Module manager: Dr J. Niesen
Email: jitse@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2008/09
A good A-level Mathematics grade or equivalent.
This module is approved as an Elective
The first part of this module introduces vectors as a powerful tool for solving geometric and kinematic problems in 2 and 3 dimensions. The second part introduces the concept of discrete (as opposed to continuous) rates of change and uses this to model simple systems that arise in numerical calculation, biology, finance and economics.
To Introduce a variety of stimulating applications of mathematics and to formulate important classes of such problems in order to establish the foundations of modelling for subsequent applied modules. To acquaint students with some essential tools for solving problems in applied mathematics. By the end of this module, students should be able to: a) understand vector algebra and be able to apply vectors to diverse problems involving lines and planes in 2 and 3 dimensions; b) differentiate and integrate time-dependent vectors and apply this to kinematics in 2 and 3 dimensions; c) distinguish between continuous and discrete processes; d) derive and solve difference equations describing simple discrete processes.
a) Vectors: vector algebra, (addition, linear independence, components, scalar and vector multiplication, triple products). Geometry of lines and planes. Time-dependent vectors (differentiation and integration). Kinematics of particles in 2 and 3 dimensions. b) Discrete systems: Quantization of time increments, rates of change, discrete models, iteration, difference equations. Linear first order difference equations (general solutions, fixed points, stability). Non-linear first order difference equations (fixed points, cobweb diagrams, stability, cycles). Second order linear difference equations (general solutions, fixed points, stability). Applications to numerical algorithms, biology, finance (e.g. mortgages etc.) and economics. One dimensional logistic equations (period doubling).
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Tutorial | 11 | 1 | 11 |
| Private study hours | 67 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 100 | ||
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 7/8/2008
Errors, omissions, failed links etc should be notified to the Catalogue Team