Numerical Methods

University of Cape Town

Course Description

  • Course Name

    Numerical Methods

  • Host University

    University of Cape Town

  • Location

    Cape Town, South Africa

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    At least 40% in MAM2080W or equivalent courses.

  • 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.

    Hours & Credits

  • Host University Units

    12
  • Recommended U.S. Semester Credits
    2
  • Recommended U.S. Quarter Units
    3
  • 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.