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 
Lab Supported SelfStudy Computing Module
Weeks 1  5
Supported by weekly computing laboratory sessions the student is introduced, using a specially developed selfstudy module, to the concepts of scientific programming and the use of a computing tool appropriate for engineering computation. The selfstudy module consists of five main units that broadly cover:
1. Basic Concepts,
2. Plotting,
3. Scripts and Functions,
4. Decision Making,
5. Loops.
Each individual unit contains many exercises with example solutions and some that have stepbystep instructions presented as video screencasts.
Lectures: Titles & Contents
Lectures are used to present the foundations of key numerical methods and their use in solving engineering problems. Emphasis is given on the application of the numerical methods and their implementation as computer algorithms.
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: nonlinear equations
Introduction to nonlinear equations. Civil engineering applications; advantages and pitfalls of numerical solution techniques. Adhoc iteration (fixed point method): use, method and examples. Alternative strategies: bisection, regula falsi, NewtonRaphson. Analyse problems using different strategies, importance of understanding the function.
L4 and L5: 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 NewtonCotes rules, use of one and twopoint Gauss rules. Threepoint and higher rules. Use, errors, examples. Summary of rules.
L6 and L7: 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.
L8 and L9: 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.
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: Nonlinear Equations
Students are asked to develop computer programs 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 that look difficult from an algebraic viewpoint can be simple numerically, and vice versa.
Computer Exercise 2: Numerical Integration
Students are asked to develop simple programs for carrying out numerical integration using the quadrature rules discussed in the lectures.
Computer Exercise 3: ODE's
Students are asked to develop simple computer programs for the solution of ODE's. Example scripts will be provided for some of these, others must be developed from scratch.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Additional Costs  None 
Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2015/16, Available to all students (SV1)

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 )

Assessment (Further Info) 
Written Exam
0 %,
Coursework
50 %,
Practical Exam
50 %

Additional Information (Assessment) 
Competence in Computing Class Test: 50%
Coursework 50% 
Feedback 
Mid Semester "Start, Stop, Continue"
Oral Feedback during Computing Laboratory Sessions
Written Feedback on submitted coursework
End of course "postmortem" 
No Exam Information 
Learning Outcomes
On completion of this course, the student will be able to:
 demonstrate skills in using computer programming tools for engineering calculations;
 demonstrate ability to construct simple computer algorithms using a programming tool;
 apply simple numerical methods to solve mathematical problems with relevance to civil engineering;
 appreciate the limitations and the applicability of the numerical methods;
 apply computerbased numerical methods for the solution of engineering problems.

Learning Resources
1. An Interactive Introduction to MATLAB
http://www.see.ed.ac.uk/teaching/courses/matlab/ 
Additional Information
Graduate Attributes and Skills 
Not entered 
Additional Class Delivery Information 
11 Lectures (1 in Week 1 and 10 in Weeks 6  10)
10 Computing Laboratory Sessions 
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)51 7073
Email: Lucy.Davie@ed.ac.uk 

