Computational and Statistical Methods for Chemical Engineering

ISBN-13: 9781032013244 / Angielski / Twarda / 2022 / 400 str.

Switzerlan Ernst C. (USI Universita della Svizzera italiana

Opis

Before the data revolution, most books focused either on mathematical modeling of chemical processes or exploratory chemometrics. This book aims to combine these two approaches and provide aspiring chemical engineers a single, comprehensive account of computational and statistical methods. Each chapter is accompanied by extensive exercises.

Spis treści

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. 2.3. Functions. 2.4. Differentiation. 2.5. Maxima and Minima. 2.6. Integration. 2.7. Differential Equations. 2.8. Complex Numbers and Functions. 2.9. Exercises. 3. Probability Essentials. 3.1. Probability of Events. 3.2. Random Variables. 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. 4.2. Numerical Methods for Solving Differential Equations. 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. 5.4. Functions that Depend on Two Variables. 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. 6.4. Testing Chemical Hypotheses related to Measurement Models. 6.5. General Inference Paradigm. 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. 7.3. Model Diagnostics. 7.4. Model Selection. 7.5. Specific Linear Models. 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. 8.3. Inverse Regression. 8.4. Generalized Linear Models. 9. Chemodynamics and Stoichiometry. 9.1. Stoichiometry of Systems of Reactions. 9.2. Stochastic Models for Particle Dynamics. 9.3. Estimating Reaction Rates. 9.4. Mean-field Approximation of Reaction System. 10. Multivariate Exploration. 10.1. Data Visualisation. 10.2. Matrix Decomposition. 10.3. Principal Components Analysis. 10.4. Regression using a Subspace. 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. 11.2. Analysis of Variance. 11.3. Analysis of the Response Surface. 11.4. 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. 12.2. Robust Estimation. 12.3. Robust Linear Regression. 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. 13. Basics of R Computing Environment. 13.1. R Basics. 13.2. Useful Functions. 13.3. Model Notation.13.4. Finding Help. 13.5. Exercises