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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: Cauchyï¿½ï¿½ï¿½s Theorem | |

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Cauchyï¿½ï¿½ï¿½s 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 | |