Undergraduate Course: Computational Methods and Modelling 3 (MECE09033)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 9 (Year 3 Undergraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | To model real-world problems, simplifications and approximations always need to be made. This course will introduce students to computational methods to support mathematical modelling for engineering design, analysis and decision-making. The course will introduce the fundamentals of numerical and asymptotic computational methods, including optimisation, and apply these methods to engineering problems. |
| Course description |
The course will consist of lectures and computer lab sessions, supporting 4 small individual assignments, 1 group assignment and 1 open-book computer-based exam, needing four postgrad tutors.
Lectures:
1.Introduction to modelling and approximation: dimensional analysis, scaling/similitude, self-similarity, orders of magnitude, identification of small parameters.
2.Numerical methods:computer precision, solving implicit equations, simultaneous equations and matrix operations, interpolation, integration, ordinary differential equations (Runge-Kutta).
3.Asymptotic methods: Taylor-series expansions, regular and singular perturbations, function inversion, integrals, method of multiple scales.
4.Optimisation methods: one-dimensional optimization (golden section search, direct and gradient methods, genetic algorithms), multi-dimensional optimization, constrained optimization, static and dynamic optimization.
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Course Delivery Information
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| Academic year 2017/18, Not available to visiting students (SS1)
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Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 15,
Seminar/Tutorial Hours 18,
Feedback/Feedforward Hours 1,
Summative Assessment Hours 2,
Revision Session Hours 1,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
61 )
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| Assessment (Further Info) |
Written Exam
35 %,
Coursework
65 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
«br /»
Exam %: 35«br /»
Course work %: 65 «br /»
«br /»
Four smaller individual coursework exercises [7.5% each]. «br /»
Students submit one page maximum with graphs and text, attaching their code.«br /»
1.Implicit and simultaneous equations.«br /»
2.Numerical integrationand ordinary differential equations.«br /»
3.Asymptotic methods.«br /»
4.Optimisation.«br /»
«br /»
One larger group coursework exercise [35%]. «br /»
Students will be given an open-ended engineering (optimisation)challenge and be asked to develop a model and implement a range of asymptotic and numerical methods to devise a solution. Marks will be awarded for originality, accuracy and efficiency. Students will write a 5-page report in groups of 4. «br /»
«br /»
One individual open-book computer based exam [35%] |
| Feedback |
More than half of contact time (18hours) will be committed to supported computer lab tutorials,where example problems are solved using elementary algorithms. As the course progresses, these lab sessions will increasingly support the assignments. The four smaller assignments will provide a good opportunity for regular feedback during the first half of the course. |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | | 2:00 | | | Resit Exam Diet (August) | | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Solve different types of equations(systems, implicit equations, ordinary differential equations), their derivatives and integrals using numerical and asymptotic techniques and perform optimisation;
- Program such solutions techniques in MATLAB;
- Develop mathematical models of ¿real-life¿ engineeringproblems, making and justifying simplifying assumptions in the process, and provide solutions to the resulting equations using the computational methods studied in the lectures.
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Reading List
Numerical Methods for Engineers, 6th edition, S.C. Chapra, R.P Canale, McGraw-Hill, 2010.
An Introduction to Programming and Numerical Methods in MATLAB, SR Otto, JP Denier, Springer, 2005.
A First Course in Numerical Methods, U. Ascher & C.Greif, SIAM, 2011.
Perturbation Methods (any edition), E. J. Hinch, Cambridge University Press, 1995. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Computational Methods,Numerical and asymptotic approximation,optimisation,mathematical modelling |
Contacts
| Course organiser | Dr Edward Mccarthy
Tel: (0131 6)50 4867
Email: ed.mccarthy@ed.ac.uk |
Course secretary | Mrs Lynn Hughieson
Tel: (0131 6)50 5687
Email: Lynn.Hughieson@ed.ac.uk |
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