;
• Integral transforms: Fourier series, Laplace transforms, inverse Laplace transforms, Laplace transforms of a derivative, tables of Laplace transforms;
• Statistics: interpretation and use of the mean, mode, median, range, variance, standard deviation on sets of data, method of least squares; correlation and regression;
• Probability: conditional probability, probability distributions, expected value.