Undergraduate Course: Honours Differential Equations (MATH10066)
Course Outline
School | School of Mathematics |
College | College of Science and Engineering |
Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Availability | Available to all students |
SCQF Credits | 20 |
ECTS Credits | 10 |
Summary | Core course for Honours Degrees involving Mathematics.
This is a second course on differential equations discussing higher order linear equations, Laplace transforms, systems of First Order Linear ODEs, non-linear systems of ODEs, Fourier Series, use of separation of variables in standard PDEs and Sturm-Liouville Theory.
In the skills¿ section of the course, we will work on symbolic manipulation, computer algebra, graphics and a final project. Platform: Maple in computer labs. |
Course description |
Higher order linear ordinary equations with emphasis on those with constant coefficients.
Laplace transform to solve initial value problems based on linear ODEs with constant coefficients; addition of generalised functions as sources; .convolution theorem.
Systems of First Order Linear ODEs with constant coefficients using linear and matrix algebra methods.
Non-linear systems of ODEs : critical points, linear approximation around a critical point, classification of critical points, phase trajectory and phase portrait. Introduction to non-linear methods : Lyapunov functions, limit cycles and the Poincare-Bendixson theorem.
Fourier Series as an example of a solution to a boundary problem, orthogonality of functions and convergence of the series.
Separation of variables to solve linear PDEs. Application to the heat, Wave and Laplace equations.
Sturm-Liouville Theory : eigenfunctions, eigenvalues, orthogonality and eigenfunction expansions.
Skills :Use of a selection of basic Maple commands for symbolic manipulation for computer algebra and calculus; use of 2d and 3d Maple graphics; some applications in differential equations.
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Information for Visiting Students
Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
High Demand Course? |
Yes |
Course Delivery Information
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Academic year 2017/18, Available to all students (SV1)
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Quota: None |
Course Start |
Semester 1 |
Timetable |
Timetable |
Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 35,
Seminar/Tutorial Hours 10,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
138 )
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Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Coursework 20%, Examination 80%
Students must pass exam and course overall. |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
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Resit Exam Diet (August) | Honours Differential Equations (MATH10066) Resit | 3:00 | | Main Exam Diet S1 (December) | Honours Differential Equations (MATH10066) | 3:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- To know the general theory of linear ODEs, and to use the Laplace transform technique to solve initial value problems.
- To identify the critical points of non-linear systems of ODEs, to use linear algebra methods to describe their linear approximation and behaviour and extend these claims to the non-linear regime.
- To use the method of separation of variables to solve boundary problems in linear PDEs using the Sturm-Liouville theory.
- To perform symbolic manipulation, computer algebra, calculus and use of graphics in Maple confidently.
- To develop experience of working on a small individual project in Maple and reporting on the outcomes.
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Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley
(continuing students should already have a copy from year 2). |
Additional Information
Graduate Attributes and Skills |
Not entered |
Keywords | HDEq |
Contacts
Course organiser | Dr Jacques Vanneste
Tel: (0131 6)50 6483
Email: J.Vanneste@ed.ac.uk |
Course secretary | Ms Hannah Burley
Tel: (0131 6)50 4885
Email: Hannah.Burley@ed.ac.uk |
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