Undergraduate Course: Numerical Methods and Computing 2 (CIVE08017)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Credits | 10 |
| Home subject area | Civil |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course includes lectures on numerical methods for solution of mathematical problems, with engineering examples, and application of the methods on computers using MATLAB. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
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| Delivery period: 2011/12 Semester 2, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | | 18-27 | | 11:10 - 12:00 | | | | | King's Buildings | Tutorial | NMC2 tutorials | 19-27 | | | | | 11:10 - 12:00 | | King's Buildings | Laboratory | NMC2 labs | 20-27 | 14:00 - 17:00 | or 14:00 - 17:00 | | | or 14:00 - 17:00 |
| First Class |
Week 18, Tuesday, 11:10 - 12:00, Zone: King's Buildings. Lecture Theatre 2, Hudson Beare Building |
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
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| Main Exam Diet S2 (April/May) | | 1:30 | | | | Resit Exam Diet (August) | | 1:30 | | |
Summary of Intended Learning Outcomes
By the end of the course students should be able to:
- apply numerical methods to solve a variety of mathematical problems with relevance to engineering;
- demonstrate an understanding of the limitations and applicability of the methods
- demonstrate skills in solving similar problems using MATLAB programs |
Assessment Information
Coursework 20%
Examination 80% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Lectures: Titles & Contents
L1 Introduction to numerical methods
Introduction to numerical methods $ú relevance and usefulness. Overview of the course - aims and scope. Assessment and resources information. Preliminaries $ú general terms and concepts (convergence/divergence, stability, errors, iteration).
L2 and L3 Solution of algebraic equations: non-linear equations
Introduction to non-linear equations. civil engineering applications; advantages and pitfalls of numerical solution techniques. Ad-hoc iteration (fixed point method): use, method, examples. Alternative strategies: bisection, regula fals1, Newton-Raphson. Analyse problems using different strategies, importance of understanding the function. [Associated MATLAB exercises run in labs during same period]
L4 and L5 Numerical solution of ODE&©s
Introduction to solution of Ordinary Differential Equations, derivation and application of the Euler Method. Application of Euler, Euler-Cauchy and Runge-Kutta Methods. [Associated MATLAB exercises run in labs during same period]
L6 and L7 Numerical integration:
Reasons for integration arising in civil engineering problems; nature of integration, differences between numerical and algebraic integration, format of integration schemes, notation. Trapezium, Simpson&©s, Simpson&©s 3/8 and Boole&©s rules. For each: use, method, validity, effort, errors, and examples. Summary of rules. Style of Gauss rules, advantages over Newton-Cotes rules, use of one- and two-point Gauss rules. Three-point and higher rules. Use, errors, examples. Summary of rules.
L8 and L9 Numerical differentiation
Nature of the problem: situations in which it arises in civil engineering problems. Finite difference formulae. The concept of finite differences, two, three and higher point formulae. Errors. Central, backward and forward differences. Method order. Application of difference formulae to estimate derivatives. Examples.
L10 Revision
Applications and worked examples, to further demonstrate use of methods for solving Civil Engineering problems with guidance on checking correct implementation and common errors to avoid.
Tutorials: Titles & Contents
Some exercises in this module are undertaken in the Computer Laboratory using MATLAB. The aim is to build on the course Computer Tools for Civil Engineers 2 (CTC2) to give further experience and confidence in the use of numerical analysis packages on computers. Other examples are worked into revision exercises.
Computer Exercise 1: Non-linear Equations
This computer lab exercise is undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of non-linear equations using Fixed Point, Newton-Raphson, Bisection and False Position methods. Example scripts are provided for some of these, others must be developed from scratch. These are then applied to the solution of various mathematical problems, with investigation of issues such as convergence and tolerances. The lab exercises are designed to teach the student that problems which look difficult from an algebraic viewpoint can be simple numerically, and vice versa.
Computer Exercise 2: ODE&©s
This computer lab exercise is also undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of ODE&©s. The methods used are Euler, Euler-Cauchy and Runge Kutta. Example scripts are provided for some of these, others must be developed from scratch. These are then applied to the solution of various mathematical problems, some set in the context of Civil Engineering problem, with investigation of issues such as numerical errors and convergence and tolerances.
Assessment of the coursework is undertaken in the fifth week of labs, with a set of short questions testing ability to apply the above methods to some similar problems. It is conducted using MATLAB, with submission via the course intranet pages on WebCT.
There are also revision exercises for completion by hand run in weekly tutorial sessions. These will cover the same material as that of the teaching course, but provide the hands-on experience that students require to gain confidence in application of the methods, learning to resolve difficulties, correct misunderstandings, etc. The examples provided are typical of the questions asked during the examinations.
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| Transferable skills |
Not entered |
| Reading list |
1. Mathews, J.H. & Fink, K.D. &«Numerical Methods Using MATLAB&ª, Prentice Hall, 1999
2. Otto, S.R. & Denier, J.P. &«An introduction to Programming and Numerical Methods in MATLAB&ª, Springer, 2005
3. Morris, J.Ll. &«Computational Methods in Elementary Numerical Analysis&ª, Wiley, 1983
4. Elementary Numerical Analysis, K. Atkinson, W. Han., 3rd ed., Wiley, 2003 (cf. http://www.math.uiowa.edu/~atkinson/ena_master.html)
5. Numerical analysis on wikipedia http://en.wikipedia.org/wiki/Numerical_analysis
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| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Stephen Welch
Tel: (0131 6)50 5734
Email: S.Welch@ed.ac.uk |
Course secretary | Mrs Sharon Potter
Tel: (0131 6)51 7079
Email: Sharon.Potter@ed.ac.uk |
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