1 The role of models in chemical engineering 1.1 Introduction 1.2 The idea of a model 1.4 Model analysis 1.5 Model solution strategies 1.6 Summary 1.7 Exercises 2 Errors in computer simulations 2.1 Introduction 2.

2 Significant digits 2.3 Round-off and truncation errors 2.4 Break errors 2.5 Loss of digits 2.6 Ill-conditioned problems 2.7 (Un-)stable methods 2.8 Summary 2.9 Exercises 3 Linear equations 3.

1 Introduction 3.2 MATLAB 3.3 Linear systems 3.4 The inverse of a matrix 3.5 The determinant of a matrix 3.6 Useful properties 3.7 Matrix ranking 3.8 Eigenvalues and eigenvectors 3.

9 Spectral decomposition 3.10 Summary 3.11 Exercises 4 Elimination methods 4.1 Introduction 4.2 MATLAB 4.3 Gaussian elimination 4.4 LU factorization 4.5 Summary 4.

6 Exercises 5 Iterative methods 5.1 Introduction 5.2 Laplace''s equation 5.3 LU factorization 5.5 The Jacobi method 5.6 Example for the Jacobi method 5.7 Summary 5.8 Exercises 6 Nonlinear equations 6.

1 Introduction 6.2 Newton method 1D 6.3 Newton method 2D 6.4 Reduced Newton step method 6.5 Quasi-Newton method 6.6 Summary 6.7 Exercises 7 Ordinary differential equations 7.1 Introduction 7.

2 Euler''s method 7.3 Accuracy and stability of Euler''s method 7.4 The implicit Euler method 7.5 Stability of the implicit Euler method 7.6 Systems of ODEs 7.7 Stability of ODE systems 7.8 Stiffness of ODE systems 7.9 Higher-order methods 7.

10 Summary 7.11 Exercises 8 Numerical integration 8.1 Introduction 8.2 Euler''s method 8.3 The trapezoid method 8.4 Simpson''s method 8.5 Estimation of errors using numerical integration 8.6 The Richardson correction 8.

7 Summary 8.8 Exercises 9 Partial differential equations 9.1 Introduction 9.2 Transport PDEs 9.3 Finite volumes 9.4 Discretizing the control volumes 9.5 Transfer of heat to fluid in a pipe 9.6 Simulation of the heat PDE 9.

7 Summary 9.8 Exercises 10 Data regression and curve fitting 10.1 Introduction 10.2 The least squares method 10.3 Residual analysis 10.4 ANOVA analysis 10.5 Confidence limits 10.6 Summary 10.

7 Exercises 11 Optimization 11.1 Introduction 11.2 Linear programming 11.3 Nonlinear programming 11.4 Integer programming 11.5 Summary 11.6 Exercises 12 Basics of MATLAB 12.1 Introduction 12.

2 The MATLAB user interface 12.3 The array structure 12.4 Basic calculations 12.5 Plotting 12.6 Reading and writing data 12.7 Functions and m-files 12.8 Repetitive operations 13 Numerical methods in Excel 13.1 Introduction 13.

2 Basic functions in Excel 13.3 The Excel solver 13.4 Solving nonlinear equations in Excel 13.5 Differentiation in Excel 13.6 Curve fitting in Excel 14 Case studies 14.1 Introduction 14.2 Modeling a separation system 14.3 Modeling a chemical reactor system 14.

4 PVT behavior of pure substances 14.5 Dynamic modeling of a distillation column 14.6 Dynamic modeling of an extraction cascade (ODEs) 14.7 Distributed parameter models for a tubular reactor 14.8 Modeling of an extraction column 14.9 Fitting of kinetic data 14.10 Fitting of NRTL model parameters 14.11 Optimizing a crude oil refinery 14.

12 Planning in a manufacturing line Bibliography Index t;BR>4.2 MATLAB 4.3 Gaussian elimination 4.4 LU factorization 4.5 Summary 4.6 Exercises 5 Iterative methods 5.1 Introduction 5.2 Laplace''s equation 5.

3 LU factorization 5.5 The Jacobi method 5.6 Example for the Jacobi method 5.7 Summary 5.8 Exercises 6 Nonlinear equations 6.1 Introduction 6.2 Newton method 1D 6.3 Newton method 2D 6.

4 Reduced Newton step method 6.5 Quasi-Newton method 6.6 Summary 6.7 Exercises 7 Ordinary differential equations 7.1 Introduction 7.2 Euler''s method 7.3 Accuracy and stability of Euler''s method 7.4 The implicit Euler method 7.

5 Stability of the implicit Euler method 7.6 Systems of ODEs 7.7 Stability of ODE systems 7.8 Stiffness of ODE systems 7.9 Higher-order methods 7.10 Summary 7.11 Exercises 8 Numerical integration 8.1 Introduction 8.

2 Euler''s method 8.3 The trapezoid method 8.4 Simpson''s method 8.5 Estimation of errors using numerical integration 8.6 The Richardson correction 8.7 Summary 8.8 Exercises 9 Partial differential equations 9.1 Introduction 9.

2 Transport PDEs 9.3 Finite volumes 9.4 Discretizing the control volumes 9.5 Transfer of heat to fluid in a pipe 9.6 Simulation of the heat PDE 9.7 Summary 9.8 Exercises 10 Data regression and curve fitting 10.1 Introduction 10.

2 The least squares method 10.3 Residual analysis 10.4 ANOVA analysis 10.5 Confidence limits 10.6 Summary 10.7 Exercises 11 Optimization 11.1 Introduction 11.2 Linear programming 11.

3 Nonlinear programming 11.4 Integer programming 11.5 Summary 11.6 Exercises 12 Basics of MATLAB 12.1 Introduction 12.2 The MATLAB user interface 12.3 The array structure 12.4 Basic calculations 12.

5 Plotting 12.6 Reading and writing data 12.7 Functions and m-files 12.8 Repetitive operations 13 Numerical methods in Excel 13.1 Introduction 13.2 Basic functions in Excel 13.3 The Excel solver 13.4 Solving nonlinear equations in Excel 13.

5 Differentiation in Excel 13.6 Curve fitting in Excel 14 Case studies 14.1 Introduction 14.2 Modeling a separation system 14.3 Modeling a chemical reactor system 14.4 PVT behavior of pure substances 14.5 Dynamic modeling of a distillation column 14.6 Dynamic modeling of an extraction cascade (ODEs) 14.

7 Distributed parameter models for a tubular reactor 14.8 Modeling of an extraction column 14.9 Fitting of kinetic data 14.10 Fitting of NRTL model parameters 14.11 Optimizing a crude oil refinery 14.12 Planning in a manufacturing line Bibliography Index r methods 7.10 Summary 7.11 Exercises 8 Numerical integration 8.

1 Introduction 8.2 Euler''s method 8.3 The trapezoid method 8.4 Simpson''s method 8.5 Estimation of errors using numerical integration 8.6 The Richardson correction 8.7 Summary 8.8 Exercises 9 Partial differential equations 9.

1 Introduction 9.2 Transport PDEs 9.3 Finite volumes 9.4 Discretizing the control volumes 9.5 Transfer of heat to fluid in a pipe 9.6 Simulation of the heat PDE 9.7 Summary 9.8 Exercises 10 Data regression and curve fitting 10.

1 Introduction 10.2 The least squares method 10.3 Residual analysis 10.4 ANOVA analysis 10.5 Confidence limits 10.6 Summary 10.7 Exercises 11 Optimization 11.1 Introduction 11.

2 Linear programming 11.3 Nonlinear programming 11.4 Integer programming 11.5 Summary 11.6 Exercises 12 Basics of MATLAB 12.1 Introduction 12.2 The MATLAB user interface 12.3 The array structure 12.

4 Basic calculations 12.5 Plotting 12.6 Reading and writing data 12.7 Functions and m-files 12.8 Repetitive operations 13 Numerical methods in Excel 13.1 Introduction 13.2 Basic functions in Excel 13.3 The Excel solver 13.

4 Solving nonlinear equations in Excel 13.5 Differentiation in Excel 13.6 Curve fitting in Excel 14 Case studies 14.1 Introduction 14.2 Modeling a separation system 14.3 Modeling a chemical reactor system 14.4 PVT behavior of pure substances 14.5 Dynamic modeling of a distillation column 14.

6 Dynamic modeling of an extraction cascade (ODEs) 14.7 Distributed parameter models for a tubular reactor 14.8 Modeling of an extraction column 14.9 Fitting of kinetic data 14.10 Fitting of NRTL model parameters 14.11 Optimizing a crude oil refinery 14.12 Planning in a manufacturing line Bibliography Index ction 11.2 Linear programming 11.

3 Nonlinear programming 11.4 Integer programming 11.5 Summary 11.6 Exercises 12 Basics of MATLAB 12.1 Introduction 12.2 The MATLAB user interface 12.3 The array structure 12.4 Basic calculations 12.

5 Plotting 12.6 Reading and writing data 12.7 Functions and m-files 12.8 Repetitive operations 13 Numerical methods in Excel 13.1 Introduction 13.2 Basic functions in Excel 13.3 The Excel solver 13.4 Solving nonlinear equations in Excel 13.

5 Differentiation in Excel 13.6 Curve fitting in Excel 14 Case studies 14.1 Introduction 14.2 Modeling a separation system 14.3 Modeling a chemical reactor system 14.4 PVT behavior of pure substances 14.5 Dynamic modeling of a distillation column 14.6 Dynamic modeling of an extraction cascade (ODEs) 14.

7 Distributed parameter models for a tubular reactor 14.8 Modeli.