CSC336 Numerical Methods, Fall 2025

The first meeting of CSC336 is Wednesday, September 3, 2025, 13:00-15:00, at UC 150.

• Aims
• Outline
• References
• Prerequisites
• Schedule for Fall 2025
• Marking scheme for Fall 2025
• 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 Ask for Custom Printed version of book at the bookstore> It is cheaper>

General Numerical Analysis
Michael Heath	Scientific Computing: an introductory survey	SIAM 2018 or McGraw-Hill Inc. 2002+
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, python, C or FORTRAN.
• Other Mathematics: induction.

Schedule for Fall 2025

Lectures	Wednesday 1-3 PM	Room UC 150
Tutorial	Friday 1-2 PM	Room BA 1160
Office Hours	Tuesday 1:30-2:30 PM	Room BA4226

Both lecture and tutorial times may be used for either purposes, depending on how the course material proceeds.
As the course proceeds, there will be more office hours, depending on due dates.

Tentative marking scheme for Fall 2025

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.