15-859B: Syllabus for Introduction to Scientific Computing

The first 2/3 of the course will follow Heath's book (chapters 1-11)
fairly closely.

The following is tentative.

    introduction
	what is scientific computing?
	approximations
	floating point
    systems of linear equations, briefly
	Gaussian elimination
	norms, residual
    linear least squares
	overdetermined systems
	orthogonalization
	QR factorization
    eigenvalues, eigenvectors, and singular values
    nonlinear equations
	Newton's method
    optimization
	one-dimensional
	multidimensional
	Levenberg-Marquardt method
	constrained optimization
    interpolation
	B-splines
    numerical integration and differentiation
	Gaussian quadrature
    initial value problems for ordinary differential equations
	Euler's method
	stability
	Runge-Kutta
    boundary value problems for ordinary differential equations
	finite difference methods
	finite element methods
    partial differential equations
	sparse systems of equations
	iterative methods for solving linear systems
	conjugate gradient method
	preconditioning
	multigrid
	applications in stress analysis, heat diffusion, fluid flow,
	    radiation, computer graphics
    wavelets
	review of basis functions
	orthogonal functions
	nested function spaces
	Haar and higher order wavelets
	orthonormal, compact wavelets
	applications
	    image compression
	    solving PDE's
    mesh generation
	Delaunay triangulation
	element shape and mesh quality
	finite element method on complex geometries
    variational methods (time permitting)