# Molecular Bioengineering (MEng)

## Mathematics and Engineering 1

### Module aims

The aims of this module are to: Provide a common depth and breadth of mathematical understanding irrespective of pre-university mathematics qualification. Enable you to understand how to select the most appropriate mathematical technique for problem solving. Introduce the basic principles of physics, electrical and mechanical engineering as required for other modules in the Molecular bioengineering programme. Provide you with practice in solving mathematical, electrical and mechanical problems posed in a Bioengineering context. To encourage you to become an independent learner

### Learning outcomes

Upon successful completion of this module you will be able to: 1 - Use calculus techniques to solve complex mathematical equations including 1st and 2nd order differential equations. 2 - Identify and describe the properties of functions, including hyperbolic functions and sketch curves of given functions. 3 - Apply vector and matrix algebra to solve problems in multiple dimensions. 4 - Apply all forms of complex numbers to solve equations and represent solutions on an Argand diagram. 5 - Express functions in terms of mathematical series and use these expressions to solve posed problems. 6 - Explain why Fourier transforms are used and apply Fourier transforms to described functions. 7 - Describe commonly employed electronic circuits and how they work and undertake circuit design at an elementary level. 8 - Be able to describe Newton's laws and express them in vector form to solve both simple static and dynamic mechanics problems

### Module syllabus

This modules will cover the following topics: Maths: Limits Differentiation Integration Functions and Curve sketching Vector algebra Matrix algebra Complex numbers Hyperbolic functions 1st and 2nd order differential equations Series: Maclaurin, Taylor, Fourier Fourier Transforms Electrical Engineering Introduction to Analog Systems: Ohm's Law, KCL, KVL, Equivalent Circuits, Energy Storage Devices, Filters, Operational Amplifiers, Semiconductor Devices, Circuit Simulation using LTSpice Mechanics Laws of motion (linear and angular) / rigid body mechanics / statics (forces and moments) Simple harmonic motion and forced oscillations

### Teaching methods

Students will be taught over two terms using a combination of lectures and study groups. Lecture sessions will be made available online or 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.

### Assessments

• Written exam : Maths Alpha Beta Mastery weighting 20%
• Written exam : Maths Alpha Beta Mastery weighting 20%
• Written exam : Engineering exam weighting 60%