The role of models in chemical engineering Introduction The idea of a model Model building Model analysis Model solution strategies Summary Exercises Errors in computer simulations Introduction Significant digits Round off and truncation errors Break errors Loss of digits Ill conditioned problems (Un-)stable methods Summary Exercises Linear equations Introduction MATLAB Linear systems The inverse of a matrix The determinant of a matrix Useful properties Matrix ranking Eigenvalues and eigenvectors Spectral decomposition Summary Exercises Elimination methods Introduction MATLAB Gaussian elimination LU factorization Summary Exercises Iterative methods Introduction Laplace's equation LU factorization Iterative methods The Jacobi method Example for the Jacobi method Summary Exercises Nonlinear equations Introduction Newton's method D Newton's method D Reduced Newton step method Quasi Newton's method Summary Exercises Ordinary differential equations Introduction Euler's method Accuracy and stability of Euler's method The implicit Euler method Stability of the implicit Euler method Systems of ODE's Stability of ODE systems Stiffness of ODE systems Higher order methods Summary Exercises Partial differential equations 1 Introduction Types of PDE's The method of the lines Stability Summary Exercises Partial differential equations 2 Introduction Transport PDE's Finite Volumes Discretizing the control volumes Transfer of heat to fluid in a pipe Simulation of the heat PDE Summary Exercises Data regression and curve fitting Introduction The least squares method Residual analysis ANOVA analysis Confidence limits Summary Exercises Optimization Introduction Linear programming Nonlinear programming Integer programming Summary Exercises Basics of Matlab Introduction The Matlab user interface The array structure Basic calculations Plotting Reading and writing data Functions and m-files Repetitive operations Numerical methods in Excel Introduction Basic functions in Excel The Excel solver Solving nonlinear equations in Excel Differentiation Excel Curve fitting in Excel Case studies Introduction Modeling a separation system Modeling a chemical reactor system PVT behavior of pure substances Dynamic modeling of a distillation column Dynamic modeling of an extraction cascade (ODE's) Distributed parameter models for a tubular reactor Modeling of an extraction column Fitting of kinetic data Fitting of NRTL model parameters Optimizing a crude oil refinery Planning in a manufacturing line Bibliography.