2009 Spring MATH 225-01
Bulletin Course Description Approximation theory: Fourier series, orthogonal polynomials, interpolating polynomials and splines. Numerical differentiation and integration. Numerical methods for ordinary differential equations: finite difference methods for initial and boundary value problems, and stability analysis. Introduction to finite element methods. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title SCIENTIFIC COMPUTING II Department MATH Course Number 2009 Spring 225 Section Number 01 Primary Instructor Maggioni,Mauro Prerequisites Prerequisite: Mathematics 224 and familiarity with ODEs at the level of Mathematics 107 or 131. Course Homepage www.math.duke.edu/~mauro/teaching.html
Synopsis of course content
This course will develop the theoretical basis and computational techniques for: (i) the approximation of functions; (ii) the numerical differentiation and integration; (iii) the solution of initial value problems for ordinary differential equations and (iv) random number generators, simulation of Markov chains and techniques for one-dimensional stochastic differential equations. Error analysis and formulation of convergent mathematical schemes will be used to derive stable, reliable, efficient, and accurate numerical methods for large classes of problems.
Textbooks
An Introduction to Numerical Analysis, 2d Edition,
by Kendall E. Atkinson
Assignments
Weekly problem sets will include theory, analysis and computational projects.
Exams
There will be a midterm and a final.
Grade to be based on
Course grade will be based on the problem sets and tests.
