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 | 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 and matrix algebra methods.
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.
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 | This is a Year 3, Honours level course. Visiting students are expected to have an academic profile equivalent to the first two years of the BSc (Hons) Mathematics programme (UTMATHB). Students should have passed courses equivalent to Several Variable Calculus and Differential Equations (MATH08063), or Introductory Fields and Waves (PHYS08053). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
| Course Start Date |
15/09/2025 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 33,
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
140 )
|
| 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 |
Minutes |
|
| Main Exam Diet S1 (December) | Honours Differential Equations (MATH10066) | 180 | |
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.
|
Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, Wiley
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | HDEq |
Contacts
| Course organiser | Dr Tom MacKay
Tel: (0131 6)50 5058
Email: T.Mackay@ed.ac.uk |
Course secretary | Miss Greta Mazelyte
Tel:
Email: greta.mazelyte@ed.ac.uk |
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