Introduction. 1. Computational Linear Algebra. Basic concepts and methods. Linear programming. LU decomposition. Inversion of symmetric, positive definite matrices. Tridiagonal systems of equations. Eigenvalues and eigenvectors of a symmetric matrix. Accuracy in algebraic computations. Ill-conditioned problems. Applications and further problems. 2. Nonlinear Equations and Extremum Problems. Nonlinear equations in one variable. Minimum of functions in one dimension. Systems of nonlinear equations. Minimization in multidimensions. Applications and further problems. 3. Parameter Estimation. Fitting a straight line by weighted linear regression. Mutivariable linear regression. Nonlinear least squares. Linearization, weighting and reparameterization. Ill-conditioned estimation problems. Multiresponse estimation. Equilibrating balance equations. Fitting error-in-variables models. Fitting orthogonal polynomials. Applications and further problems. 4. Signal Processing. Classical methods. Spline functions in signal processing. Fourier transform spectral methods. Applications and further problems. 5. Dynamical Models. Numerical solution of ordinary differential equations. Stiff differential equations. Sensitivity analysis. Quasi steady state approximation. Estimation of parameters in differential equations. Identification of linear systems. Determining the input of a linear system by numerical deconvolution. Applications and further problems. Subject Index.