Finite precision arithmetic, error analysis, conditioning and stability
Linear systems of equations: LU and Cholesky factorization, condition
Interpolation: polynomial, spline and trigonometric interpolation
Nonlinear equations: fixed point iteration, root finding algorithms, Newton's method
Linear and nonlinear least squares problems: normal equations, Gram Schmidt and Householder orthogonalization, singular value decomposition, regularizatio, Gauss-Newton and Levenberg-Marquardt methods
Eigenvalue problems: power iteration, inverse iteration, QR algorithm