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DRPS : Course Catalogue : School of Engineering : Civil

Undergraduate Course: Numerical Methods and Computing 2 (CIVE08017)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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 Self-Study Computing Module

Weeks 1 - 5

Supported by weekly computing laboratory sessions the student is introduced, using a specially developed self-study module, to the concepts of scientific programming and the use of a computing tool appropriate for engineering computation. The self-study 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 step-by-step instructions presented as video screen-casts.

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: 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 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.

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, Euler-Cauchy and Runge-Kutta 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: 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: 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)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements None
Additional Costs None
Information for Visiting Students
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 "post-mortem"
No Exam Information
Learning Outcomes
On completion of this course, the student will be able to:
  1. demonstrate skills in using computer programming tools for engineering calculations;
  2. demonstrate ability to construct simple computer algorithms using a programming tool;
  3. apply simple numerical methods to solve mathematical problems with relevance to civil engineering;
  4. appreciate the limitations and the applicability of the numerical methods;
  5. apply computer-based numerical methods for the solution of engineering problems.
Learning Resources
1. An Interactive Introduction to 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
KeywordsNot entered
Course organiserDr Antonios Giannopoulos
Tel: (0131 6)50 5728
Course secretaryMiss Lucy Davie
Tel: (0131 6)51 7073
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