CSC336S Numerical Methods

The first meeting of CSC336 is Thursday, January 12, 2023, 18:00-21:00.

• Aims
• Outline
• References
• Prerequisites
• Schedule for Spring 2023
• Marking scheme for Spring 2023
• 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

References

General Numerical Analysis
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
William W. Hager	Applied Numerical Linear Algebra	Prentice Hall 1988

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, 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.

Schedule for Spring 2023

Lectures	Thursday 6-8 PM	Room BA 1190
Tutorial	Thursday 8-9 PM	Room BA 1190
Office Hours	Thursday 4:30-5:30 PM	Room BA4226 or online

Both lecture and tutorial times may be used for either purposes, depending on how the course material proceeds.

Tentative marking scheme for Spring 2023

Problem set 1	13%
Problem set 2	13%
Problem set 3	13%
Term test 1	21%
Final exam	40%

The problem sets include computer work.