Undergraduate Course: Differential Equation Modelling & Solution (MATH08022)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 1 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Year 1) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | *In 2011-12, this course is available only to students retaking it and will be assessed on an 'exam only' basis.*
First year course, primarily for Honours Degrees in Mathematics and/or Statistics. Syllabus summary: Rate of change as a derivative. Velocity, acceleration, Newton's second law, including resistance. Modelling of population dynamics. Analytical methods for solving separable ordinary differential equations (ODEs) and linear first order ODEs with constant coefficients. Numerical and graphical methods of solution (including use of Maple). Truncation error and order. The idea of equilibrium. The topics will be developed through examples and practical questions, such as "Why do small hailstones not kill you?"; the motion of falling bodies; conservation of fish stocks: the effects of harvesting and overcrowding; Lotka-Volterra two-component models. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
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| Delivery period: 2012/13 Semester 2, Available to all students (SV1)
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WebCT enabled: No |
Quota: 3 |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| No Classes have been defined for this Course |
| First Class |
First class information not currently available |
| Additional information |
Tutorials: F at 0900, 1000 and 1110. |
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
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| Main Exam Diet S2 (April/May) | | 2:00 | | | | Resit Exam Diet (August) | | 2:00 | | |
Summary of Intended Learning Outcomes
1. Familiarity with Newton's second law for linear motion under gravity, with linear or quadratic resistance, or with buoyancy: and familiarity with formulating one-dimensional dynamics as an O.D.E. with initial condition(s).
2. Familiarity with the notions of dependent and independent variable, and order of a differential equation (up to second).
3. Ability to recognise and solve separable equations (analytically).
4. Ability to recognise and solve (analytically) linear first-order equations with constant coefficient and right-hand side equal to zero, constant, exponential, sine or cosine. Solution of y' = ky to be written at sight.
5. Ability to sketch direction fields and solution in simple cases (y' a function of x or of y only).
6. Ability to solve and plot solutions numerically (using Maple). Understanding of the concepts of truncation error (local and global), and order. Ability to apply Euler's method for one or two steps.
7. Understanding of the basic models of population dynamics: Malthus, constant harvesting, logistic; their solution, interpretation and comparison with experimental evidence.
8. Formulating and solving simple compartment models (e.g. mixing).
9. Knowledge of equivalence of system of two first order equations to a given second order equation. Finding phase plane equation for autonomous system of two first-order equations, and an integral.
10. Familiarity with the qualitative behaviour of the solutions of the Lotka-Volterra system, including its equilibrium and a first integral.
11. Ability to recognise the equation of displaced simple harmonic motion, and to write down the solution of the SHM equation at sight. Knowledge of its period. |
Assessment Information
| Coursework (which may include a Project): 15%; Degree Examination: 85%. |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
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| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | DMS |
Contacts
| Course organiser | Dr Toby Bailey
Tel: (0131 6)50 5068
Email: |
Course secretary | Ms Louise Durie
Tel: (0131 6)50 5050
Email: |
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