## Numerical Analysis Classes

Numerical Analysis 1 - Introduction: MTH 443/643(Each Fall semester).  Prerequisites: MTH 331 Linear Algebra, and CS 205 Scientific Computing (may take concurrently)

Topics include: floating point number systems; rates of convergence - algebraic and geometric; nonlinear equations and nonlinear systems; introduction to numerical linear algebra: condition numbers, LU factorizations, backward stability; basis functions: monomials, orthogonal polynomials, radial basis functions; interpolation; Runge-Kutta methods for the solution of ODEs.

ODE Lab - Applet that illustrates properties of numerical methods for ODE initial value problems.

Numerical Analysis 2 - Linear Algebra:  MTH 442/642 (Each Spring semester). Prerequisites: MTH 443/643.

Topics include: Orthogonal matrices, Householder transformations, QR factorization, least squares problems; the singular value decomposition (SVD); symmetric positive definite matrix factorizations; eigenvalues and pseudospectra; iterative methods for linear systems; and Gaussian quadrature.

Text:  Numerical Linear Algebra.   Supplemental text(s): Numerical Linear Algebra and Applications

Numerical Analysis 3 - PDEs: MTH 667 (Offered in response to student demand.  A graduate level course, (well-qualified undergraduates may take the course).  Prerequisites: MTH 443/643 (may take concurrently).

Topics include: numerical differentiation in physical space - differentiation matrices; Fourier and Chebyshev approximation; numerical differentiation in transform space; the fast Fourier transform (FFT) and the fast cosine transform (FCT); Clenshaw-Curtis quadrature; the method of lines and stability; diffusion and advection diffusion problems; wave propagation problems; dispersion and dissipation; boundary value problems;  discontinuous problems; spectral viscosity.

Text:  Spectral Methods in xxxxxx.   Supplemental text(s):  Chebyshev and Fourier Spectral Methods

Numerical Advection - Applet that solves the 1d advection equation with periodic boundary conditions using a large number of different numerical methods.

Removal of Gibbs' oscillations - Applet that illustrates post-processing methods to remove Gibbs' oscillations from Fourier and Chebyshev approximations of functions that have discontinuities.