2006 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 2006 Spring 225 Section Number 01 Primary Instructor Trangenstein,John Permission required? N Course Homepage www.math.duke.edu/~johnt/math224
Prerequisites
Mathematics 224 (Scientific Computing I) and undergraduate-level background in ODEs (at the level of Math 111 or 131).
Synopsis of course content
This course will develop the theoretical basis and computational techniques for: (i) the approximation of functions - interpolation, extrapolation, splines and orthogonal bases, (ii) the numerical differentiation and integration, and (iii) the solution of ordinary differential equations - both initial value problems and boundary value problems. 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
(Available On-Line) Scientific Computing by John Trangenstein (22 August 2000) (Chapters 9-12).
Assignments
There will be weekly problem sets. These will involve analysis and some computing assignments in Fortran or C/C++.
Exams
No exams
Grade to be based on
Course grade will be based on the problem sets.
