DAY COURSE

Prerequisite:

MATH 152 or MATH 155 or MATH 158, and MATH 232, and knowledge of a high level computer language such as FORTRAN, C, PASCAL or MODULA 2. Students with credit for MATH 406 or MATH 316 may not receive further credit for MACM 316.

Textbook:

Numerical Analysis, 8th edition by Burden & Faires, published by ITP Nelson. ISBN #: 0-534-39200-8.

Calendar Description:

A presentation of the problems commonly arising in numerical analysis and scientific computing and the basic methods for their solutions.

Outline:

Number systems and errors [1.5 weeks]

Representation of numbers; error propagation and error estimation.

Solution of nonlinear equations [2 weeks]

Bisection, secant method, Newton's method; fixed point iteration and acceleration.

Systems of linear equations [3 weeks]

Elimination method - factorization, pivoting, inverse calculation; iterative methods;

eigenvalue problems.

Interpolation and Approximation [2 weeks]

Interpolating polynomial, Lagrange form, error formula; spline interpolation;

>dd> trigonometric interpolation and Fourier Series.

Differentiation and Integration [1.5 weeks]

Numerical differentiation;

Numerical quadrature-Romberg scheme, composite rules, Gaussian quadrature.

Initial Value Problems [2 weeks]

Euler's method, Taylor and Runge-Kutta methods;

convergence, stability, trapezoid method;

stiff equations.

Grading Scheme

Assignments - 25%

Midterm - 30%

Final Exam - 45%

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester.