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CS514: Numerical Analysis

Fall '00.
Tu, Th, 10:30 - 11:50 AM

Course Announcements:

Important announcements relating to the course will be made here. Please look at this area of the web page periodically. Announcements will include (but are not limited to) release of assignments, erratas, and grades.

Academic Dishonesty Policy:

Please read this policy before starting as I intend on enforcing it strictly.

Qualifier results determined by the committee (Prof. A. Sameh, Head, Computer Sciences, A. Grama, Asst. Professor, Computer Sciences).

Final letter grades.

Course Contents:

  • MACHINE ARITHMETIC, ERROR PROPAGATION AND THE CONDITIONING OF PROBLEMS

    Real numbers, machine numbers, rounding.
    Machine arithmetic.
    Propagation of rounding errors, cancellation errors.
    Conditioning of problems, examples.

  • APPROXIMATION AND INTERPOLATION

    Least squares approximation and data fitting.
    Orthogonal polynomials.
    Polynomial interpolation, Lagrange's formula.
    Interpolation error and convergence.
    Interpolation at Chebyshev points, Chebyshev polynomials.
    Newton's form of the interpolation polynomial.
    Hermite interpolation.
    Inverse interpolation.
    Interpolation by means of spline functions; minimal properties of spline interpolants.

  • NUMERICAL DIFFERENTIATION AND INTEGRATION

    Finite difference approximation of derivatives.
    Numerical integration by composite trapezoidal and Simpson rules.
    Newton-Cotes formulae.
    Gaussian quadrature formulae.
    Approximation of linear functionals, methods of interpolation and undetermined coefficients.
    Extrapolation methods, Romberg integration.

  • NONLINEAR EQUATIONS

    Examples.
    Iterative methods, order of convergence.
    Bisection method.
    Secant method and its convergence properties.
    Newton's method, local and global convergence.
    Algebraic equations.
    Systems of nonlinear equations

  • ORDINARY DIFFERENTIAL EQUATIONS

    One-step methods, local and global error.
    Runge-Kutta methods.
    Stiff equations.
    Multistep methods.

    Notes on solving ODES from the CSEP book

  • PARTIAL DIFFERENTIAL EQUATIONS

    Notes on solving PDES from the CSEP book

Grading policy

  • 50 percent of your grade is determined by 7-8 homeworks through the semester. All homeworks count for the same weight.
  • 20 percent of your grade is determined by your midterm.
  • 30 percent of your grade is determined by the final.
Additional References:
  • Finite Element Analysis: From concepts to applications, David S. Burnett, Addison Wesley, 1987.
  • Scientific Computation: An Introductory Survey, Michael T. Heath, McGraw Hill, 1996. (For the iterative solvers, preconditioners, and eigenvalue problems).