Instructor: Gerard Richter
   richter@cs.rutgers.edu, 732-445-2001 x2097
   314 Core Building
   office hrs: Monday 12-1 pm, Tuesday 1:30-3 pm, or by appointment
 

Teaching assistant: Runhe(Bruce) Tian
   rtian@cs.rutgers.edu
   Hill 402
   office hours: Monday, 3-5 pm, or by appointment  

Texts (reference) - first two on reserve in Math Sciences Library (Hill Center):

• M. T. Heath, Scientific Computing, An Introductory Survey, 2nd edition, McGraw-Hill, 2002 (primary reference - available in bookstore)
• G. Dahlquist & A. Bjorck, Numerical Methods, Prientice-Hall, 1974, 2003, 2008
• G. H. Golub & C. F. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996.
• Matlab tutorial + links to other references
  

Grading:

• written homework, computer programs ~ 20%
• midterm ~ 35%
• final exam ~ 45%

Outline of topics...

• Floating point numbers and roundoff error
• Solution of nonlinear algebraic equations
• bisection method, regula falsi, fixed point iteration, secant method, Newton's method
• convergence rates (linear, quadratic)
• systems of nonlinear equations - Newton's method
• Solution of linear algebraic systems
• Gaussian elimination/ LU decomposition
• special cases: symmetric, banded, sparse matrices
• error analysis, norms, condition number
• iterative methods (SOR, convergence rates)
• algorithms for parallel computers
• overdetermined systems, least squares solutions
• Other numerical linear algebra topics + applications
  • QR decomposition
  • Singular value decomposition
  • Web search - PageRank
• Interpolation, approximation of functions
• the interpolating polynomial (its construction and error term)
• piecewise polynomial interpolation, splines
• Numerical differentiation and integration
• quadrature formulas, error terms
• adaptive quadrature, Gaussian quadrature
• numerical differentiation, error terms
• Numerical solution of ordinary differential equations
• basic methods (Taylor methods, Runge-Kutta methods, multistep methods)
• stability, consistency, convergence
• higher order equations, systems