# KC5002 - Advanced Engineering Mathematics

## What will I learn on this module?

This module is designed to provide You with a basic course in Laplace Transforms, their use in solving ordinary differential equations arising from physical problems, and their use in describing the behaviour of simple control systems. You will be introduced to the concept of the harmonic components of a periodic waveform and be shown how this is useful in matching general solutions of partial differential equations to particular boundary or initial conditions. The solution of systems of linear ordinary differential equations using matrix methods will also be considered.

The module will be delivered using a combination of lectures and seminars.

Assessment is by formal examination.

Outline Syllabus
Laplace Transforms: Definition, simple transforms, linearity. First shift theorem. Inverse transforms, linearity, use of the first shift theorem and partial fractions. Transforms of derivatives. Transforms of an integral. The Heaviside Unit Step function. The second shift theorem. Solution of linear ordinary differential equations with constant coefficients, including systems of such equations. The Delta function and the Impulse Response function; transfer function. Initial and final-value theorems. Convolution and the convolution theorem. Poles of the transfer function and stability. Steady-state response. (50%)

Periodic functions and Fourier series. Full-range and half-range series. Even and odd functions.
Coefficients in complex form. Application to the solution of partial differential equations by the method of separation of variables. (25%)

Matrices, eigenvalues and eigenvectors. Algebraic evaluation of the eigenvalues and eigenvectors of a matrix. Application to the solution of a
system of linear ordinary differential equations. (25%)

### How will I learn on this module?

A wide range of learning and teaching approaches are used in this module. The module will be delivered using a combination of lectures, set work and seminars in which you will be able to obtain help with problems associated with the module. Lectures allow you to experience and understand the formalism of advanced mathematical techniques and include relevant examples. Furthermore, you will have an opportunity to enhance your understanding of the subject through seminars which promote independent learning and tackle relevant problems. You will be provided with formative feedback to problems in seminars and have the opportunity to problem solve within peer groups. The mathematical rigour associated with this module naturally increases your employability and is a highly transferrable skill.

Summative assessment is composed of a closed book written examination worth 100% of the module mark. The examination requires you to analyse and solve problems associated with the module. Examination assesses all Module Learning Outcomes. Summative feedback in seminars support the 100% examination assessment.

Summative assessment is composed of a closed book written examination worth 100% of the module mark. The examination requires students to analyse and solve problems associated with the module. Examination assesses all Module Learning Outcomes. Summative feedback in seminars support the 100% examination assessment.

### How will I be supported academically on this module?

In addition to direct contact with the module team during lectures and seminars, you are encouraged to develop your curiosity by making direct contact with the module team either via email or the open door policy operated throughout the programme. You will also be regularly referred to supporting resources including relevant texts and relevant multimedia materials.

References to these resources will be made available through the e-learning portal and in lectures and seminars.

### What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

### What will I be expected to achieve?

Knowledge & Understanding:
• Knowledge and understanding of scientific principles underpinning the mathematics in electrical engineering discipline (UK-Spec, 3rd Ed. SM1m, EA1m, SM2m). These include:
o Find the Fourier Series of a periodic waveform, and find the separated solutions of a partial differential equation.
o Determine the eigenvalues and eigenvectors of a matrix and use to solve a system of linear ordinary differential equations.

Intellectual / Professional skills & abilities:
• Ability to analyse and create solutions to engineering problems using mathematics (UK-Spec, 3rd Ed. D4m), including:
o Determine the overall transfer function of a system compromising interconnected subsystems using block-diagram techniques.
o Find the impulse-response and transfer functions of a system, and determine the behaviour of a system and its stability.
• Ability to identify, classify and describe performance of systems and components using mathematic principles and methods (UK-Spec, 3rd Ed. EA2m, EA4m)

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
• Increases awareness and curiosity through the formulation of simple physical problems as ordinary differential equations and the use of Laplace Transforms to obtain their solution.

### How will I be assessed?

SUMMATIVE
1. Examination (100%) – KU1, KU3, IPSA1, IPSA3, PVA5

FORMATIVE
1. Seminar problems – KU1, KU3, IPSA1, IPSA3, PVA5

Feedback is provided to students individually and in a plenary format both written and verbally to help students improve and promote dialogue around the assessment.

### Pre-requisite(s)

KC4010 or equivalent knowledge

N/A

### Module abstract

This module is designed to introduce advanced, but relevant, concepts in Mathematics – essential techniques you will need in your degree and future career. We will introduce the concept of Laplace Transforms, their use in solving ordinary differential equations arising from physical problems, and their use in describing the behaviour of simple control systems. You will also be introduced to the concept of the harmonic components of a periodic waveform and be shown how this is useful in matching general solutions of partial differential equations to particular boundary or initial conditions. The solution of systems of linear ordinary differential equations using matrix methods will also be considered. Assessment of the module is by one formal examination (100%) and the module will be delivered using a combination of lectures and seminars. Overall, the module is designed to provide students with a useful preparation for employment or postgraduate study in an engineering environment.

### Course info

UCAS Code H600

Credits 20

Mode of Study 3 years full-time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2022 or September 2023

## Electrical and Electronic Engineering BEng (Hons)

All information on this course page is accurate at the time of viewing.

Our Campus based courses starting in 2022 and 2023 will be delivered on-campus with supporting online learning content. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to adjust the delivery of our education accordingly to ensure the health and safety of our students and staff.

On-campus contact time is subject to increase or decrease in line with any additional restrictions, which may be imposed by the Government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors. This could potentially mean increased or fully online delivery, should such restrictions on in-person contact time be required.

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