Numerical Methods I
Cross listed as G63.2010.001,
NUMERICAL METHODS I.
Thursday, 5:10-7:00 A.
Room 101 Courant.
Prerequisites: a solid
knowledge of undergraduate linear algebra, and
experience with writing computer programs (in Fortran, C, or other
language). Prior knowledge of Matlab is not required, but you will be
expected to learn it as the course progresses.
Floating point arithmetic; conditioning and stability; numerical linear
algebra, including systems of linear equations, least squares, and
eigenvalue problems; LU, Cholesky, QR and SVD factorizations; conjugate
gradient and Lanczos methods; interpolation by polynomials and cubic
splines; Gaussian quadrature. Computer programming assignments form an
essential part of the course.
Text: Numerical Linear Algebra,
Trefethen & Bau,
SIAM, 1997 (mandatory)
Tentative Syllabus: I
will attempt to cover the material in the course description (as well
as the textbook). If students are not familar with some fundamental
material, I may try and cover/review those topics as well. Such
topics include: Numerical methods for ODEs, Finite difference methods
for elliptic PDEs, Fast Fourier Transforms.