# 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 course 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 course 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 the mathematical techniques to the solution of engineering problems encountered using appropriate mathematical software tools

### Indicative content

The topics listed under the indicative content below are the underpinning areas of knowledge and understanding that would be obtained from the course delivery (see: Learning and Teaching Activities). The content in the four areas listed below is indicative.

Foundations of Engineering Mathematics
• 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: existence of solutions, bisection method, fixed-point iteration (simple iteration), convergence criteria, Newton - Raphson method and convergence of, the secant method, the trapezoidal rule, 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;

Engineering Applications
• Statics: Mass, force and weight, forces in equilibrium, parallelogram of forces, resolution of, polygon of, moment of, couple, principle of moments, resolution of a force into a force and a couple, general conditions of equilibrium, free-body diagrams,;
• Frameworks: forces in frameworks, analytical methods (methods of sections, method of resolution);
• Determinate structures: axial force, shear force, bending moment, torque;
• Stress and strain: concepts of force and stress, deformation and strain, stress/stain relationships, uniaxial, biaxial, pure shear, strain energy, plane stress and strain, bulk solids handling;
• Electrical filters: RC filters, transfer functions, frequency response, transient response, Bode plots;
• Fourier analysis: RF spectrum, communications channels, channel blocking;
• Cryptography: cryptographic algorithms and protocols, key exchange, decryption techniques;
• Probability: dealing with uncertainty in engineering, game theory.

### Teaching and learning activity

Learning and teaching take place through a combination of lectures, tutorials and independent study. The course is presented in the context of engineering challenges that the student is expected to solve with the underpinning material supplied through the tutorial sessions and supplementary material provided through the course online resources. Each topic will be introduced with a ‘problem of the week’ that will be solved using the key mathematical topic(s). The listings in the indicative content are examples of the concepts that need to be covered in the problems posed to the student.

The lecture sessions concentrate on the application of mathematics from an engineering perspective. This can be achieved in a specific engineering subject context, for example mechanics, structural analysis, the use of statistics in data analysis, numbers systems that are used in computer systems, communication and computer network systems, or the use of mathematics in business. These areas of applied mathematics are further reinforced with the appropriate mathematical simulation and/or analysis software tools.

The tutorial sessions concentrate on fundamental mathematical principles in order to provide a firm foundation in the core principles required for an understanding of various mathematic concepts, how to carry out appropriate mathematical calculations, use appropriate mathematical notation and terminology, and then be able to manipulate expressions and equations in a suitable manner. Each fundamental aspect of the topic for each week will be supported through mathematical software tools (e.g. Excel, MATLAB).

IEng:
Underpinning Science and Mathematics, and Associated Disciplines: US2i
Engineering Analysis: EA1i, EA2i, EA3i, EA4i

Partial CEng:
Underpinning Science and Mathematics, and Associated Disciplines: US2, US3
Engineering Analysis: EA1, EA2, EA3, EA4

Scholarship
& Autonomy
SA1 Have an informed
understanding of their
discipline or professional practice, and the ability to question its principles, practices
and boundaries.

SA2 Think independently, analytically and creatively,
and engage imaginatively
with new areas of
investigation.
SA3 Appreciate disciplines and
forms of
professional
practice beyond their own and draw connections
between
them.
SA4 Are intellectually curious,
responsive to challenges,and demonstrate initiative and resilience.
Creativity
& Enterprise
CE1 Recognise and create
opportunities, and respond effectively to unfamiliar or
unprecedented situations or problems.
CE2 Generate new ideas and
develop creative solutions
or syntheses.

CE3 Communicate clearly and
effectively, in a range of
forms, taking account of
different audiences
.

CE4 Make use of familiar and
emerging information &
communication technologies.
CE5 Seize and shape the
opportunities open to them on leaving university.
Cross‐cultural
&
International
Awareness
CCI1 Engage effectively in
groups whose members are from diverse backgrounds

CCI2 Appreciate the importance of behaving sustainably

CCI3 Move fluently between
different cultural,social and political contexts

CCI4 Value the ability to
communicate in more than one language

### Assessment

All elements of summative assessment must be passed to pass the course.
In order to meet professional body requirements, students are expected to pass this course at 40% overall and with a minimum of 30% for each component.

Report - 40%
LO - 3-4.
Pass mark - 40%
7 Pages each, ACM CHI publication format.
A report on the development of a solution to an engineering problem.

Exam - 60%
LO - 1-3.
Pass mark - 40%
2 hour unseen paper.

Nature of FORMATIVE assessment supporting student learning:
Mock exam in term 2 in addition to online Moodle quizzes.