3rd Edition

Applied Mathematical Methods for Chemical Engineers

ISBN 9781466552999
Published October 5, 2015 by CRC Press
545 Pages 47 B/W Illustrations

USD $155.00

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Book Description

Focusing on the application of mathematics to chemical engineering, Applied Mathematical Methods for Chemical Engineers addresses the setup and verification of mathematical models using experimental or other independently derived data. The book provides an introduction to differential equations common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations. Later chapters examine Sturm–Liouville problems, Fourier series, integrals, linear partial differential equations, regular perturbation, combination of variables, and numerical methods emphasizing the method of lines with MATLAB® programming examples.

Fully revised and updated, this Third Edition:

  • Includes additional examples related to process control, Bessel Functions, and contemporary areas such as drug delivery
  • Introduces examples of variable coefficient Sturm–Liouville problems both in the regular and singular types
  • Demonstrates the use of Euler and modified Euler methods alongside the Runge–Kutta order-four method
  • Inserts more depth on specific applications such as nonhomogeneous cases of separation of variables
  • Adds a section on special types of matrices such as upper- and lower-triangular matrices
  • Presents a justification for Fourier-Bessel series in preference to a complicated proof
  • Incorporates examples related to biomedical engineering applications
  • Illustrates the use of the predictor-corrector method
  • Expands the problem sets of numerous chapters

Applied Mathematical Methods for Chemical Engineers, Third Edition uses worked examples to expose several mathematical methods that are essential to solving real-world process engineering problems.

Table of Contents

Differential Equations
Model Development

First-Order Ordinary Differential Equations
Linear Equations
Additional Information on Linear Equations
Nonlinear Equations
Problem Setup

Linear Second-Order and Systems of First-Order Ordinary Differential Equations
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

Sturm–Liouville Problems
Classification of Sturm–Liouville Problems
Eigenfunction Expansion

Fourier Series and Integrals
Fourier Coefficients
Arbitrary Interval
Cosine and Sine Series
Convergence of Fourier Series
Fourier Integrals

Partial Differential Equations
Separation of Variables
Nonhomogeneous Problem and Eigenfunction Expansion
Laplace Transform Methods
Combination of Variables
Fourier Integral Methods
Regular Perturbation Approaches

Applications of Partial Differential Equations in Chemical Engineering
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

Dimensional Analysis and Scaling of Boundary Value Problems
Classical Approach to Dimensional Analysis
Finding the Πs
Scaling Boundary Value Problems

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

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

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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.