1. Approximation 1.1 Uniform approximation 1.2 Approximation in the 2-norm 1.3 Orthogonal polynomials 1.4 Gaussian quadrature 1.5 Trigonometric interpolation and approximation 1.6 The Fast Fourier Transform (FFT)
2. Computation of eigenvalues and eigenvectors 2.1 The power method 2.2 Householder transformation; reduction to tridiagonal forms 2.3 The QR method 2.4 Singular Value Decomposition
3. Ordinary differential equations 3.1 Introduction: existence and uniqueness 3.2 One-step methods 3.3 Runge-kutta methods 3.4 Multistep methods 3.5 System of equations 3.6 Stiff problems