| Unit name | Mathematical Methods |
|---|---|
| Unit code | MATH30800 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Tourigny |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
MATH20402 Applied Partial Differential Equations 2 |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Why is this unit important?
This unit is concerned with analytical methods in mathematics. They have considerable intrinsic interest, but their importance for applications is the driving motive behind this lecture course, in which we will derive many practical methods for solving partial differential equations
How does this unit fit into your programme of study
This unit is a natural progression from Applied Partial Differential Equations 2 and develops methods useful in a wide range of applied mathematics topics. The techniques introduced in this course are developed further in the Asymptotics unit, and are used in Advanced Fluid Dynamics.
An overview of content
The course is a development of some of the topics introduced in the pre-requisite unit APDE2 for the solution of partial differential equations.
Beginning with the Fourier transform, we undertake the systematic study of generalised functions, which facilitate the application of Fourier transforms to the problems that arise in practical situations. We then go on to discuss other useful transforms, such as the Laplace transform and (very briefly) the Mellin transform. Finally, Green’s functions are computed for a variety of ordinary and partial differential problems. In treating these topics, much use will be made of complex variable techniques.
Learning Outcomes
At the end of the unit, the students should be able to
The unit will be taught through a selection of lectures, online materials, independent activities such as problem sheets and other exercises, problem classes, support sessions and office hours.
Tasks which help you learn and prepare you for summative tasks (formative)
Problem sheets, which a couple of questions set as formative homework, will be issued every week.
Tasks which count towards your unit mark (summative)
90% Timed examination
10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
When assessment does not go to plan
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment (or, in certain scenarios, if you had failed the assessment), you will normally be required to complete it in the reassessment period. Please refer to your official results for the details of your reassessments. The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH30800).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
