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Enables chemical engineers to use mathematics to solve common on-the-job problemsWith its clear explanations, examples, and problem sets, Applied Mathematics and Modeling for Chemical Engineers has enabled thousands of chemical engineers to apply mathematical principles to successfully solve practical problems. The book introduces traditional techniques to solve ordinary differential equations as well as analytical methods to deal with important classes of finite-difference equations. It then explores techniques for solving partial differential equations from classical methods to finite-transforms, culminating with??numerical methods??including orthogonal collocation.This Second Edition demonstrates how classical mathematics solves a broad range of new applications that have arisen since the publication of the acclaimed first edition. Readers will find new materials and problems dealing with such topics as:* Brain implant drug delivery* Carbon dioxide storage* Chemical reactions in nanotubes* Dissolution of pills and pharmaceutical capsules* Honeycomb reactors used in catalytic converters* New models of physical phenomena such as bubble coalescenceLike the first edition, this Second Edition provides plenty of worked examples that explain each step on the way to finding a problem's solution. Homework problems at the end of each chapter are designed to encourage readers to more deeply examine the underlying logic of the mathematical techniques used to arrive at the answers. Readers can refer to the references, also at the end of each chapter, to explore individual topics in greater depth. Finally, the text's appendices provide additional information on numerical methods for solving algebraic equations as well as a detailed explanation of numerical integration algorithms.Applied Mathematics and Modeling for Chemical Engineers is recommended for all students in chemical engineering as well as professional chemical engineers who want to improve their ability to use mathematics to solve common on-the-job problems.

Applied Mathematics And Modeling For Chemical Engineers

Preface to the Second Edition xiPart I. 11. Formulation of Physicochemical Problems 31.1 Introduction 31.2 Illustration of the Formulation Process (Cooling of Fluids) 31.3 Combining Rate and Equilibrium Concepts (Packed Bed Adsorber) 71.4 Boundary Conditions and Sign Conventions 81.5 Models with Many Variables: Vectors and Matrices 101.6 Matrix Definition 101.7 Types of Matrices 111.8 Matrix Algebra 121.9 Useful Row Operations 131.10 Direct Elimination Methods 141.11 Iterative Methods 181.12 Summary of the Model Building Process 191.13 Model Hierarchy and its Importance in Analysis 19Problems 252. Solution Techniques for Models Yielding Ordinary Differential Equations 312.1 Geometric Basis and Functionality 312.2 Classification of ODE 322.3 First-Order Equations 322.4 Solution Methods for Second-Order Nonlinear Equations 372.5 Linear Equations of Higher Order 422.6 Coupled Simultaneous ODE 552.7 Eigenproblems 592.8 Coupled Linear Differential Equations 592.9 Summary of Solution Methods for ODE 60Problems 60References 733. Series Solution Methods and Special Functions 753.1 Introduction to Series Methods 753.2 Properties of Infinite Series 763.3 Method of Frobenius 773.4 Summary of the Frobenius Method 853.5 Special Functions 86Problems 93References 954. Integral Functions 974.1 Introduction 974.2 The Error Function 974.3 The Gamma and Beta Functions 984.4 The Elliptic Integrals 994.5 The Exponential and Trigonometric Integrals 101Problems 102References 1045. Staged-Process Models: The Calculus of Finite Differences 1055.1 Introduction 1055.2 Solution Methods for Linear Finite Difference Equations 1065.3 Particular Solution Methods 1095.4 Nonlinear Equations (Riccati Equations) 111Problems 112References 1156. Approximate Solution Methods for ODE: Perturbation Methods 1176.1 Perturbation Methods 1176.2 The Basic Concepts 1206.3 The Method of Matched Asymptotic Expansion 1226.4 Matched Asymptotic Expansions for Coupled Equations 125Problems 128References 136Part II. 1377. Numerical Solution Methods (Initial Value Problems) 1397.1 Introduction 1397.2 Type of Method 1427.3 Stability 1427.4 Stiffness 1477.5 Interpolation and Quadrature 1497.6 Explicit Integration Methods 1507.7 Implicit Integration Methods 1527.8 Predictor-Corrector Methods and Runge-Kutta Methods 1527.9 Runge-Kutta Methods 1537.10 Extrapolation 1557.11 Step Size Control 1557.12 Higher Order Integration Methods 156Problems 156References 1598. Approximate Methods for Boundary Value Problems: Weighted Residuals 1618.1 The Method of Weighted Residuals 1618.2 Jacobi Polynomials 1798.3 Lagrange Interpolation Polynomials 1728.4 Orthogonal Collocation Method 1728.5 Linear Boundary Value Problem: Dirichlet Boundary Condition 1758.6 Linear Boundary Value Problem: Robin Boundary Condition 1778.7 Nonlinear Boundary Value Problem: Dirichlet Boundary Condition 1798.8 One-Point Collocation 1818.9 Summary of Collocation Methods 1828.10 Concluding Remarks 183Problems 184References 1929. Introduction to Complex Variables and Laplace Transforms 1939.1 Introduction 1939.2 Elements of Complex Variables 1939.3 Elementary Functions of Complex Variables 1949.4 Multivalued Functions 1959.5 Continuity Properties for Complex Variables: Analyticity 1969.6 Integration: Cauchy's Theorem 1989.7 Cauchy's Theory of Residues 2019.8 Inversion of Laplace Transforms by Contour Integration 2029.9 Laplace Transformations: Building Blocks 2049.10 Practical Inversion Methods 2099.11 Applications of Laplace Transforms for Solutions of ODE 2119.12 Inversion Theory for Multivalued Functions: the Second Bromwich Path 2159.13 Numerical Inversion Techniques 218Problems 221References 22510. Solution Techniques for Models Producing PDEs 22710.1 Introduction 22710.2 Particular Solutions for PDES 23110.3 Combination of Variables Method 23310.4 Separation of Variables Method 23810.5 Orthogonal Functions and Sturm-Liouville Conditions 24110.6 Inhomogeneous Equations 24510.7 Applications of Laplace Transforms for Solutions of PDES 248Problems 254References 27111. Transform Methods for Linear PDEs 27311.1 Introduction 27311.2 Transforms in Finite Domain: Sturm-Liouville Transforms 27311.3 Generalized Sturm-Liouville Integral Transforms 289Problems 297References 30112. Approximate and Numerical Solution Methods for PDEs 30312.1 Polynomial Approximation 30312.2 Singular Perturbation 31012.3 Finite Difference 31512.4 Orthogonal Collocation for Solving PDEs 32412.5 Orthogonal Collocation on Finite Elements 330Problems 335References 342Appendix A. Review of Methods for Nonlinear Algebraic Equations 343Appendix B. Derivation of the Fourier-Mellin Inversion Theorem 351Appendix C. Table of Laplace Transforms 357Appendix D. Numerical Integration 363References 372Appendix E. Nomenclature 373Postface 377Index 379