# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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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. 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 skills section of the course, we will work on symbolic manipulation, computer algebra, graphics and a final project. Platform: Python in computer labs. Course description Syllabus : Systems of First Order Linear ODEs with constant coefficients using linear andmatrix algebra methods. Numerical methods: Euler, Heun, RK Nonlinear systems of ODEs: critical points, linear approximation around a critical point; introduction to nonlinear methods: Lyapunov functions. Fourier series PDEs by separation of variables Sturm-Liouville theory Laplace transform Skills : Python brush up: functions, plotting. Systems of 1st order ODEs: plotting phase portraits, using SciPy ODE solvers. Nonlinear systems: exploring dynamical systems (limit cycles, chaos in the Lorenz model, in the periodically perturbed pendulum...) using SciPy ODEsolvers. Numerical methods for ODEs: implementing Euler, Heun, etc. Fourier: comparison function/truncated series, perhaps computation of Fourier coefficients. PDEs: plots of 2D functions, animations.
 Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) OR Introductory Fields and Waves (PHYS08053) Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. High Demand Course? Yes
 Academic year 2019/20, 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 ) 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 Resit Exam Diet (August) Honours Differential Equations (MATH10066) Resit 3:00 Main Exam Diet S1 (December) 3:00
 On completion of this course, the student will be able to: Know the general theory of linear ODEs, and to use the Laplace transform technique to solve initial value problems.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.Use the method of separation of variables to solve boundary problems in linear PDEs using the Sturm-Liouville theory.Solve ordinary differential equations, symbolically and numerically, in Python with confidence.Develop experience of working on a small individual project in Python 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 Keywords HDEq
 Course organiser Dr Jacques Vanneste Tel: (0131 6)50 6483 Email: J.Vanneste@ed.ac.uk Course secretary Miss Sarah McDonald Tel: (0131 6)50 5043 Email: sarah.a.mcdonald@ed.ac.uk
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