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look at this area of the web page periodically. Announcements will include
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Please read this policy before starting as I intend on enforcing it
MACHINE ARITHMETIC, ERROR PROPAGATION AND THE CONDITIONING OF PROBLEMS
Real numbers, machine numbers, rounding.
Propagation of rounding errors, cancellation errors.
Conditioning of problems, examples.
APPROXIMATION AND INTERPOLATION
Least squares approximation and data fitting.
Polynomial interpolation, Lagrange's formula.
Interpolation error and convergence.
Interpolation at Chebyshev points, Chebyshev polynomials.
Newton's form of the interpolation polynomial.
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.
Gaussian quadrature formulae.
Approximation of linear functionals, methods of interpolation and undetermined coefficients.
Extrapolation methods, Romberg integration.
Iterative methods, order of convergence.
Secant method and its convergence properties.
Newton's method, local and global convergence.
Systems of nonlinear equations
ORDINARY DIFFERENTIAL EQUATIONS
One-step methods, local and global error.
Notes on solving ODES from the CSEP book
PARTIAL DIFFERENTIAL EQUATIONS
Notes on solving PDES from the CSEP book
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.
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).