Undergraduate Course: Numerical Methods and Computing 2 (CIVE08017)
|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
|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.
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,
3. Scripts and Functions,
4. Decision Making,
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.
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.
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)
||Other requirements|| None
|Additional Costs|| None
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2017/18, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 10,
Supervised Practical/Workshop/Studio Hours 20,
Formative Assessment Hours 1,
Summative Assessment Hours 8,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Competence in Computing Class Test: 50%
||Mid Semester "Start, Stop, Continue"
Oral Feedback during Computing Laboratory Sessions
Written Feedback on submitted coursework
End of course "post-mortem"
|No Exam Information
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 computer-based numerical methods for the solution of engineering problems.
|1. An Interactive Introduction to MATLAB|
|Graduate Attributes and Skills
|Additional Class Delivery Information
10 Computing Laboratory Sessions
|Course organiser||Dr Antonios Giannopoulos
Tel: (0131 6)50 5728
|Course secretary||Miss Lorna Brown
Tel: (0131 6)51 7073