The University of Southampton
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# MATH2047 Mathematics for Electronics & Electrical Engineering Part II

## Module Overview

The aims of this module are to: - Give students a solid grounding in mathematical methods and ideas in areas relevant to applications in engineering: Laplace transforms, eigenvalues, eigenvectors and eigenfunctions, complex variable theory,and partial differential equations. Feedback and student support during module study (formative assessment) - 3 coursework assignments which are collected up, marked and returned. - coursework assignments, solutions and past examination papers are available on website.

### Aims and Objectives

#### Module Aims

• The coursework assignments cover the full range of topics of study, with all the questions being compulsory. They include multi-part questions to help students start and then develop solutions to quite substantial problems. • Completion of the coursework assignments should engender confidence in the use of all the mathematical methods needed to deal with the examination questions • To obtain full credit on coursework and examinations problems will require accuracy, and a coherent and logical presentation of solutions

#### Learning Outcomes

##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Write up in an accurate, coherent and logical manner your solutions to a range of mathematical problems
• Demonstrate organisational and time-management skills
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Solve a variety of mathematical problems relevant to engineering
• Show logical thinking in problem solving

### Syllabus

• Laplace transform theory. Use of Laplace transforms in solving simple ODEs with constant coefficients and given boundary conditions. Step functions and their transforms. Laplace transforms of standard functions. Elementary properties – linearity, first and second shifting theorems, change of scale. Transforms of derivatives, integrals and of products with powers of t. Transforms of periodic functions. • Eigenvalues, eigenvectors and eigenfunctions. Matrix eigenvalue problems. Examples of Sturm-Liouville problems. Sturm-Liouville Theory. Fourier series representation of a function in terms of solutions to Sturm-Liouville problem. • Fourier analysis. Fourier Series. Fourier transforms. Discrete Fourier transforms. • Partial differential equations Classification of second-order linear PDEs. The technique of separation of variables with particular application to the wave equation.

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include - Standard “chalk and talk” lectures, using either blackboard or whiteboard, tutorials, coursework problems, material on Blackboard. Learning activities include - Individual study. - Note-taking at lecture classes. - Working through coursework assignments and submitting to specified deadlines. - Preparation for a written examination.

TypeHours
Teaching48
Independent Study102
Total study time150

#### Resources & Reading list

Spiegel MR. Theory and Problems of Laplace Transforms, Schaum Outline Series.

Spiegel MR. Theory and Problems of Vector Analysis, Schaum Outline Series.

Greenberg MD. Advanced Engineering Mathematics.

Kreyzig E,. Advanced Engineering Mathematics.

Stephenson G and Radmore PM. Advanced Mathematical Methods for Engineering and Science Students.

Jeffrey A. Mathematics for Engineers and Scientists.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 20%
Exam 80%

#### Referral

MethodPercentage contribution
Coursework %

### Linked modules

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
MATH1055Mathematics for Electronic and Electrical Engineering

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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