# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2021/2022

### Information in the Degree Programme Tables may still be subject to change in response to Covid-19

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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 2021/22, 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 70 %, Coursework 30 %, Practical Exam 0 % Additional Information (Assessment) Coursework 30%, Examination 70% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) 3:00
 On completion of this course, the student will be able to: Solve systems of linear ordinary differential equations, selecting the most appropriate method, including Laplace transform.Describe the behaviour of solutions of systems of nonlinear ordinary differential equations, locally by identifying critical points and determining their nature, and globally by identifying periodic orbits.Apply the method of separation of variables to solve simple linear PDEs (heat, wave and Laplace equations and similar), and demonstrate understanding of the Sturm-Liouville theory underpinning the method.Use appropriate symbolic and numerical methods in Python to solve and analyse differential equations.Carry out a small individual investigation, making use of Python, and produce a written report 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 Greta Mazelyte Tel: Email: greta.mazelyte@ed.ac.uk
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