# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2014/2015 Archive for reference only THIS PAGE IS OUT OF DATE

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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. 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)
 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)
 Pre-requisites None
 Academic year 2014/15, 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 2014/15, 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
 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.
 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 Study Abroad Not Applicable. Keywords HDEq
 Course organiser Dr Joan Simon Soler Tel: (0131 6)50 8571 Email: J.Simon@ed.ac.uk Course secretary Mrs Kathryn Mcphail Tel: (0131 6)50 4885 Email: k.mcphail@ed.ac.uk
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