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 computing and a series of lectures and computing lab sessions on important numerical methods often used for the solution of mathematical problems encountered in Civil Engineering. |
| Course description |
Self-Study Module (Weeks 1 - 5)
The self-study module consists of five main units that broadly cover: 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.
The self-study module on computer programming is supported by weekly computing laboratory sessions (Weeks 1 - 5)
Lectures: Titles & Contents
Week 1
L1: Introduction to numerical methods and computing
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).
Weeks 6 - 10
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.
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.
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.
Computing Laboratory Sessions (Weeks 7 - 10) (Compulsory attendance)
In the remaining Computing Laboratory sessions a number of exercises are undertaken. These will at least cover three key numerical methods and their applications as follows:
Computer Exercise 1: Non-linear Equations
Students are asked to develop computer programs 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 that look difficult from an algebraic viewpoint can be simple numerically, and vice versa.
Computer Exercise 2: ODE's
Students are asked to develop computer programs 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.
Computer Exercise 3: Numerical Integration
Students are asked to develop simple programs for carrying out numerical integration using the quadrature rules discussed in the lectures.
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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 |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2015/16, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 11,
Supervised Practical/Workshop/Studio Hours 15,
Formative Assessment Hours 1,
Summative Assessment Hours 8,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
63 )
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| Assessment (Further Info) |
Written Exam
0 %,
Coursework
50 %,
Practical Exam
50 %
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| Additional Information (Assessment) |
Competence in Computing Class Test: 50%
Coursework 50% |
| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- apply numerical methods to solve a variety of mathematical problems with relevance to civil engineering;
- demonstrate an understanding of the limitations and applicability of these methods;
- demonstrate skills in using computer programming tools for engineering calculations;
- demonstrate ability to construct simple computer algorithms using the programming tool;
- demonstrate skills in applying computer-based numerical methods for the solution of civil engineering problems.
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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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