Applied Mathematical Methods for Chemical Engineers, Second Edition

DIFFERENTIAL EQUATIONS
Introduction
Ordinary Differential Equations
Model Development
References
FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Linear Equations
Additional Information on Linear Equations
Nonlinear Equations
Problem Setup
Problems
References
LINEAR SECOND-ORDER AND SYSTEMS OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Introduction
Fundamental Solutions of the Homogeneous Equation
Homogeneous Equations with Constant Coefficients
Nonhomogeneous Equations
Variable Coefficient Problems
Alternative Methods
Summary
Applications of Second-Order Differential Equations
Systems of First-Order Ordinary Differential Equations
Problems
References
STURM–LIOUVILLE PROBLEMS
Introduction
Classification of Sturm–Liouville Problems
Eigenfunction Expansion
Problems
References
FOURIER SERIES AND INTEGRALS
Introduction
Fourier Coefficients
Arbitrary Interval
Cosine and Sine Series
Convergence of Fourier Series
Fourier Integrals
Problems
References
PARTIAL DIFFERENTIAL EQUATIONS
Introduction
Separation of Variables
The Nonhomogeneous Problem and Eigenfunction
Expansion
Laplace Transform Methods
Combination of Variables
Fourier Integral Methods
Regular Perturbation Approaches
Problems
References
APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN CHEMICAL ENGINEERING
Introduction
Heat Transfer
Mass Transfer
Comparison between Heat and Mass Transfer Results
Simultaneous Diffusion and Convection
Simultaneous Diffusion and Chemical Reaction
Simultaneous Diffusion, Convection, and Chemical Reaction
Viscous Flow
Problems
References
DIMENSIONAL ANALYSIS AND SCALING OF BOUNDARY VALUE PROBLEMS
Introduction
A Classical Approach to Dimensional Analysis
Finding the Πs
Scaling Boundary Value Problems
Problems
References
SELECTED NUMERICAL METHODS AND AVAILABLE SOFTWARE PACKAGES
Introduction and Philosophy
Solution of Nonlinear Algebraic Equations
Solution of Simultaneous Linear Algebraic Equations
Solution of Ordinary Differential Equations
Solution of Partial Differential Equations
Summary
Problems
References
APPENDIX A
APPENDIX B
INDEX