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 skillsż 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.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063)	Co-requisites
Prohibited Combinations		Other requirements	Students must not have taken : MATH10033 Complex Variable & Differential Equations or MATH09014 Differential Equations (VS1)

Information for Visiting Students
Pre-requisites	None
High Demand Course?	Yes

Course Delivery Information

Academic year 2015/16, 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 S2 (April/May)	Honours Differential Equations		3:00

Academic year 2015/16, Part-year visiting students only (VV1)		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 (Semester 1 Visiting Students only)		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.