Introduction to Numerical Computations II
(same as AS/SC/MATH3242.03)
Section M Winter Tue, Thu 10:00-11:30
Section N Winter Wed 19:00-22:00
Section N is an Atkinson course. Students may complete this course for Arts
or Science credit. However, Section N may differ slightly from Section M.
For instance, Section N may have a different examination time which is not
posted in the regular examination schedule.
The course includes a study of algorithms and computer
methods for differentiation, integration, and solution of
ordinary differential equations. Nonlinear equations of
one variable, systems of nonlinear equations,
optimization of functions of one and several variables
and their relation to nonlinear equations are also
covered. The emphasis of the course is on the
development of numerical algorithms, the use of
intelligent mathematical software and the interpretation
of the results obtained on some assigned problems.
Topics covered may include the following.
- Solution of Nonlinear Equations and Unconstrained
Optimization - single nonlinear equation; systems of
nonlinear equations; unconstrained optimization.
- Numerical Differentiation and Integration - methods
of estimating derivatives; error analysis for
differentiation; the rectangle and trapezoid rule for
integration; Simpson's rule; Romberg's integration;
adaptive quadrature routines; truncation and round-off
errors in integration; improper integrals.
- Solution of Ordinary Differential Equations -
introduction; analytical versus numerical solutions;
basic numerical methods; Euler's, Heun's methods;
Taylor series methods; order of a method; local and
global errors; Runge-Kutta methods; Predictor-
corrector methods; systems of differential equations;
boundary value problems.
Prerequisites: for computer science majors general
prerequisites; COSC3121.03; MATH2270.03
Degree Credit Exclusion: MATH3242.03