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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -
- ARCHIVE as at 1 September 2013 for reference only
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Honours Differential Equations (MATH10066)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) Credits20
Home subject areaMathematics Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionCore 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.
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)
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?No
Course Delivery Information
Delivery period: 2013/14 Semester 1, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Course Start Date 16/09/2013
Breakdown of 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 Notes Students must pass exam and course overall.
Breakdown of Assessment Methods (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S2 (April/May)Honours Differential Equations3:00
Delivery period: 2013/14 Semester 1, Part-year visiting students only (VV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Course Start Date 16/09/2013
Breakdown of 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 Notes Students must pass exam and course overall.
Breakdown of Assessment Methods (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S1 (December)Honours Differential Equations (Semester 1 Visiting Students only)2:00
Summary of Intended 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.
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus 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)
Transferable skills Not entered
Reading list Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley
(continuing students should already have a copy from year 2).
Study Abroad Not Applicable.
Study Pattern See 'Breakdown of Learning and Teaching activities' above.
KeywordsHDEq
Contacts
Course organiserDr Joan Simon Soler
Tel: (0131 6)50 8571
Email: J.Simon@ed.ac.uk
Course secretaryMrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk
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