# Math 690, Fall 2012

## Exam Schedule

Exam 1: Take home test, Due October 1.
Exam 2: Take home test, Due November 12. Answers.
Final: Take home test, Due Monday, December 10.

### Worksheets

Cancellation.pdf:  Loss of digits due to taking differences.

Newton.pdf:  Newton’s Method.

RichardsonExtrapolation.pdf:  First look at Richardson Extrapolation.

LagrangeFunctions.pdf:  Lagrange basis functions.

VandermondeMatrix.pdf:  First look at the Vandermonde matrix.

RungeFunction.pdf:  Interpolation for the Runge function.

NewtonCotesFormulae.pdf:  First look at Newton-Cotes formulae.

RungeErrorControlForIntegration.pdf:  Runge Error Control.

GaussianIntegration.pdf:  Gaussian Integration with a weight function.

BSplines.pdf:  B-Splines.

EulerAndModifiedEulerAndRungeKutta.pdf:  Euler’s Method, the Modified Euler Method, and the Runge-Kutta Method.

Lorenz.pdf:  Lorenz Butterfly.

Lorenz.mw:  Lorenz Butterfly.

PolySolver.pdf:  Very simple polynomial solver.

Newton2D.pdf:  Two-dimensional Newton’s method and Griewank’s example.

Shooting.pdf:  Shooting Method (W. Hao) .

linear_ODE.pdf:  Linear ODEs (W. Hao).

fdiff3.pdf:  Linear ODEs (T. McCoy).

fdiff6.pdf:  Linear ODEs (T.McCoy).

SVD_Schur_QR.pdf:  Some Matrix Decompositions.

Galerkin.pdf:  Galerkin Example.

Griewank.pdf:  Griewank’s Example of a polynomial system root that Newton’s method cannot reach.