A numerical primer for the chemical engineer

 Content: 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 di erential 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   Sti ness of ODE systems   Higher order methods   Summary   Exercises   Partial di erential equations 1   Introduction    Types of PDE's   The method of the lines   Stability    Summary   Exercises   Partial di erential 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   Di erentiation 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
 Abstract:             "This book emphasizes the deriviation and use of a variety of numerical methods for solving chemical engineering problems. The algorithms are used to solve linear equations, nonlinear equations, ordinary differential equations and partial differential equations. It also includes chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is adopted as the programming environment throughout the book. MATLAB is a high performance computing program. An introductory chapter on MATLAB basics has been added and Excel users can find a chapter on the implementation of numerical methods in Excel. Another chapter with worked out exaples are given in the Case study chapter to demonstrate the numerical techniques. Most of the examples were written in MATLAB and are compatible with the latest versions of MATLAB. It is important to mention that the main purpose of this book is to give the students a flavor of numerical methods and problem solving, rather than to be an in depth guide to numerical analysis. The chapters end with small exercises that students can use to familiarize them selves with the numerical methods. The material in this book has been used in undergraduate and graduate courses in the chemical engineering department of Eindhoven University of Technology. To aid lecturers and students course materials have also been made available on the web at http://webpage.com. The author would finally thank everybody who has been helpful and supportive in the creation of this book, especially some of the Ph.D. students at Eindhoven University that have assisted during lectures and directly influenced the content of this book: Juan Pablo Gutierrez, Esayas Barega and Arend Dubbelboer"