Math 307 (Fall 2010) Course
Outline
Instructor: Dr. George Chen
Textbook: Numerical
Analysis, 9th edition, 2010, by Richard Burden and Douglas Faires
Exclusion: Credit cannot be obtained for both Math 307 and Math 252/Chem 302
Objectives:
Students will learn how to solve applied problems which
will guide their exploration of the field of engineering and other applied
sciences. They will also learn how
to use computational tools, such as MATLAB or MAPLE to numerically solve those
problems. Topics will
generally include: the analysis of various
numerical integration, differentiation, numerical solution of ordinary
differential equations (ODEs), finding roots of nonlinear equations, the
solution of linear and non-linear of equations, and their error analysis. The
basic concepts and information needed to solve these problems will be provided
during lecture and lab time but students will be expected to carry out research
to find ways to solve these problems.
Outline:
Representation of numbers; error propagation and estimation; iterative algorithms.
Bisection, secant method, Newton's method; fixed point iteration and
acceleration.
Direct method - factorization, pivoting, inverse calculation; fixed
precision arithmetic and iteration method.
Interpolating polynomial, Lagrange form, error formula; cubic spline
interpolation;
trigonometric interpolation.
Finite-difference approximation; Numerical quadrature-Romberg scheme; composite
rules; Gaussian quadrature; Simpson’s rules.
Euler's method, Runge-Kutta and Adams methods; Multistep methods; convergence
and stability; stiff equations.
Marking Scheme:
Assignments 25%
Midterm/projects 30%
Final 45%