CSC260F Introduction to Scientific, Symbolic and Graphical Computation
- 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;
- 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;
- 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
|Radford Neal, Christina Christara
||CSC260 Lecture Slides (and brief guides on Maple and MATLAB)
||To be available after each lecture
||An Introduction to Scientific, Symbolic and Graphical Computation
||A. K. Peters 1995
| General Numerical Methods
||Scientific Computing: an introductory survey
||McGraw-Hill Inc. 2003
|S. D. Conte and Carl de Boor
||Elementary Numerical Analysis
|Richard L. Burden and J. Douglas Faires
||Brooks/Cole 2001, 7th edition
|Keith Geddes, George Labahn and Michael Monagan
||Maple 12 Advanced Programming Guide
|M. B. Monagan ... [et al.]
||Maple V programming guide
|K. M. Heal, M. L. Hansen and K. M. Rickard
||Maple V learning guide
|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.
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.
Manipulation of polynomials, factorization, roots, etc.
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
The problem sets include computer work (programming, testing).
| 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 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.