Differential Equations
Introduction
ODE
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 Homogeneous Equations
Homogeneous Equations with Constant Coefficients
Nonhomogeneous Equations
Variable Coefficient Problems
Alternative Methods
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
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
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
Numerical Solution of Partial Differential Equations
Summary
Problems
References
Appendices
Elementary Properties of Determinants and Matrices
Numerical Method of Lines Example Using MATLAB®
Program for a Transport and Binding Kinetics Model of an Analyte
Programmed Model of a Drug Delivery System
Biography
Norman W. Loney is professor and was department chair of the Otto H. York Department of Chemical, Biological and Pharmaceutical Engineering at New Jersey Institute of Technology (NJIT). He has authored or coauthored more than 70 publications and presentations related to the use of applied mathematics to solve transport phenomena-related problems in chemical engineering since joining the department in 1991. Dr. Loney has been awarded several certificates of recognition from the National Aeronautics and Space Administration and the American Society for Engineering Education for research contributions. He has also been honored with the Newark College of Engineering Teaching Excellence award, the Saul K. Fenster Innovation in Engineering Education award, and the Excellence in Advising award. Dr. Loney is a fellow of the American Institute for Chemical Engineers. Prior to joining NJIT, Dr. Loney, a licensed professional engineer, practiced engineering at Foster Wheeler, M.W. Kellogg Company, Oxirane Chemical Company, and Exxon Chemical Company.
