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.
Author(s): Wim P. Krijnen, Ernst C. Wit
Publisher: CRC Press/Chapman & Hall
Year: 2022
Language: English
Pages: 398
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Foreword
Symbols
Author Bios
I. Preliminaries
1. What to Expect in This Book?
2. Calculus and Linear Algebra Essentials
2.1. Scalars, Vectors, and Matrices
2.2. Sequences and Series
2.2.1. Sequences
2.2.2. Series
2.3. Functions
2.3.1. Continuity
2.3.2. Composition of functions
2.3.3. Inverse functions and solving equations
2.3.4. Multivariate functions
2.3.5. Linear transformations, matrix inverses, and matrix decompositions
2.4. Differentiation
2.4.1. Multivariate derivatives
2.4.2. Taylor series
2.5. Maxima and Minima
2.5.1. Second derivative test, saddle points, and inflection points
2.5.2. Newton-Raphson algorithm for finding optima
2.6. Integration
2.6.1. Improper integrals
2.6.2. Practical integration rules
2.6.3. Multiple integrals
2.6.4. Interchange integration and differentiation
2.7. Differential Equations
2.7.1. Equilibrium solutions of differential equations
2.7.2. First-order equations with separable variables
2.8. Complex Numbers and Functions
2.9. Exercises
3. Probability Essentials
3.1. Probability of Events
3.1.1. Basic set theory
3.1.2. Laplace’s definition of probability
3.1.3. General definition of probability
3.1.4. Independence
3.2. Random Variables
3.2.1. Definition of random variables
3.2.2. Distribution functions
3.2.3. Moments of a random variable
3.2.4. Some standard probability distributions
3.2.5. Joint and marginal distribution functions
3.2.6. Independent random variables
3.2.7. Conditional distributions
3.2.8. Random variables related to the normal
3.2.9. Multivariate normal distribution
3.2.10. Exponential family of distributions
3.3. Pseudo Random Number Generation
3.4. Notes and Comments
3.5. Notes on Using R
3.6. Exercises
II. Numerics and Error Propagation
4. Introduction to Numerical Methods
4.1. Fixed Point Problems
4.1.1. Fixed point iteration
4.1.2. Newton iteration
4.2. Numerical Methods for Solving Differential Equations
4.2.1. Euler’s iterative method
4.2.2. Runge-Kutta iterative method
4.3. Differential Algebraic Equations
4.4. Notes and Comments
4.5. Notes on Using R
4.6. Exercises
5. Laws on Propagation of Error
5.1. Absolute and Relative Error of Measurement
5.2. Mean and Variance
5.3. Functions that Depend on One Variable
5.3.1. First-order approximation
5.3.2. Second-order approximation
5.4. Functions that Depend on Two Variables
5.4.1. Covariance and correlation
5.4.2. First-order approximation
5.4.3. Second-order approximation
5.5. Notes and Comments
5.6. Notes on Using R
5.7. Exercises
III. Various Types of Models and Their Estimation
6. Measurement Models for a Chemical Quantity
6.1. Measurement Model
6.2. Law of Large Numbers
6.3. Constructing Confidence Intervals
6.3.1. Confidence interval from the central limit theorem
6.3.2. Confidence interval from the bootstrap
6.3.3. Confidence interval from the normal distribution
6.4. Testing Chemical Hypotheses related to Measurement Models
6.4.1. Testing for the presence of bias
6.4.2. Testing for equality of two means
6.4.3. Testing for equality of variance
6.5. General Inference Paradigm
6.5.1. Maximum likelihood estimation (MLE)
6.5.2. Consistency of the MLE
6.5.3. Efficiency of the MLE
6.5.4. Confidence intervals using the MLE
6.5.5. Testing hypotheses with the MLE
6.5.6. Testing multiple parameters with likelihood ratio test
6.5.7. Model comparison
6.6. Notes and Comments
6.7. Notes on Using R
6.8. Exercises
7. Linear Models
7.1. Linear Model
7.2. Estimation and Prediction
7.2.1. Parameter estimation
7.2.2. Outcome prediction
7.3. Model Diagnostics
7.3.1. Diagnostics for high leverage points
7.3.2. Diagnostics for outlying observations
7.3.3. Diagnostics for influential observations
7.3.4. Diagnostics for linear dependency among predictors
7.4. Model Selection
7.4.1. Marginal testing of parameters
7.4.2. Testing a subset of parameters
7.4.3. AIC
7.4.4. SCAD penalized regression
7.5. Specific Linear Models
7.5.1. Simple linear regression
7.5.2. Polynomial regression
7.6. Notes and Comments
7.7. Notes on Using R
7.8. Exercises
8. Non-linear Models
8.1. Some Non-linear Functions Modeling Chemical Processes
8.2. Non-linear Regression
8.2.1. Non-linear least squares parameter estimation
8.2.2. Estimating a function of the parameters
8.2.3. Using the bootstrap
8.3. Inverse Regression
8.3.1. Inverse linear regression
8.3.2. Inverse non-linear regression
8.4. Generalized Linear Models
8.4.1. Estimation of a generalized linear model
8.4.2. Binary dose-response models
8.4.3. Count models
8.5. Semi-parametric Models
8.6. Notes and Comments
8.7. Notes on Using R
8.8. Exercises
9. Chemodynamics and Stoichiometry
9.1. Stoichiometry of Systems of Reactions
9.2. Stochastic Models for Particle Dynamics
9.2.1. Gillespie algorithm for simulating reactions
9.2.2. Euler-Maruyama approximation
9.3. Estimating Reaction Rates
9.4. Mean-Field Approximation of Reaction System
9.4.1. Chemical reaction system as ODE
9.4.2. Estimating reaction rates
9.5. Exercises
10. Multivariate Exploration
10.1. Data Visualization
10.2. Matrix Decomposition
10.2.1. QR decomposition
10.2.2. Eigen decomposition
10.2.3. Singular value decomposition
10.3. Principal Components Analysis
10.4. Regression Using a Subspace
10.4.1. Principal components regression
10.4.2. Partial least squares regression
10.4.3. Determining the number of components by cross-validation
10.5. Notes and Comments
10.6. Notes on Using R
10.7. Exercises
IV. Analysis of Designed Experiments
11. Analysis of Data from Designed Experiments
11.1. Concepts of Factorial Designs
11.1.1. Two-level one-factor design
11.1.2. Two-level two-factor design
11.1.3. Two-level k-factor designs
11.1.4. Two-level k-factor fractional designs
11.2. Analysis of Variance
11.2.1. One-way analysis of variance
11.2.2. Two-way analysis of variance
11.2.3. Blocking factors
11.3. Analysis of the Response Surface
11.4. Mixed Effects Models
11.4.1. Linear random effects models
11.4.2. Linear mixed effects models
11.4.3. Nonlinear mixed effects models
11.5. Notes and Comments
11.6. Notes on Using R
11.7. Exercises
12. Robust Analysis of Models
12.1. Outlying Data Points
12.1.1. A classical test for detecting an outlier
12.1.2. The effect of an outlier on the estimated curve
12.2. Robust Estimation
12.2.1. Robust estimation a location parameter
12.2.2. Robust estimation of scale
12.3. Robust Linear Regression
12.3.1. Robust one-way analysis of variance
12.3.2. Robust two-way analysis of variance
12.4. Robust Nonlinear Regression
12.5. Dealing with Heterogeneity
12.6. Appendix: Scale Tau Estimator
12.7. Notes and Comments
12.8. Notes on Using R
12.9. Exercises
V. Appendix
A. Basics of R Computing Environment
A.1. R Basics
A.1.1. Installing packages
A.1.2. Reading data
A.1.3. Types of objects
A.2. Useful Functions
A.2.1. Functions on scalars
A.2.2. Functions on vectors
A.2.3. Functions on matrices of data frames
A.2.4. Some statistical functions in R
A.2.5. Writing your own functions and source code
A.2.6. Writing a function
A.2.7. For and while loops
A.2.8. Logical arguments
A.2.9. Functions for plotting
A.3. Model Notation
A.4. Finding Help
A.5. Exercises
Bibliography
Index
