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, nonlinear systems of ODEs, Fourier Series, use of separation of variables in standard PDEs and SturmLiouville 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.
Nonlinear systems of ODEs : critical points, linear approximation around a critical point, classification of critical points, phase trajectory and phase portrait. Introduction to nonlinear methods : Lyapunov functions, limit cycles and the PoincareBendixson 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.
SturmLiouville 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
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2016/17, 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 )

Additional Information (Learning and Teaching) 
Students must pass exam and course overall.

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Honours Differential Equations  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 nonlinear systems of ODEs, to use linear algebra methods to describe their linear approximation and behaviour and extend these claims to the nonlinear regime.
 To use the method of separation of variables to solve boundary problems in linear PDEs using the SturmLiouville 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.

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 Joan Simon Soler
Tel: (0131 6)50 8571
Email: J.Simon@ed.ac.uk 
Course secretary  Mrs Kate Ainsworth
Tel: (0131 6)51 7761
Email: Kate.Ainsworth@ed.ac.uk 

