Mathematics for Electronics & Electrical Engineering Part II | MATH2047

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

Linked modules

Pre-requisite: MATH1055

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:

Demonstrate organisational and time-management skills
Write up in an accurate, coherent and logical manner your solutions to a range of mathematical problems

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.

Study time
Type	Hours
Teaching	48
Independent Study	102
Total study time	150

Resources & Reading list

Textbooks

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

Greenberg MD. Advanced Engineering Mathematics. CUP.

Kreyzig E,. Advanced Engineering Mathematics. Wiley.

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

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

Jeffrey A. Mathematics for Engineers and Scientists. Nelson.

Assessment

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Exam	100%

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Breakdown
Method	Percentage contribution
Exam	100%

Repeat Information

Repeat type: Internal & External