Module Details |
| The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
| Title | NUMERICAL METHODS | ||
| Code | MATH266 | ||
| Coordinator |
Dr I Thompson Mathematical Sciences Ian.Thompson@liverpool.ac.uk |
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| Year | CATS Level | Semester | CATS Value |
| Session 2016-17 | Level 5 FHEQ | Second Semester | 15 |
Aims |
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To provide an introduction to the main topics in Numerical Analysis and their relation to other branches of Mathematics |
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Learning Outcomes |
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After completing the module students should be able to: • write simple mathematical computer programs in Maple, • understand the consequences of using fixed-precision arithmetic, • analyse the efficiency and convergence rate of simple numerical methods, • develop and implement algorithms for solving nonlinear equations, • develop quadrature methods for numerical integration, • apply numerical methods to solve systems of linear equations and to calculate eigenvalues and eigenvectors, • solve boundary and initial value problems using finite difference methods. |
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Syllabus |
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| 1 |
• Elements of computer programming: variables, conditionals, loops, arrays and procedures. • Rounding, error propagation and cancellation. • Solving nonlinear equations; bisector, false position, secant and Newton-Raphson methods. • Newton-Cotes and Gaussian quadrature. • Numerical methods for linear systems: Gaussian elimination, LU factorisation and iterative methods. • Norms and conditioning. • Calculation of eigenvalues and eigenvectors via the power algorithm and the inverse power algorithm. • Numerical solution of ordinary and partial different ial equations by finite difference methods. • Numerical solution of Fredholm integral equations. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. Explanation of Reading List: |
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Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
| MATH101; MATH102; MATH103 |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
| G100 Year:2 G101 Year:2 G110 Year:2 G1F7 Year:2 G1R9 Year:2 GG13 Year:2 GN11 Year:2 GL11 Year:2 GR11 Year:2 GV15 Year:2 GG1A Year:2 BCG0 Year:2 L000 Year:2 Y001 Year:2 X390 Year:2 |
Assessment |
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| EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Unseen Written Exam | 2.5 hours | Second semester | 90 | Yes | Assessment 2 Notes (applying to all assessments) Assessment 1: Assignments are not marked anonymously. Assessment 2: Answer all of Section A and THREE questions from Section B. The marks shown against questions, or parts of questions, indicate their relative weight. Section A carries 55% of the available marks. Candidates who attempt more than three questions in section B will receive marks for the best three answers only. | |
| CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Coursework | Second semester | 10 | No reassessment opportunity | Standard UoL penalty applies | Assessment 1 There is no reassessment opportunity, | |