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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
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryCore 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) OR Introductory Fields and Waves (PHYS08053)
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesVisiting 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
Course Delivery Information
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%

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Exam Information
Exam Diet Paper Name Hours & Minutes
Resit Exam Diet (August)Honours Differential Equations (MATH10066) Resit3:00
Main Exam Diet S1 (December)3:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Know the general theory of linear ODEs, and to use the Laplace transform technique to solve initial value problems.
  2. 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.
  3. Use the method of separation of variables to solve boundary problems in linear PDEs using the Sturm-Liouville theory.
  4. Solve ordinary differential equations, symbolically and numerically, in Python with confidence.
  5. Develop experience of working on a small individual project in Python and reporting on the outcomes.
Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley
(continuing students should already have a copy from year 2).
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Jacques Vanneste
Tel: (0131 6)50 6483
Course secretaryMiss Sarah McDonald
Tel: (0131 6)50 5043
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