- Aims
- Outline
- References
- Prerequisites
- Schedule for Spring 2021
- Marking scheme for Spring 2021
- Announcements for current students

- Introduce numerical methods for solving linear and nonlinear equations, and approximation problems.
- Evaluate numerical methods with respect to their accuracy, time and memory complexity.
- Develop and practice computer skills in implementing numerical methods efficiently on the computer.
- Use high level software for studying numerical methods.

- Computer Arithmetic and Computational Errors

Representation of numbers, machine arithmetic, round-off error, error propagation, conditioning, stability - Solving square linear systems of equations

Gauss elimination, LU factorisation, pivoting, scaling, forward and back substitution,

Vector and matrix norms, condition numbers for systems - Solving nonlinear equations

Bisection, secant, Fixed point iteration, Newton's method, Convergence, Newton's method for systems, Jacobian matrix - Interpolation

Polynomial interpolation, existence and uniqueness of polynomial interpolant, Piecewise polynomial interpolation, Spline interpolation

General Numerical Analysis |
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Michael Heath | Scientific Computing: an introductory survey | SIAM 2018 or McGraw-Hill Inc. 2002+ |

Ask for Custom Printed version of book at the bookstore | It is cheaper | |

Cleve Moler | Numerical Computing with MATLAB | SIAM - Cambridge University Press |

David Kahaner, Cleve Moler and Stephen Nash | Numerical Methods and Software | Prentice Hall 1989 |

S. D. Conte and Carl de Boor | Elementary Numerical Analysis | McGraw-Hill Inc., or SIAM |

David Kincaid and Ward Cheney | Numerical Analysis | Brooks/Cole 2002 (1996) |

Richard L. Burden and J. Douglas Faires | Numerical Analysis | Brooks/Cole 2001 (1997) |

James Epperson | An introduction to Numerical Methods and Analysis | Wiley 2003 |

Numerical Linear Algebra |
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William W. Hager | Applied Numerical Linear Algebra | Prentice Hall 1988 |

- General: Ability to handle notation and to do algebraic manipulation.
- Calculus: Differentiation and integration of polynomial, trigonometric, exponential, logarithmic and rational functions, continuity, limits, graphs of functions, Taylor series, Rolle's theorem, mean-value theorem, de l' Hospital's rule.
- Linear Algebra: Matrix and vector addition and multiplication, elementary row operations, linear (in)dependence, inverse matrix, etc.
- Programming: knowledge of some programming language, such as MATLAB, C or FORTRAN.
- Other Mathematics: induction.

Lectures | Tuesday 1-3 | Room Virtual |

Tutorial | Thursday 1-2 | Room Virtual |

Office Hours | Monday 3:30-4:30 | Room Virtual |

** Tentative marking scheme for Spring 2021 **

Problem set 0 | 10% |

Problem set 1 | 12% |

Problem set 2 | 13% |

Problem set 3 | 13% |

Term test 1 | 13% |

Term test 2 | 13% |

Final exam | 26% |