# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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# 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 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.
 Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) OR Introductory Fields and Waves (PHYS08053) Co-requisites Prohibited Combinations Other requirements None
 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
 Academic year 2018/19, Available to all students (SV1) 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 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % 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 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 Not entered Keywords HDEq
 Course organiser Dr Jacques Vanneste Tel: (0131 6)50 6483 Email: J.Vanneste@ed.ac.uk Course secretary Miss Sarah McDonald Tel: (0131 6)50 5043 Email: sarah.a.mcdonald@ed.ac.uk
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