Undergraduate Course: Numerical Methods and Computing 2 (CIVE08017)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This course includes an introduction to the concepts of scientific programming using MATLAB and a series of lectures and computing lab sessions on numerical methods for the solution of mathematical problems, with engineering examples, and application of these methods on computers using MATLAB. |
| Course description |
Self-Study Module
"An interactive Introduction to MATLAB" is a self-study module that consists of five main units that broadly cover: MATLAB Basic Concepts, Plotting, Scripts and Functions, Decision Making and Loops. Each individual unit contains many exercises with example solutions and some that have step-by-step instructions presented as video screen-casts.
Lectures: Titles & Contents
L1: Introduction to numerical methods
Introduction to numerical methods - relevance and usefulness. Overview of the course - aims and scope. Assessment and resources information. Preliminaries - 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 and examples. Alternative strategies: bisection, regula falsi, 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 after the completion of the Self study module "An interactive introduction to MATLAB", 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.
There are also revision computer based exercises for completion in weekly lab sessions in conjunction with the series of lectures. 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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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 |
Course Delivery Information
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| Academic year 2014/15, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 10,
Seminar/Tutorial Hours 9,
Supervised Practical/Workshop/Studio Hours 12,
Formative Assessment Hours 1,
Summative Assessment Hours 3.5,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
62 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
0 %,
Practical Exam
20 %
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| Additional Information (Assessment) |
Coursework 20%
Examination 80% |
| Feedback |
Not entered |
| 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 | |
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 using computer tools such as MATLAB for engineering calculations;
- demonstrate skills in applying numerical methods for the solution of engineering problems using MATLAB programs.
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Reading List
1. Mathews, J.H. & Fink, K.D. "Numerical Methods Using MATLAB", Prentice Hall, 1999
2. Otto, S.R. & Denier, J.P. "An introduction to Programming and Numerical Methods in MATLAB", Springer, 2005
3. Morris, J.Ll. "Computational Methods in Elementary Numerical Analysis", 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 |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Antonios Giannopoulos
Tel: (0131 6)50 5728
Email: A.Giannopoulos@ed.ac.uk |
Course secretary | Miss Lucy Davie
Tel: (0131 6)50 5687
Email: Lucy.Davie@ed.ac.uk |
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