Mathematics 1

Module aims

 This modules aim to:

- provide the class with a common depth and breadth of mathematical understanding irrespective of pre-university mathematics qualification.
- introduce you to mathematics as a logical and structured discipline.
- enable you to understand how to select the most appropriate mathematical technique for problem solving
- provide a platform of mathematical knowledge required for other courses in the Biomedical Engineering degree programme.
- encourage independent learning of engineering mathematics.

Learning outcomes

 Upon successful completion of this module you will be able to: 

Use calculus techniques to solve complex mathematical equations including 1st and 2nd order differential equations.
Identify and describe the properties of functions, including hyperbolic functions and sketch curves of given functions.
Apply vector and matrix algebra to solve problems in multiple dimensions.
Apply all forms of complex numbers to solve equations and represent solutions on an Argand diagram. 
Express functions in terms of mathematical series and use these expressions to solve posed problems.
Explain why Fourier transforms are used and apply Fourier transforms to described functions.
Apply the previously described mathematical methods, tools and notations in the analysis and solution of mathematical problems described in a biomedical context.
 

Module syllabus

This module will cover the following topics:

Limits
Differentiation
Integration
Functions and Curve sketching
Vector algebra
Matrix algebra
Complex numbers
Hyperbolic functions
1st & 2nd order differential equations
Series: Maclaurin, Taylor, Fourier
Fourier Transforms
 

Pre-requisites

 A-level maths or equivalent

Teaching methods

Students will be taught over two terms using a combination of lectures and study groups. Lecture sessions will be made available on Panopto for review and supplemented with technologies to promote active engagement during the lecture such as 'learning catalytics'. Study groups focusing on problem sheets will be based on taught content from lectures to reinforce these topics and allow students to test their understanding. A number of formative online quizzes/problems sheets will also be available to supplement the material.

Lectures: 36 hours
Study groups: 20 hours

Assessments

 The module will be assessed by two combined mastery/final exams covering all learning outcomes and designed to ensure a broad base level of understanding. In each exam the mastery component must be passed and will contribute as 20% of the grade for the module. If the students do not pass the mastery component they may resit this part.

Examinations:
●  Written exam: Combined mastery & final examination - Alpha and Beta; 50% weighting
Duration 1 hr 30mins comprising of a mastery component (15 multiple choice questions) and 2 further questions A mock exam paper and revision materials are also available for each sub-course.
No type of previous exam answers or solutions will be available


●  Written exam: Combined mastery & final examination - Gamma and Delta; 50% weighting
Duration 1 hr 30mins comprising of a mastery component (15 multiple choice questions) and 2 further questions A mock exam paper and revision materials are also available for each sub-course.
No type of previous exam answers or solutions will be available

Feedback : General feedback on formative assessments such as class polls, online quizzes and problem sheets will be given either orally in lectures and study groups or electronically as an email or announcement on Blackboard. Individual feedback on formative online quizzes will be given as scores online. General feedback on whole class performance for mastery examinations will be provided either orally in a lecture or as an email within 10 days of completion. Numerical results for the final examination will be communicated after the examiners board meeting.

Reading list