Applied mathematics and modeling for chemical engineers. (2023)

• Record Type: Book
• Authors: Rice, Richard G; Do, Duong D; Maneval, James E
• Other Names: Rice, Richard G
• Contents: PART I 1 Formulation of Physicochemical Problems 1.1 Introduction, 1.2 Illustration of the Formulation Process (Cooling of Fluids), 1.2.1 Model I: Plug Flow, 1.2.2 Model II: Parabolic Velocity, 1.3 Combining Rate and Equilibrium Concepts (Packed Bed Adsorber), 1.4 Boundary Conditions and Sign Conventions, 1.5 Summary of the Model Building Process, 1.6 Model Hierarchy and its Imprtance in Analysis, Problems, References, 2 Modeling with Linear Algebra and Matrices 2.1 Introduction, 2.2 Basic Concepts of System of Linear Equations, 2.3 Matrix Notation, 2.3.1 Matrices, 2.3.2 Vectors, 2.3.3 Scalars, 2.3.4 Matrices and Vectors with Special Structure, 2.4 Matrix Algebra and Calculus Operations, 2.4.1 Equality, 2.4.2 Addition and Subtraction, 2.4.3 Multiplication, 2.4.4 Division, 2.4.5 Further Algebraic Properties of Matrices, 2.4.6 Basic Dufferetial and Integral Relations for Matrices, 2.5 Problem 1 : Solution of N equations in N Unknowns, 2.5.1 Analytical Results, 2.5.2 Computational Approach : Gauss Elimination, 2.6 Problem 2 : The Matrix Eigenvalue Problem, 2.6.1 Problem Statement and Formal Solution, 2.6.2 Computing Eigensystems : Basic Procedure, 2.7 Singular Systems, 2.7.1 Consistent and Inconsistent Systems, 2.7.2 Solution Structure for Consisten Systems, 2.7.3 Formulation and Characteristics of Non-Square Problems, 2.7.4 Over-Determined Systems : Least-Squares Solution, 2.7.5 Under-Determined Systems 2.8 Computational Linear Algebra, 2.8.1 The LU Factorization, 2.8.2 The QR Factorization, 2.8.3 The SVD Factorization, 2.8.4 Large-Scale Problems and Iterative Methods, Problems, References, 3 Solution Techniques for Models Yielding Ordinary Differential Equations 3.1 Geometric Basis and Functionality, 3.2 Classification of ODE, 3.3 First-Order Equations, 3.3.1 Exact Solutions, 3.3.2 Equations Composed of Homogeneous Functions, 3.3.3 Bernoulli’s Equation, 3.3.4 Riccati’s Equation, 3.3.5 Linear Coefficients, 3.3.6 First-Order Equations of Second Degree, 3.4 Solution Methods for Second-Order Nonlinear Equations, 3.4.1 Derivative Substitution Method, 3.4.2 Homogeneous Function Method, 3.5 Linear Equations of Higher Order, 3.5.1 Second-Order Unforced Equations: Complementary Solutions, 3.5.2 Particular Solution Methods for Forced Equations, 3.5.3 Summary of Particular Solution Methods, 3.6 Coupled Simultaneous ODE, 3.7 Coupled First-Order Differential Equations, 3.8 Summary of Solution Methods for ODEs, Problems, References, 4 Series Solution Methods and Special Functions 4.1 Introduction to Series Methods, 4.2 Properties of Infinite Series, 4.3 Method of Frobenius, 4.3.1 Indicial Equation and Recurrence Relation, 4.4 Summary of the Frobenius Method, 4.5 Special Functions, 4.5.1 Bessel’s Equation, 4.5.2 Modified Bessel’s Equation, 4.5.3 Generalized Bessel’s Equation, 4.5.4 Properties of Bessel Functions, 4.5.5 Differential, Integral, and Recurrence Relations, Problems, References, 5 Integral Functions 5.1 Introduction, 5.2 The Error Function, 5.2.1 Properties of Error Function, 5.3 The Gamma and Beta Functions, 5.3.1 The Gamma Function, 5.3.2 The Beta Function, 5.4 The Elliptic Integrals, 5.5 The Exponential and Trigonometric Integrals, Problems, References, 6 Staged-Process Models: The Calculus of Finite Differences 6.1 Introduction, 6.1.1 Modeling Multiple Stages, 6.2 Solution Methods for Linear Finite Difference Equations, 6.2.1 Complementary Solutions, 6.3 Particular Solution Methods, 6.3.1 Method of Undetermined Coefficients, 6.3.2 Inverse Operator Method, 6.4 Nonlinear Equations (Riccati Equation), Problems, References, 7 Probability and Statistical Modeling 7.1 Concepts and Results from Probability Theory, 7.1.1 Experiments and Random Variables, 7.1.2 Probabilities and Distribution Functions, 7.1.3 Characteristics of Distribution Functions, 7.1.4 The Cumulative Distribution Function, 7.2 Concepts and Results from Mathematical Statistics, 7.2.1 Populations, Samples, and Sampling, 7.2.2 Sample Statistics and Sampling Distributions, 7.3 Statistical Analysis and Modeling, 7.3.1 Confidence Interval for the Mean of a Population, 7.3.2 Hypothesis Tests for the Population Mean, 7.3.3 Hypothesis Tests : Comparing Multiple Means, 7.3.4 Linear Models and Linear Regression, Problems, References 8 Approximate Solution Methods for ODE: Perturbation Methods 8.1 Perturbation Methods, 8.1.1 Introduction, 8.2 The Basic Concepts, 8.2.1 Gauge Functions, 8.2.2 Order Symbols, 8.2.3 Asymptotic Expansions and Sequences, 8.2.4 Sources of Nonuniformity, 8.3 The Method of Matched Asymptotic Expansion, 8.3.1 Outer Solutions, 8.3.2 Inner Solutions, 8.3.3 Matching, 8.3.4 Composite Solutions, 8.3.5 General Matching Principle, 8.3.6 Composite Solution of Higher Order, 8.4 Matched Asymptotic Expansions for Coupled Equations, 8.4.1 Outer Expansion, 8.4.2 Inner Expansion, 8.4.3 Matching, Problems, References, PART II 9 Numerical Solution Methods (Initial Value Problems) 9.1 Introduction, 9.2 Type of Method, 9.3 Stability, 9.4 Stiffness, 9.5 In
• Edition: Third edition
• Publisher Details: Hoboken : John Wiley & Sons, Inc
• Publication Date: 2023
• Extent: 1 online resource (432 pages)
• Subjects: 660.0151; Chemical engineering -- Mathematics; Chemical engineering -- Mathematical models; Differential equations
• Languages: English
• ISBNs: 9781119833901
• Related ISBNs: 9781119833857
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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