| Title: | Numerical Methods 1 |
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| Long Title: | Numerical Methods 1 |
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| Field of Study: |
Mathematics
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| Valid From: |
Semester 1 - 2016/17 ( September 2016 ) |
| Module Coordinator: |
David Goulding |
| Module Author: |
AINE NI SHE |
| Module Description: |
This is a first course in numerical techniques, introducing the student to problem solving and algorithms. |
| Learning Outcomes |
| On successful completion of this module the learner will be able to: |
| LO1 |
Use numerical techniques to solve non-linear equations. |
| LO2 |
Quantify numerical errors and ensure numerical methods are convergent and stable. |
| LO3 |
Apply both direct and iterative methods in the solution of physical problems. |
| LO4 |
Analyse and use numerical algorithms for both integration and differentiation. |
| LO5 |
Derive and apply numerical algorithms for interpolation. |
| Pre-requisite learning |
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
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Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. |
| No incompatible modules listed |
Co-requisite Modules
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| No Co-requisite modules listed |
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
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| No requirements listed |
Module Content & Assessment
| Indicative Content |
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Number Systems and Errors
Representation of real numbers. Floating point arithmetic. Basic concepts of numerical errors: absolute, relative, inherent, truncation, roundoff. Error propagation.
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Solution of Non-Linear Equations
Iterative methods. Regula-Falsi, Bisection, Secant method, Newton-Raphson. Fixed Point Iteration including: Zeroes (real or complex) of polynomial equations. Synthetic division.
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Systems of equations
Elimination methods; Gaussian elimination, pivoting, strategies, ill-conditioned systems. Tridiagonal systems. Iterative methods, Guass-Seidel, Gauss-Jacobi, relaxation methods.
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Approximation
Discrete Least square approximation. Orthogonal Polynomials & Least Squares Approximation.
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Interpolation
Polynomial forms. Interpolation polynomial. Lagrange form, Newton form (divided difference tables), Newton Gregory forms (difference tables). Piecewise polynomials. Splines.
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Numerical Integration & Differentiation
Newton-Cotes formulae. Mid-point, trapezoidal, Simpson’s, Romberg Integration. Gaussian quadrature. Difference operators. Numerical differentiation.
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| Assessment Breakdown | % |
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| Course Work | 100.00% |
| Course Work |
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| Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
| Practical/Skills Evaluation |
Based on weekly 2-hour Laboratory sessions |
1,4 |
25.0 |
Week 6 |
| Short Answer Questions |
Written assessment |
1,4 |
25.0 |
Week 7 |
| Practical/Skills Evaluation |
Based on weekly 2-hour Laboratory sessions |
2,3,5 |
25.0 |
Week 11 |
| Short Answer Questions |
Written assessment |
2,3,5 |
25.0 |
Week 12 |
| No End of Module Formal Examination |
| Reassessment Requirement |
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.
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The institute reserves the right to alter the nature and timings of assessment
Module Workload
| Workload: Full Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Lecture |
2.0 |
Every Week |
2.00 |
| Lab |
Computer laboratory |
2.0 |
Every Week |
2.00 |
| Independent & Directed Learning (Non-contact) |
Independent study |
3.0 |
Every Week |
3.00 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
4.00 |
| Workload: Part Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Independent & Directed Learning (Non-contact) |
Independent study |
3.0 |
Every Week |
3.00 |
| Lecture |
Lecture |
2.0 |
Every Week |
2.00 |
| Lab |
Computer laboratory |
2.0 |
Every Week |
2.00 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
4.00 |
Module Resources
| Recommended Book Resources |
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- S.C.Chapra 2014, Numerical Methods for Engineers, 7th Ed., McGraw-Hill [ISBN: 978-007339792]
- S.C. Chapra 2012, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd Ed., TMH [ISBN: 978-125902743]
| | This module does not have any article/paper resources |
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| This module does not have any other resources |
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Module Delivered in
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