CSC260F Introduction to Scientific, Symbolic and Graphical Computation

• 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

References

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

Prerequisites

• 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.

Schedule for Fall 2008

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 include computer work (programming, testing).
The problem sets are to be done individually by each student.
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.