This course aims to give an introduction to the advanced applied mathematical methods that are the basic tools in many areas of applied mathematics.

Two hours of lectures a week (delivered by live video link across the Scottish Mathematical Sciences Training Council (SMSTC) network).

Ten hours of tutorial time spread over the semester.

Assessment

100% Final Exam

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

The course aims to develop analytical methods for the solution/approximate solution of ordinary differential equations. An extensive range of asymptotic methods are developed and applied to a variety of well-known ordinary differential equations. Contour integral methods are then introduced and the asymptotic

analysis is extended to these integrals.

On completion of this course the student will be expected to know and understand

the main aspects of the theory and should be able to:

1. Use asymptotic methods to approximate the solutions of ordinary differential equations, including the method of multiple scales and the methods of strained parameters;

2. Construct matched expansions for the outer, inner and composite expansions of the solutions of ordinary differential equations;

3. Resolve boundary layer behaviour and identify boundary layer location;

4. Reproduce the asymptotic analysis for the equations investigated in lectures and be able to apply this analysis to unseen equations of a similar type;

5. Apply the WKB method to unseen ordinary differential equations of similar type to those discussed in lectures;

6. Solve simple ordinary differential equations by contour integral methods and examine the asymptotic behaviour of these integral solutions by using Watson's Lemma or the method of steepest descents.

7. Describe the basic elements and issues involved in the development and use of software for the solution of ordinary and partial differential equations including matters of stability, convergence, choice of step size and error control.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.