A Numerical Primer for the Chemical Engineer, Second Edition

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