A numerical primer for the chemical engineer <P>1 The role of models in chemical engineering<BR>1.1 Introduction<BR>1.2 The idea of a model<BR>1.4 Model analysis<BR>1.5 Model solution strategies<BR>1.6 Summary<BR>1.7 Exercises< P><P>2 Errors in computer simulations<BR>2.1 Introduction<BR>2.2 Significant digits<BR>2.3 Round off and truncation errors<BR>2.4 Break errors<BR>2.5 Loss of digits<BR>2.6 Ill conditioned problems<BR>2.7 (Un )stable methods<BR>2.8 Summary<BR>2.9 Exercises< P><P>3 Linear equations<BR>3.1 Introduction<BR>3.2 MATLAB<BR>3.3 Linear systems<BR>3.4 The inverse of a matrix<BR>3.5 The determinant of a matrix<BR>3.6 Useful properties<BR>3.7 Matrix ranking<BR>3.8 Eigenvalues and eigenvectors<BR>3.9 Spectral decomposition<BR>3.10 Summary<BR>3.11 Exercises< P><P>4 Elimination methods<BR>4.1 Introduction<BR>4.2 MATLAB<BR>4.3 Gaussian elimination<BR>4.4 LU factorization<BR>4.5 Summary<BR>4.6 Exercises< P><P>5 Iterative methods<BR>5.1 Introduction<BR>5.2 Laplace’s equation<BR>5.3 LU factorization<BR>5.5 The Jacobi method<BR>5.6 Example for the Jacobi method<BR>5.7 Summary<BR>5.8 Exercises< P><P>6 Nonlinear equations<BR>6.1 Introduction<BR>6.2 Newton method 1D<BR>6.3 Newton method 2D<BR>6.4 Reduced Newton step method<BR>6.5 Quasi Newton method<BR>6.6 Summary<BR>6.7 Exercises< P><P>7 Ordinary differential equations<BR>7.1 Introduction<BR>7.2 Euler’s method<BR>7.3 Accuracy and stability of Euler’s method<BR>7.4 The implicit Euler method<BR>7.5 Stability of the implicit Euler method<BR>7.6 Systems of ODEs<BR>7.7 Stability of ODE systems<BR>7.8 Stiffness of ODE systems<BR>7.9 Higher order methods<BR>7.10 Summary<BR>7.11 Exercises< P><P>8 Numerical integration<BR>8.1 Introduction<BR>8.2 Euler’s method<BR>8.3 The trapezoid method<BR>8.4 Simpson’s method<BR>8.5 Estimation of errors using numerical integration<BR>8.6 The Richardson correction<BR>8.7 Summary<BR>8.8 Exercises< P><P>9 Partial differential equations <BR>9.1 Introduction<BR>9.2 Transport PDEs<BR>9.3 Finite volumes<BR>9.4 Discretizing the control volumes<BR>9.5 Transfer of heat to fluid in a pipe<BR>9.6 Simulation of the heat PDE<BR>9.7 Summary<BR>9.8 Exercises< P><P>10 Data regression and curve fitting<BR>10.1 Introduction<BR>10.2 The least squares method <BR>10.3 Residual analysis<BR>10.4 ANOVA analysis<BR>10.5 Confidence limits<BR>10.6 Summary<BR>10.7 Exercises< P><P>11 Optimization<BR>11.1 Introduction<BR>11.2 Linear programming<BR>11.3 Nonlinear programming<BR>11.4 Integer programming<BR>11.5 Summary<BR>11.6 Exercises< P><P>12 Basics of MATLAB<BR>12.1 Introduction<BR>12.2 The MATLAB user interface<BR>12.3 The array structure<BR>12.4 Basic calculations<BR>12.5 Plotting<BR>12.6 Reading and writing data<BR>12.7 Functions and m files<BR>12.8 Repetitive operations< P><P>13 Numerical methods in Excel<BR>13.1 Introduction<BR>13.2 Basic functions in Excel<BR>13.3 The Excel solver<BR>13.4 Solving nonlinear equations in Excel<BR>13.5 Differentiation in Excel<BR>13.6 Curve fitting in Excel< P><P>14 Case studies <BR>14.1 Introduction<BR>14.2 Modeling a separation system<BR>14.3 Modeling a chemical reactor system<BR>14.4 PVT behavior of pure substances<BR>14.5 Dynamic modeling of a distillation column<BR>14.6 Dynamic modeling of an extraction cascade (ODEs)<BR>14.7 Distributed parameter models for a tubular reactor<BR>14.8 Modeling of an extraction column<BR>14.9 Fitting of kinetic data<BR>14.10 Fitting of NRTL model parameters<BR>14.11 Optimizing a crude oil refinery<BR>14.12 Planning in a manufacturing line <BR>Bibliography<BR>Index< P>