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
|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.
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.
PDEs by separation of variables
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.
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?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 30%, Examination 70%
||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
|Course organiser||Dr Tom MacKay
Tel: (0131 6)50 5058
|Course secretary||Miss Greta Mazelyte