Representation of numbers, computer arithmetic, overflow and underflow, rounding error, cancellation error, truncation error, stopping conditions, solving f(x) = 0 (bisection, secant, Newton),interpolation (Lagrange polynomials, divided differences, splines), solving Ax = b (pivoting strategies, LU decomposition, complexity, special matrices (diagonally dominant, positive definite, banded), iterative methods (Jacobi, Gauss-Seidel, SOR, conjugate gradient) ), nonlinear systems (Newton, steepest descent, line search), approximation theory (normal equations, SVD, Legendre polynomials, Chebyshev polynomials), numerical integration (simple quadrature rules, composite rules, error estimates, Gaussian quadrature, improper integrals), numerical differentiation, numerical solutions to initial value ODE (Runge-Kutta, predictor-corrector, adaptive techniques, stiff ODE).