Undergraduate Course: Computational Methods and Modelling 3 (MECE09033)
|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
|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 computational methods, including optimisation, and apply these methods to engineering problems. Evaluate the performance and suitability of the numerical methods for the three different types of partial differential equations. Some background in programming from Second Year design courses is assumed.
The course will consist of lectures and computer lab sessions, supporting 1 individual design project assignment and 1 open-book computer-based exam, needing three postgrad tutors.
1.Introduction to programming and primary coding via Python. General introduction to real-life problem modelling and approximation principles. Introduction to error and sensitivity analysis, limits of computer precision, accuracy v. computation speed.
2. Numerical methods: solving implicit equations, simultaneous equations and matrix operations, numerical integration and differentiation, numerical solution of ordinary differential equations (Runge-Kutta) and interpolation. Use of open coding and custom commands to achieve the above.
3. Optimisation methods: one-dimensional optimization (golden ratio search, Newton's Method, gradient methods), multi-dimensional optimization, constrained optimization, static and dynamic optimization. Use of open coding and standard commands to achieve the above.
Accreditation of Higher Education Programmes Learning Outcomes: SM5m, EA1b, EA2, EA3b, D3b, P2, P4, P6, P8, and G1.
Course Delivery Information
|Academic year 2021/22, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Exam %: 50
Course work %: 50
One larger group coursework exercise [50%].
Students will be given an open-ended engineering (optimisation) challenge and be asked to develop a model and implement a range of 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.
One individual open-book computer based exam [50%]
||More than half of contact time (18 hours) 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 first Skills Assignment (formative assignment weighted at 0% of course final mark) will provide a grounding in basic coding skills to solve closed-form numerical problems and will be aimed at consolidating these skills via computing laboratory feedback, week by week. The Design Project report will develop creative design thinking as well as deploying the skills developed during the first Skills Assignment.
||Hours & Minutes
|Main Exam Diet S1 (December)||2:00|
|Resit Exam Diet (August)||2:00|
On completion of this course, the student will be able to:
- Solve different types of equations systems, (simultaneous and implicit equations), ordinary differential equations), their derivatives and integrals, optimisation.
- Program such solution techniques in Python using both open coding and in-built commands.
- Develop mathematical models of real-life engineering problems, making and justifying simplifying assumptions in the process, and provide solutions to the resulting equations using the computational methods studied in the lectures.
|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.
|Graduate Attributes and Skills
|Keywords||Computational Methods,optimisation,mathematical modelling,numerical integration,error analysis
|Course organiser||Dr Antonio Attili
|Course secretary||Mrs Michelle Burgos Almada