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:
- Show logical thinking in problem solving
- Solve a variety of mathematical problems relevant to engineering
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.
| Type | Hours |
|---|---|
| Independent Study | 102 |
| Teaching | 48 |
| Total study time | 150 |
Resources & Reading list
Textbooks
Kreyzig E,. Advanced Engineering Mathematics. Wiley.
Stephenson G and Radmore PM. Advanced Mathematical Methods for Engineering and Science Students. CUP.
Spiegel MR. Theory and Problems of Laplace Transforms, Schaum Outline Series. McGraw-Hill.
Jeffrey A. Mathematics for Engineers and Scientists. Nelson.
Greenberg MD. Advanced Engineering Mathematics. CUP.
Spiegel MR. Theory and Problems of Vector Analysis, Schaum Outline Series. McGraw-Hill.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Repeat Information
Repeat type: Internal & External