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| Module Availability |
| Autumn Semester |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Assignment 1: Solution of system of algebraic equations (including writing of computer program)
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15
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Assignment 2: Solution of system of differential equations
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15
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Examination
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70
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Qualifying Condition(s)
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| Module Overview |
| FORTRAN programming revision. Numerical methods for: Systems of linear and non-linear algebraic equations; Eigenvalue problems; Ordinary differential equations (ODEs); Partial differential equations (PDEs). |
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| Prerequisites/Co-requisites |
Completion of the progress requirements of Level 2 & Modules SE0201 and SE0202 or equivalent. |
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| Module Aims |
Module Aims
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To build on previous learning, to introduce further numerical methods used in the solution of engineering problems and to link the Numerical Methods with Computer Programming and Computer simulations.
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| Learning Outcomes |
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Learning Outcomes
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Students should have an awareness of the numerical techniques available to them for the solution of engineering problems and an understanding of their applicability to different problems and associated issues in computer simulations, and be able to implement them in a suitable programming language.
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| Module Content |
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Module Content
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Roots of a non-linear equation
Roots of non-linear equations:
Further methods and extension to systems of non-linear equations.
Systems of Linear Equations:
LU decomposition, ill-conditioning, iterative methods, Jacobi, Gauss-Seidel, convergence of methods.
Numerical Solution of ODE's:
One-step, multi-step, predictor-corrector methods for initial value problems, including Euler's method and modifications, Runge-Kutta etc.; consideration of truncation and propagation errors, stability, step size control; extension to systems of equations for initial value problems; boundary value problems.
Numerical Solution of PDE's by Finite Difference Methods:
Solution of elliptic equations, implicit and explicit methods for parabolic equations, stability and convergence, representation of boundary conditions.
Matrices and Eigenvalue Problems:
Eigenvalues and eigenvectors, power method for the largest and smallest eigenvalues, deflation and shifting to determine intermediate eigenvalues, transformation methods eg. Jacobi.
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| Methods of Teaching/Learning |
Methods of Teaching/Learning
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22 lectures, 11 computer laboratory sessions, 67 hours independent learning time.
Total student learning time 100 hours.
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Methods of Assessment and Weighting
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Components of Assessment
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Method(s)
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Weighting
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Examination
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2-hour paper
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60%
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Coursework
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2 assignments
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40%
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| Selected Texts/Journals |
Selected Texts/Journals
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Recommended reading
Chapra SC
and Canale RP, Numerical Methods for Engineers,4th ed, McGraw Hill, 2002. (ISBN 0072431938)
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| Last Updated |
30/9/10 |
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