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