- Aims
- Outline
- References
- Prerequisites
- Schedule for Fall 2008
- Marking scheme for Fall 2008
- Announcements for current students

- Introduce techniques of transforming elementary (continuous) problems to (discrete) mathematical models.
- Give examples of computational (symbolic and numerical) methods for solving selected mathematical problems, such as those arising in graphics.
- Point out possible inadequacies of naive computer solutions and introduce techniques to remedy the inadequacies.
- Use high level software for solving mathematical problems.

- Examples of symbolic and numerical computations in Maple
- Representations of numbers; fixed-point and floating-point representations; rounding errors
- Approximating functions; Taylor series and other methods; evaluating polynomials
- Explicit, implicit, and parametric representations of curves and surfaces
- Rendering lines and curves for computer display
- Examples of numerical computations in MATLAB
- Solving differential equations; dynamical simulations
- Lagrange and piecewise polynomial interpolation; natural cubic splines; basis functions
- Finding zeros of functions symbolically and numerically
- Integrating functions symbolically and numerically
- Deriving mathematical results
- Approximation using Fourier series
- Filtering signals and images

Main Reference |
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Radford Neal, Christina Christara | CSC260 Lecture Slides (and brief guides on Maple and MATLAB) | To be available after each lecture |

Eugene Fiume | An Introduction to Scientific, Symbolic and Graphical Computation | A. K. Peters 1995 |

General Numerical Methods |
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Michael Heath | Scientific Computing: an introductory survey | McGraw-Hill Inc. 2003 |

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

Richard L. Burden and J. Douglas Faires | Numerical Analysis | Brooks/Cole 2001, 7th edition |

Maple |
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Keith Geddes, George Labahn and Michael Monagan | Maple 12 Advanced Programming Guide | MapleSoft 2008 |

M. B. Monagan ... [et al.] | Maple V programming guide | Springer-Verlag 1998 |

K. M. Heal, M. L. Hansen and K. M. Rickard | Maple V learning guide | Springer-Verlag 1998 |

Matlab |
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Charles F. Van Loan | Introduction to Scientific Computing: A matrix-vector approach using MATLAB | Prentice Hall 2000 |

- 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, basic knowledge on Taylor series, Rolle's theorem, mean-value theorem, de l' Hospital's rule, sequences and series, introduction to differential equations, etc.
- Algebra: Manipulation of polynomials, factorization, roots, etc.
- Linear Algebra: Matrix and vector addition and multiplication, elementary row operations, linear (in)dependence, orthogonality, inverse matrix, etc.
- Programming: knowledge of some (conventional) programming language, exposure to various programming techniques.
- Computer skills: ability to use a text editor (e.g. vi, emacs, nedit, etc.) to edit files under Unix, ability to use the basic Unix commands.
- Other Mathematics: induction.

Lectures | Wednesday 7-9 | Room BA 1230 |

Tutorial | Wednesday 6-7 | Room BA 1230 |

Office Hours | Wednesday 5-6 (other hours by appointment) | Room BA 4226 |

** Tentative marking scheme for Fall 2008 **

Problem set 1 | 8% | Wed, Oct 8 |

Midterm test | 24% | Wed, Oct 22 |

Problem set 2 | 8% | Wed, Nov 5 |

Problem set 3 | 8% | Wed, Nov 19 |

Problem set 4 | 8% | Wed, Dec 3 |

Final exam | 44% |

The problem sets are to be done

Must get at least 33% in the final exam.

Must get at least 33% in the computer work part of the problem sets.

Midterm test and Final exam: Calculators are the only aids permitted.