Module overview
This course is designed to develop fundamental mathematical skills which Biomedical engineers need in order to tackle a wide variety of engineering and design problems. There is a particular focus on developing an understanding of mathematics as a toolbox through practical examples based on case studies from academia and industry
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Critically analyse and solve mathematical problems.
- Manipulate algebraic expressions of real and complex numbers, vectors, and matrices.
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Mathematical methods both in the abstract and in relation to specific example problems from technical engineering subjects.
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Demonstrate organisational and time-management skills.
- Plan learning and revision activities in a self-study environment.
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Perform calculations of simple problems and work through longer examples.
- Show logical thinking in problem solving.
Syllabus
Functions:
- Inverse; trigonometric; exponential, logarithmic and hyperbolic.
Calculus
- Differentiation: basic rules; differentiation of standard functions; Newton's method for finding roots; partial differentiation.
- Differentiation: maxima, minima and points of inflection; curve sketching; parametric, implicit and logarithmic differentiation; Taylor and Maclaurin series.
- Integration: definition of integral; standard integrals; substitution; integration by parts; numerical integration.
Differential Equations
- Classification; simple first and second order differential equations.
- Solution of first order ODEs (separable, homogenous, linear and exact).
Matrix algebra
- Terminology; addition, subtraction and multiplication of matrices; determinants.
- Inverse of a matrix using cofactors; systems of linear equations; inverse of a matrix using the elimination method.
- rank; eigenvalues and eigenvectors; Symmetric, Skew-Symmetric, and Orthogonal Matrices; Eigenbases. Diagonalization. Quadratic Forms
Statistics:
- Statistics: probability; conditional probability; combinations and permutations; discrete and continuous random variables.
- Statistics: mean and standard error of sample data; normal distribution; sampling; confidence intervals; hypothesis testing.
Discrete Mathematics:
- Mathematical proof: by case analysis, by contradiction. Induction and recursion.
- Sets and relations.
- Logic: Propositional logic. Predicate calculus. Soundness and completeness.
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.
| Type | Hours |
|---|---|
| Tutorial | 24 |
| Preparation for scheduled sessions | 24 |
| Problem Classes | 24 |
| Revision | 14 |
| Completion of assessment task | 31 |
| Wider reading or practice | 33 |
| Total study time | 150 |
Assessment
Assessment strategy
The module is assessed by a combination of formative and summative problem sheets, self-testing and mini-tests on each block and a written examination paper as the final assessment.
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Written exam | 70% |
| Problem Sheets | 10% |
| Test | 20% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Written exam | 100% |