CSC336S Numerical Methods

The first meeting of CSC336 is Monday, January 7, 2008, 6-9 p.m., in BA 1180.
Note the start time! (6 p.m.)
This Monday, there will be no tutorial. We will use two to two and a half hours of lecture.
Tutorials will start on Monday, January 14, 2008.

• Aims
• Outline
• References
• Prerequisites
• Schedule for Spring 2008
• Marking scheme for Spring 2008
• Announcements for current students

• Introduce numerical methods for solving (linear, nonlinear, differential) equations, approximation problems and integration 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
• Interpolation
  Polynomial interpolation Piecewise polynomial interpolation Spline interpolation
• Numerical Quadrature Simple quadrature rules Compound quadrature rules Gauss quadrature rules
• Least-Squares (non-square linear systems)
  normal equations, QR factorisation
• Solving nonlinear equations
  Bisection, secant Fixed point iteration, Newton's method Convergence Newton's method for systems, Jacobian matrix
• Ordinary Differential Equations Euler's method, forward and backward Multistep methods

References

General Numerical Analysis
Michael Heath	Scientific Computing: an introductory survey	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.
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 FORTRAN, C or MATLAB.
• Other Mathematics: induction.

Schedule for Spring 2008

Lectures	Monday 7-9(*)	Room BA 1180
Tutorial	Monday 6-7	Room BA 1180
Office Hours	Tuesday 4-5	Room BA 4226

(*) The first Monday, we start at 6 and end around 8:15 or so.

Tentative marking scheme for Spring 2008

Problem set 1	8%
Problem set 2	8%
Problem set 3	8%
Problem set 4	8%
Midterm test	20%
Final exam	48%

The problem sets include computer work.