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E-raamat: Computational and Statistical Methods for Chemical Engineering

(University of Groningen, The Netherlands), (USI Università della Svizzera italiana, Switzerland)
  • Formaat: 308 pages
  • Ilmumisaeg: 19-Dec-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781000822625
  • Formaat - EPUB+DRM
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  • Formaat: 308 pages
  • Ilmumisaeg: 19-Dec-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781000822625

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In the recent decades, the emerging new molecular measurement techniques and their subsequent availability in chemical database has allowed easier retrieval of the associated data by the chemical analyst. Before the data revolution, most books focused either on mathematical modeling of chemical processes or exploratory chemometrics. Computational and Statistical Methods for Chemical Engineering aims to combine these two approaches and provide aspiring chemical engineers a single, comprehensive account of computational and statistical methods.

The book consists of four parts:











Part I discusses the necessary calculus, linear algebra, and probability background that the student may or may not have encountered before. Part II provides an overview on standard computational methods and approximation techniques useful for chemical engineering systems. Part III covers the most important statistical models, starting from simple measurement models, via linear models all the way to multivariate, non-linear stochiometric models. Part IV focuses on the importance of designed experiments and robust analyses.

Each chapter is accompanied by an extensive selection of theoretical and practical exercises. The book can be used in combination with any modern computational environment, such as R, Python and MATLAB. Given its easy and free availability, the book includes a bonus chapter giving a simple introduction to R programming.

This book is particularly suited for undergraduate students in Chemical Engineering who require a semester course in computational and statistical methods. The background chapters on calculus, linear algebra and probability make the book entirely self-contained. The book takes its examples from the field of chemistry and chemical engineering. In this way, it motivates the student to engage actively with the material and to master the techniques that have become crucial for the modern chemical engineer.
Foreword xiii
Symbols xix
Author Bios xxi
I Preliminaries
1(96)
1 What to Expect in This Book?
3(4)
2 Calculus and Linear Algebra Essentials
7(48)
2.1 Scalars, Vectors, and Matrices
7(3)
2.2 Sequences and Series
10(6)
2.2.1 Sequences
10(3)
2.2.2 Series
13(3)
2.3 Functions
16(9)
2.3.1 Continuity
18(1)
2.3.2 Composition of functions
19(1)
2.3.3 Inverse functions and solving equations
19(2)
2.3.4 Multivariate functions
21(1)
2.3.5 Linear transformations, matrix inverses, and matrix decompositions
22(3)
2.4 Differentiation
25(6)
2.4.1 Multivariate derivatives
28(1)
2.4.2 Taylor series
29(2)
2.5 Maxima and Minima
31(5)
2.5.1 Second derivative test, saddle points, and inflection points
33(1)
2.5.2 Newton-Raphson algorithm for finding optima
34(2)
2.6 Integration
36(7)
2.6.1 Improper integrals
38(1)
2.6.2 Practical integration rules
39(1)
2.6.3 Multiple integrals
40(2)
2.6.4 Interchange integration and differentiation
42(1)
2.7 Differential Equations
43(6)
2.7.1 Equilibrium solutions of differential equations
45(1)
2.7.2 First-order equations with separable variables
46(3)
2.8 Complex Numbers and Functions
49(2)
2.9 Exercises
51(4)
3 Probability Essentials
55(42)
3.1 Probability of Events
55(10)
3.1.1 Basic set theory
56(1)
3.1.2 Laplace's definition of probability
57(3)
3.1.3 General definition of probability
60(3)
3.1.4 Independence
63(2)
3.2 Random Variables
65(22)
3.2.1 Definition of random variables
65(1)
3.2.2 Distribution functions
66(2)
3.2.3 Moments of a random variable
68(3)
3.2.4 Some standard probability distributions
71(3)
3.2.5 Joint and marginal distribution functions
74(2)
3.2.6 Independent random variables
76(3)
3.2.7 Conditional distributions
79(2)
3.2.8 Random variables related to the normal
81(3)
3.2.9 Multivariate normal distribution
84(1)
3.2.10 Exponential family of distributions
85(2)
3.3 Pseudo Random Number Generation
87(2)
3.4 Notes and Comments
89(1)
3.5 Notes on Using R
90(1)
3.6 Exercises
90(7)
II Numerics and Error Propagation
97(30)
4 Introduction to Numerical Methods
99(16)
4.1 Fixed Point Problems
99(7)
4.1.1 Fixed point iteration
100(2)
4.1.2 Newton iteration
102(4)
4.2 Numerical Methods for Solving Differential Equations
106(4)
4.2.1 Euler's iterative method
106(1)
4.2.2 Runge-Kutta iterative method
107(3)
4.3 Differential Algebraic Equations
110(1)
4.4 Notes and Comments
111(1)
4.5 Notes on Using R
112(1)
4.6 Exercises
112(3)
5 Laws on Propagation of Error
115(12)
5.1 Absolute and Relative Error of Measurement
115(2)
5.2 Mean and Variance
117(1)
5.3 Functions that Depend on One Variable
118(2)
5.3.1 First-order approximation
118(1)
5.3.2 Second-order approximation
119(1)
5.4 Functions that Depend on Two Variables
120(3)
5.4.1 Covariance and correlation
121(1)
5.4.2 First-order approximation
122(1)
5.4.3 Second-order approximation
122(1)
5.5 Notes and Comments
123(1)
5.6 Notes on Using R
123(1)
5.7 Exercises
123(4)
III Various Types of Models and Their Estimation
127(156)
6 Measurement Models for a Chemical Quantity
129(52)
6.1 Measurement Model
130(3)
6.2 Law of Large Numbers
133(2)
6.3 Constructing Confidence Intervals
135(8)
6.3.1 Confidence interval from the central limit theorem
135(5)
6.3.2 Confidence interval from the bootstrap
140(1)
6.3.3 Confidence interval from the normal distribution
141(2)
6.4 Testing Chemical Hypotheses related to Measurement Models
143(4)
6.4.1 Testing for the presence of bias
143(1)
6.4.2 Testing for equality of two means
144(2)
6.4.3 Testing for equality of variance
146(1)
6.5 General Inference Paradigm
147(23)
6.5.1 Maximum likelihood estimation (MLE)
147(2)
6.5.2 Consistency of the MLE
149(3)
6.5.3 Efficiency of the MLE
152(3)
6.5.4 Confidence intervals using the MLE
155(1)
6.5.5 Testing hypotheses with the MLE
156(5)
6.5.6 Testing multiple parameters with likelihood ratio test
161(2)
6.5.7 Model comparison
163(7)
6.6 Notes and Comments
170(1)
6.7 Notes on Using R
171(1)
6.8 Exercises
172(9)
7 Linear Models
181(28)
7.1 Linear Model
182(1)
7.2 Estimation and Prediction
182(4)
7.2.1 Parameter estimation
183(3)
7.2.2 Outcome prediction
186(1)
7.3 Model Diagnostics
186(5)
7.3.1 Diagnostics for high leverage points
186(1)
7.3.2 Diagnostics for outlying observations
187(1)
7.3.3 Diagnostics for influential observations
188(1)
7.3.4 Diagnostics for linear dependency among predictors
189(2)
7.4 Model Selection
191(7)
7.4.1 Marginal testing of parameters
192(1)
7.4.2 Testing a subset of parameters
193(1)
7.4.3 AIC
193(2)
7.4.4 SCAD penalized regression
195(3)
7.5 Specific Linear Models
198(3)
7.5.1 Simple linear regression
198(1)
7.5.2 Polynomial regression
199(2)
7.6 Notes and Comments
201(2)
7.7 Notes on Using R
203(1)
7.8 Exercises
203(6)
8 Non-linear Models
209(36)
8.1 Some Non-linear Functions Modeling Chemical Processes
210(1)
8.2 Non-linear Regression
211(8)
8.2.1 Non-linear least squares parameter estimation
211(4)
8.2.2 Estimating a function of the parameters
215(2)
8.2.3 Using the bootstrap
217(2)
8.3 Inverse Regression
219(3)
8.3.1 Inverse linear regression
219(2)
8.3.2 Inverse non-linear regression
221(1)
8.4 Generalized Linear Models
222(10)
8.4.1 Estimation of a generalized linear model
223(3)
8.4.2 Binary dose-response models
226(4)
8.4.3 Count models
230(2)
8.5 Semi-parametric Models
232(6)
8.6 Notes and Comments
238(2)
8.7 Notes on Using R
240(1)
8.8 Exercises
240(5)
9 Chemodynamics and Stoichiometry
245(20)
9.1 Stoichiometry of Systems of Reactions
246(3)
9.2 Stochastic Models for Particle Dynamics
249(3)
9.2.1 Gillespie algorithm for simulating reactions
250(1)
9.2.2 Euler-Maruyama approximation
251(1)
9.3 Estimating Reaction Rates
252(3)
9.4 Mean-Field Approximation of Reaction System
255(5)
9.4.1 Chemical reaction system as ODE
255(1)
9.4.2 Estimating reaction rates
256(4)
9.5 Exercises
260(5)
10 Multivariate Exploration
265(18)
10.1 Data Visualization
266(1)
10.2 Matrix Decomposition
267(3)
10.2.1 QR decomposition
267(1)
10.2.2 Eigen decomposition
268(2)
10.2.3 Singular value decomposition
270(1)
10.3 Principal Components Analysis
270(3)
10.4 Regression Using a Subspace
273(3)
10.4.1 Principal components regression
273(1)
10.4.2 Partial least squares regression
274(1)
10.4.3 Determining the number of components by cross-validation
275(1)
10.5 Notes and Comments
276(2)
10.6 Notes on Using R
278(1)
10.7 Exercises
278(5)
IV Analysis of Designed Experiments
283(68)
11 Analysis of Data from Designed Experiments
285(42)
11.1 Concepts of Factorial Designs
285(7)
11.1.1 Two-level one-factor design
286(1)
11.1.2 Two-level two-factor design
286(3)
11.1.3 Two-level k-factor designs
289(1)
11.1.4 Two-level k-factor fractional designs
290(2)
11.2 Analysis of Variance
292(11)
11.2.1 One-way analysis of variance
292(5)
11.2.2 Two-way analysis of variance
297(4)
11.2.3 Blocking factors
301(2)
11.3 Analysis of the Response Surface
303(2)
11.4 Mixed Effects Models
305(11)
11.4.1 Linear random effects models
306(3)
11.4.2 Linear mixed effects models
309(3)
11.4.3 Nonlinear mixed effects models
312(4)
11.5 Notes and Comments
316(3)
11.6 Notes on Using R
319(1)
11.7 Exercises
320(7)
12 Robust Analysis of Models
327(24)
12.1 Outlying Data Points
328(3)
12.1.1 A classical test for detecting an outlier
328(1)
12.1.2 The effect of an outlier on the estimated curve
329(2)
12.2 Robust Estimation
331(6)
12.2.1 Robust estimation a location parameter
331(3)
12.2.2 Robust estimation of scale
334(3)
12.3 Robust Linear Regression
337(5)
12.3.1 Robust one-way analysis of variance
340(1)
12.3.2 Robust two-way analysis of variance
341(1)
12.4 Robust Nonlinear Regression
342(2)
12.5 Dealing with Heterogeneity
344(1)
12.6 Appendix: Scale Tau Estimator
345(1)
12.7 Notes and Comments
345(1)
12.8 Notes on Using R
346(1)
12.9 Exercises
346(5)
V Appendix
351(14)
A Basics of R Computing Environment
353(1)
A.1 R Basics
353(3)
A.1.1 Installing packages
354(1)
A.1.2 Reading data
355(1)
A.1.3 Types of objects
356(1)
A.2 Useful Functions
356(4)
A.2.1 Functions on scalars
356(1)
A.2.2 Functions on vectors
356(1)
A.2.3 Functions on matrices of data frames
356(1)
A.2.4 Some statistical functions in R
357(1)
A.2.5 Writing your own functions and source code
357(1)
A.2.6 Writing a function
358(1)
A.2.7 For and while loops
358(1)
A.2.8 Logical arguments
359(1)
A.2.9 Functions for plotting
359(1)
A.3 Model Notation
360(1)
A.4 Finding Help
361(4)
A.5 Exercises
361(4)
Bibliography 365(8)
Index 373
Wim P. Krijnen is a lecturer at the Faculty of Science and Engineering at the University of Groningen. He has been teaching a course called "Computational and Statistical Methods" for several years to undergraduate students in Chemical Engineering. In addition, he has taught courses on linear algebra, probability theory, mathematical statistics, statistical modeling, statistical consulting to bachelors and masters students in various fields. He is a professor of Applied Statistical Research Methods at the Hanze University of Applied Sciences in Groningen.

Ernst C. Wit is the Fondazione Leonardo Professor of Data Science at the Universita della Svizzera italiana in Switzerland. He has 30 years of experience in teaching statistics, applied mathematics and data science courses to students from many fields, including chemical engineering. His course in philopsophy is about combining theoretical insights with practical skills, as he believes that the former without the latter is pointless whereas the latter without the former aimless.