Undergraduate Course: Honours Differential Equations (MATH10066)
Course Outline
| 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.
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Information for Visiting Students
| 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 |
Course Delivery Information
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| 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 )
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| 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 |
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| Main Exam Diet S1 (December) | | 3:00 | |
Learning Outcomes
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.
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Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley (continuing students should already have a copy from year 2).
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | HDEq |
Contacts
| 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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