Undergraduate Course: Honours Differential Equations (MATH10066)
|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
|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.
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.
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?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
Students must pass exam and course overall.
||Hours & Minutes
|Resit Exam Diet (August)||Honours Differential Equations (MATH10066) Resit||3:00|
|Main Exam Diet S1 (December)||Honours Differential Equations (MATH10066)||3:00|
On completion of this course, the student will be able to:
- Know the general theory of linear ODEs, and to use the Laplace transform technique to solve initial value problems.
- 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.
- Use the method of separation of variables to solve boundary problems in linear PDEs using the Sturm-Liouville theory.
- Perform symbolic manipulation, computer algebra, calculus and use of graphics in Maple confidently.
- Develop experience of working on a small individual project in Maple and reporting on the outcomes.
|Elementary Differential Equations and Boundary Value Problems, Boyce|
and DiPrima, Wiley
(continuing students should already have a copy from year 2).
|Graduate Attributes and Skills
|Course organiser||Dr Jacques Vanneste
Tel: (0131 6)50 6483
|Course secretary||Miss Sarah McDonald
Tel: (0131 6)50 5043