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On cancellation errors and ill-conditioned problems: Trying to compute cos(x).
On finding roots using the bisection method
On finding roots using the Newton-Raphson method
On finding roots using the Secant method
On interpolation
On finite-difference approximations of the first derivative.
On numerical integration.
On Gaussian elimination
On LU decompositions
On using iterative methods to solve A x = b
On linear transformations and norms in R^n
On ordinary differential equations.
On systems of ordinary differential equations.
On solving the heat equation using finite-difference methods and spectral methods.
How matlab does its fast Fourier transform.
On solving Burgers equation using spectral methods.
On solving the advection equation.