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
Prerequisites 
None 
Displayed in Visiting Students Prospectus? 
Yes 
Course Delivery Information

Delivery period: 2010/11 Semester 2, Available to all students (SV1)

WebCT enabled: Yes 
Quota: None 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
King's Buildings  Lecture   111   11:10  12:00     King's Buildings  Tutorial  NMC2 tutorials  211      11:10  12:00  King's Buildings  Laboratory  NMC2 labs  311  14:00  17:00  or 14:00  17:00    or 14:00  17:00 
First Class 
Week 1, Tuesday, 11:10  12:00, Zone: King's Buildings. Lecture Theatre 2, Hudson Beare Building 
Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 
Stationery Requirements 
Comments 
Main Exam Diet S2 (April/May)   1:30  12 sides   Resit Exam Diet (August)   1:30  12 sides  
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: nonlinear equations
Introduction to nonlinear equations. civil engineering applications; advantages and pitfalls of numerical solution techniques. Adhoc iteration (fixed point method): use, method, examples. Alternative strategies: bisection, regula falsa, NewtonRaphson. 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, EulerCauchy and RungeKutta 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 Bode&©s rules. For each: use, method, validity, effort, errors, and examples. Summary of rules. Style of Gauss rules, advantages over NewtonCotes rules, use of one and twopoint Gauss rules. Threepoint 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. Polynomial fitting by least squares. Algebraic differentiation. Problems likely to be encountered.
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: Nonlinear Equations
This computer lab exercise is undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of nonlinear equations using Fixed Point, NewtonRaphson, 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, EulerCauchy 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 handson 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.

Transferable skills 
Not entered 
Reading list 
1. Guide to Scientific Computing, P. R. Turner, Macmillan Press, 2000
2. Numerical Methods for Engineers, D.V. Griffiths and I.M. Smith, Blackwell Scientific Publications, 1991
3. Elementary Numerical Analysis, K. Atkinson, W. Han., 3rd ed., Wiley, 2003 (cf. http://www.math.uiowa.edu/~atkinson/ena_master.html)
4. Numerical analysis on wikipedia http://en.wikipedia.org/wiki/Numerical_analysis

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 

