Module overview
This course explores the use of mathematics as a toolbox for engineers need in order to calculate, model, visualise and design systems. The focus is on solving physical problems via equations, both analytically and numerically using computation, along with the development of representation and visualisation as a way of presenting solutions and designs.
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Mathematical methods used in technical engineering subjects (shared with ELEC1300).
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Construct mathematical models that capture the key features of an engineering problem.
- Interpret mathematical results and their implications in an engineering context.
- Represent mathematical concepts in sketches and visual forms.
- Record consistent learning and revision activities.
- Demonstrate organisational and time-management skills.
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Apply appropriate methods of mathematical analysis.
- Critically analyse and solve engineering problems.
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Show logical thinking in problem solving.
- Apply a range of numerical and computational methods (shared with ELEC1300).
Syllabus
Integration
- Line integrals and conservative vector fields.
- Green’s Theorem in the Plane
- Surface and triple Integrals
- Stokes’s theorem
- Divergence Theorem of Gauss
- Boundary and initial conditions.
Ordinary Differential Equations
- Constant coefficient linear ODEs. Euler equations.
- Homogeneous linear ODE with constant coefficients
- Nonhomogeneous ODEs
Matrix algebra:
- rank; eigenvalues and eigenvectors; Symmetric, Skew-Symmetric, and Orthogonal Matrices; Eigenbases. Diagonalization. Quadratic Forms
Further Calculus:
- Chain rule for partial derivatives; higher partial derivatives; total differentials and small errors
- Partial Differential Equations.
- Separation of variables
- Use of Fourier Series
- Two-Dimensional Wave Equations
- Rectangular Membrane. Double Fourier Series
- Heat Equation and the Laplacian
- Solution by Fourier Series.
- Steady Two-Dimensional Heat Problems.
- Laplace’s Equation in Cylindrical and Spherical Coordinates.
Numerical Mathematics
- Discrete numerics, sampling, DFT
- Numerical approximation, numerical integration, numerical differentiation
- Use of MATLAB in numerical caculaitons: curve fitting, numerical simulation of solutions to equations
Systems
- Systems of ODEs as Models in Engineering Applications
- Basic Theory of Systems of ODEs.
- Matrix Solutions to coupled second order ODEs
- Nonhomogeneous Linear Systems of ODEs
- The method of reduction of order.
- The method of variation of parameters.
- Sturm-Liouville Theory. Examples of Sturm-Liouville problems.
- Eigenfunction expansions.
Learning and Teaching
Teaching and learning methods
Taught using a blended approach, incorporating “flipped mode” teaching and traditional problem classes.
- Comprehensive explanatory video lectures on each topic
- Case study recordings
- Weekly discussion tutorials and seminars
- Case study based problem sheets
- Weekly intensive problem classes – problem sheets worked on
- Self-study notes for each topic.
- Self-testing on each block
- Mini-test at end of each block
- Past examination papers and solutions.
- Computing Labs on data analysis and numerical Computation
Type | Hours |
---|---|
Specialist Laboratory | 12 |
Problem Classes | 24 |
Preparation for scheduled sessions | 30 |
Completion of assessment task | 9 |
Wider reading or practice | 37 |
Revision | 14 |
Tutorial | 24 |
Total study time | 150 |
Assessment
Assessment strategy
The module is assessed by a combination of formative and summative problem sheets, self-testing and numerical laboratories associated with each block and a written examination paper as the final assessment.
The Laboratory assessment which covers practical Learning Outcomes is assessed in the Laboratory Programme Module which includes in-semester opportunities for redeeming failure. These marks are carried forward to the Supplementary Assessment period or External Repeat.
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Written exam | 70% |
Problem Sheets | 10% |
Laboratory | 20% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Lab Marks carried forward | 20% |
Written exam | 80% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Method | Percentage contribution |
---|---|
Lab Marks carried forward | 20% |
Written exam | 80% |