# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# 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 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 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.
 Pre-requisites Co-requisites Prohibited Combinations Other requirements None Additional Costs None
 Pre-requisites None High Demand Course? Yes
 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
 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 http://www.see.ed.ac.uk/teaching/courses/matlab/
 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
 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
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