# Engineering

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## ECMM135 - Numerical Methods (2015)

MODULE TITLE CREDIT VALUE Numerical Methods 15 ECMM135 Dr Khurram Wadee (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
 Number of Students Taking Module (anticipated) 22
DESCRIPTION - summary of the module content

Effective use of numerical methods is essential for any engineer.    This module introduces students to fundamental algorithms for solving algebraic and differential equations which are found in many engineering and other contexts.

AIMS - intentions of the module

This module aims to provide a treatment of numerical methods, simulation and optimisation techniques for the modern practising engineer. It also highlights the use of such techniques in the solution of management related problems.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge

1. Demonstrate knowledge of numerical modelling and simulation techniques and tools
2. Make appropriate and critical use of these tools to analyse and solve problems associated with engineering and management systems.

Discipline Specific Skills and Knowledge

3. Identify and formulate a problem and subsequently select an appropriate mathematical technique to solve it
4. some practical experience of using modelling or simulation techniques and tools

Personal and Key Transferable / Employment Skills and Knowledge

5. Demonstrate improved further the necessary skills for independent learning
6. Demonstrate enhanced report and presentation skills
7. Demonstrate improved IT skills

SYLLABUS PLAN - summary of the structure and academic content of the module

Introduction to numerical methods: Approximation of functions, Taylor series, First-order approximation, Errors, Error propagation. Roots of equations: Interval bisection, the Newton-Raphson technique, the secant method, stopping criteria. Solution of linear simultaneous equations: Gaussian elimination for two, three, n equations, conditioning, determinants, Gauss-Seidel method, conditioning, convergence. Curve fitting and interpolation: Linear regression, goodness of fit, normalized residuals, change of variable, logarithmic plots, polynomial or curvilinear interpolating polynomials, linear interpolation, quadratic interpolation, Lagrange interpolating polynomial, numerical differentiation, first derivatives from Taylor series, second derivatives from Taylor series. Numerical integration: Rectangular rule, trapezium rule, Simpson's rule, multiple application of Simpson's rule. Solution of ordinary differential equations (ODEs): Initial value problems, Euler-Cauchy method, Runge-Kutta methods, second-order Runge-Kutta, fourth-order Runge-Kutta.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 22 128 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning Activities 22 Lectures/tutorials Guided Independent Study 128 Assessment preparation

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 30 70 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam( closed book) 70 2 hours All Exam mark
Assignments x 2 30 2 assignments of 15% each on numerical methods. All Written

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All Above Written Examination (100%) All End of August

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 50% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk

Web based and Electronic Resources:

Other Resources: