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Course Description
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Course Name
Numerical Methods
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Host University
University of Cape Town
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Location
Cape Town, South Africa
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Area of Study
Mathematics
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Language Level
Taught In English
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Prerequisites
At least 40% in MAM2080W or equivalent courses.
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Course Level Recommendations
Lower
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
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Host University Units
12 -
Recommended U.S. Semester Credits2
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Recommended U.S. Quarter Units3
Hours & Credits
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Overview
The aim of this course is to introduce a selection of advanced topics in numerical methods. Topics include: Computational issues: finite precision, speed of algorithm, Matlab Polynomial interpolation: Lagrange form, Newton Form, error formulae, splines. Solutions to non-linear equations: bisection method, inverse interpolation, Newton's method in one dimension, error formulae, rates of convergence, Newton's method for systems. Solutions to linear equations: Gaussian elimination, pivoting, LU factorisation, QR factorisation, iterative methods. Numerical differentiation: derivation of finite difference formulae. Numerical integration: derivation of Newton-Cotes formulae, adaptive composite trapezium rule, Gaussian integration. Solutions to systems of
explicit first-order ODEs: Euler, modified Euler, Runge-Kutta. Stiffness: stability, backward Euler. Conversion of higher order explicit equations to first-order systems. Solution to PDE BVP on a rectangular domain by finite differences on a regular mesh.DP requirements: attendance at all class tests, submission of all assignments, 40% average for class tests and assignments.
Assessment: 6 computer class tests (40%), 2 assignments(10%), computer final examination (50%).
Course Disclaimer
Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.