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. Higher order linear equations; Laplace transform; Systems of First Order Linear ODEs; Non-linear systems of ODEs; Fourier Series; Intro to 3 common PDEs; Sturm-Liouville Theory. Skills: Symbolic manipulation, computer algebra, graphics, final project. Platform: Maple in computer labs.
Course description	See reading list below for relevant textbook. Higher order linear equations (Chapter 4 (25p) 2h) in particular const. coeffs, as motivation for systems. Laplace transform (Chapter 6 (50p) 4h) solving const. coeffs. ODEs, step functions, impulse functions, convolution. Systems of First Order Linear ODEs (Chapter 7 (90p) 7h) solution using eigenpairs, solution of initial value problem, matrix exponential, homog. and inhomog. systems with const. coeffs. Non-linear systems of ODEs (Chapter 9 (90p) 7h) classification of 2x2 systems, phase trajectory and phase portrait. Saddle, centre, node and focus, linearisation, Hartman-Grobman-Theorem, van-der-Pol system, trapping regions, periodic solutions, Poincare-Bendixson Theorem. Fourier Series (Chapters 10.1-10.4 (50p) 4h) periodicity, orthogonality, convergence, even/odd. Intro to 3 common PDEs (Chapters 10.5-10.8, (50p) 3h) Heat eq., Wave eq., Laplace's eq., initial and boundary conditions, separation of variables. Sturm-Liouville Theory (Chapter 11, (60p) 5h) eigenfunctions, eigenvalues, orthogonality, eigenfunction expansions, boundary value problems, Euler-Cauchy ODE, completeness, self-Adjoint differential operators. (total 32h listed) 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. (total 10h)

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
1. Higher order linear equations, in particular const. coeffs, as motivation for systems 2. Laplace transform , solving const. coeffs. ODEs, step functions, impulse functions, convolution 3. Systems of First Order Linear ODEs, solution using eigenpairs, solution of initial value problem, matrix exponential, homog. and inhomog. systems with const. coeffs. 4. Non-linear systems of ODEs, classification of 2x2 systems, phase trajectory and phase portrait. Saddle, centre, node and focus, linearisation, Hartman-Grobman-Theorem, van-der-Pol system, trapping regions, periodic solutions, Poincare-Bendixson Theorem 5. Fourier Series , periodicity, orthogonality, convergence, even/odd Intro to 3 common PDEs: Heat eq., Wave eq., Laplace's eq., initial and boundary conditions, separation of variables. 6. Sturm-Liouville Theory: eigenfunctions, eigenvalues, orthogonality, eigenfunction expansions, boundary value problems, Euler-Cauchy ODE, completeness, self-Adjoint differential operators 7. Confidence using Maple to perform symbolic manipulation in computer algebra and calculus; use of Maple graphics. 8. Investigate issues related to differential equations. 9. Experience of working on a small individual project in Maple and reporting on the outcomes.