Numerical Methods

Numerical methods are algorithms for solving practical problems in applied mathematics .
They are used extensively in many areas of science, engineering and business. They are
crucial to computational finance and portfolio management, computer games, graphics and
special effects, robotics and bioinformatics, data mining and machine learning, and many
other areas. Numerical methods are run on computers of all sizes, from laptops to workstations
to supercomputers. In fact, the need to solve large and complex problems with
numerical methods is the main reason supercomputers were developed.

Prerequisites : Informally, a basic knowledge of calculus, linear algebra and programming.
Formally, CSC207H5/270H5, 290H5; (MAT134Y5/135Y5/137Y5)/(MAT133Y5, 233H5),
MAT223H5.

Grading Scheme: Four assignments, 15% each; Midterm test, 10%; Final exam, 30%.
On all work, 20% of the mark will be for quality of presentation , including the use of
good English. The final exam and midterm will be based on the assignments and will
assume that you have completed them by yourself. Final marks may be adjusted up
or down to conform with University of Toronto grading policies. Late assignments will
not be accepted.

Text: Michael Heath, Scientific Computing: An Introductory Survey, Second Edition, Mc-
Graw Hill, 2002. Roughly the first half of the book will be covered. The relevant
chapters are being made available by McGraw hill at a special price.

Topics Covered: Numerical errors and computer arithmetic, systems of linear equations,
linear least squares , nonlinear equations, optimization, interpolation.