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| Preface to the Second Edition | |
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| Formulation of Physicochemical Problems | |
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| Introduction | |
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| Illustration of the Formulation Process (Cooling of Fluids) | |
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| Combining Rate and Equilibrium Concepts (Packed Bed Adsorber) | |
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| Boundary Conditions and Sign Conventions | |
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| Models with Many Variables: Vectors and Matrices | |
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| Matrix Definition | |
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| Types of Matrices | |
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| Matrix Algebra | |
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| Useful Row Operations | |
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| Direct Elimination Methods | |
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| Iterative Methods | |
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| Summary of the Model Building Process | |
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| Model Hierarchy and its Importance in Analysis | |
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| Problems | |
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| Solution Techniques for Models Yielding Ordinary Differential Equations | |
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| Geometric Basis and Functionality | |
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| Classification of ODE | |
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| First-Order Equations | |
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| Solution Methods for Second-Order Nonlinear Equations | |
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| Linear Equations of Higher Order | |
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| Coupled Simultaneous ODE | |
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| Eigenproblems | |
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| Coupled Linear Differential Equations | |
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| Summary of Solution Methods for ODE | |
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| Problems | |
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| References | |
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| Series Solution Methods and Special Functions | |
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| Introduction to Series Methods | |
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| Properties of Infinite Series | |
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| Method of Frobenius | |
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| Summary of the Frobenius Method | |
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| Special Functions | |
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| Problems | |
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| References | |
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| Integral Functions | |
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| Introduction | |
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| The Error Function | |
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| The Gamma and Beta Functions | |
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| The Elliptic Integrals | |
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| The Exponential and Trigonometric Integrals | |
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| Problems | |
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| References | |
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| Staged-Process Models: The Calculus of Finite Differences | |
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| Introduction | |
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| Solution Methods for Linear Finite Difference Equations | |
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| Particular Solution Methods | |
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| Nonlinear Equations (Riccati Equations) | |
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| Problems | |
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| References | |
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| Approximate Solution Methods for ODE: Perturbation Methods | |
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| Perturbation Methods | |
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| The Basic Concepts | |
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| The Method of Matched Asymptotic Expansion | |
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| Matched Asymptotic Expansions for Coupled Equations | |
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| Problems | |
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| References | |
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| Numerical Solution Methods (Initial Value Problems) | |
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| Introduction | |
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| Type of Method | |
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| Stability | |
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| Stiffness | |
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| Interpolation and Quadrature | |
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| Explicit Integration Methods | |
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| Implicit Integration Methods | |
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| Predictor-Corrector Methods and Runge-Kutta Methods | |
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| Runge-Kutta Methods | |
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| Extrapolation | |
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| Step Size Control | |
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| Higher Order Integration Methods | |
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| Problems | |
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| References | |
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| Approximate Methods for Boundary Value Problems: Weighted Residuals | |
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| The Method of Weighted Residuals | |
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| Jacobi Polynomials | |
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| Lagrange Interpolation Polynomials | |
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| Orthogonal Collocation Method | |
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| Linear Boundary Value Problem: Dirichlet Boundary Condition | |
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| Linear Boundary Value Problem: Robin Boundary Condition | |
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| Nonlinear Boundary Value Problem: Dirichlet Boundary Condition | |
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| One-Point Collocation | |
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| Summary of Collocation Methods | |
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| Concluding Remarks | |
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| Problems | |
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| References | |
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| Introduction to Complex Variables and Laplace Transforms | |
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| Introduction | |
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| Elements of Complex Variables | |
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| Elementary Functions of Complex Variables | |
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| Multivalued Functions | |
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| Continuity Properties for Complex Variables: Analyticity | |
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| Integration: Cauchy���s Theorem | |
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| Cauchy���s Theory of Residues | |
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| Inversion of Laplace Transforms by Contour Integration | |
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| Laplace Transformations: Building Blocks | |
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| Practical Inversion Methods | |
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| Applications of Laplace Transforms for Solutions of ODE | |
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| Inversion Theory for Multivalued Functions: the Second Bromwich Path | |
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| Numerical Inversion Techniques | |
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| Problems | |
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| References | |
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| Solution Techniques for Models Producing PDEs | |
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| Introduction | |
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| Particular Solutions for PDES | |
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| Combination of Variables Method | |
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| Separation of Variables Method | |
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| Orthogonal Functions and Sturm-Liouville Conditions | |
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| Inhomogeneous Equations | |
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| Applications of Laplace Transforms for Solutions of PDES | |
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| Problems | |
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| References | |
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| Transform Methods for Linear PDEs | |
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| Introduction | |
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| Transforms in Finite Domain: Sturm-Liouville Transforms | |
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| Generalized Sturm-Liouville Integral Transforms | |
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| Problems | |
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| References | |
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| Approximate and Numerical Solution Methods for PDEs | |
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| Polynomial Approximation | |
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| Singular Perturbation | |
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| Finite Difference | |
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| Orthogonal Collocation for Solving PDEs | |
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| Orthogonal Collocation on Finite Elements | |
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| Problems | |
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| References | |
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| Review of Methods for Nonlinear Algebraic Equations | |
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| Derivation of the Fourier-Mellin Inversion Theorem | |
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| Table of Laplace Transforms | |
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| Numerical Integration | |
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| Nomenclature | |
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| Postface | |
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| Index | |