The University of Southampton
Courses

# 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: Fourier series, Fourier transforms, eigenvalues, eigenvectors and eigenfunctions, linear ordinary differential equations, partial differential equations, and vector calculus. 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. Please see Blackboard for MATH2047 module information. https://blackboard.soton.ac.uk One of the pre-requisites for MATH3083 and MATH3084

### Aims and Objectives

#### Learning Outcomes

##### 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
##### 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

### Syllabus

• Fourier Series. Orthogonality relations. 2L periodic functions. Half-range series. Solutions to periodically forced ODEs. • Fourier Transforms. Fourier transform and inverse transform. Sine and cosine transform. Properties of the Fourier transform. The discrete Fourier transform. • Eigenvalues, eigenvectors and eigenfunctions. Matrix eigenvalue problems. Solution to systems of coupled ODEs. Symmetric matrices. • Linear ODEs and Sturm-Liouville problems. Boundary and initial conditions. Constant coefficient linear ODEs. Euler equations. The method of reduction of order. The method of variation of parameters. Sturm-Liouville Theory. Examples of Sturm-Liouville problems. Eigenfunction expansions. • Partial differential equations Classification of second-order linear PDEs. The technique of separation of variables with application to wave equations, diffusion equations, and Laplace’s equation. • Vector calculus The gradient, divergence and curl operators. Directional derivatives. Line integrals and conservative vector fields. Stokes’s theorem and the Divergence theorem. Alternative coordinate systems.

### 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

Jeffrey A. Mathematics for Engineers and Scientists.

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

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

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

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 100%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

Pre-requisite: MATH1055

### 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

Recommended texts for this module may be available in limited supply in the University Library and students may wish to purchase reading texts as appropriate.

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.