## 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)

15-859B, Introduction to Scientific Computing

14 Sept. 2000