Applied mathematical methods for chemical engineers / Norman W. Loney.

By: Loney, Norman W [author]
Language: English Publisher: Boca Raton : CRC Press, Taylor & Francis Group, [2016]Copyright date: c2016Edition: Third editionDescription: xix, 545 pages ; 25 cmContent type: text Media type: unmediated Carrier type: volumeISBN: 9781466552999 (hardcover : acidfree paper)Subject(s): Chemical engineering -- MathematicsDDC classification: 660.02/12 LOC classification: TP155.2.M36 | L66 2016
Contents:
Table of Contents 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
Summary: Features Focuses on the application of mathematics to chemical engineering Addresses the setup and verification of mathematical models using experimental or other independently derived data Provides an introduction to differential equations common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations Examines Sturm?Liouville problems, Fourier series, integrals, linear partial differential equations, and regular perturbation Uses worked examples to showcase several mathematical methods that are essential to solving real-world process engineering problems Summary 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. 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.
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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.

Includes bibliographical references and index.

Table of Contents

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

Features

Focuses on the application of mathematics to chemical engineering
Addresses the setup and verification of mathematical models using experimental or other independently derived data
Provides an introduction to differential equations common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations
Examines Sturm?Liouville problems, Fourier series, integrals, linear partial differential equations, and regular perturbation
Uses worked examples to showcase several mathematical methods that are essential to solving real-world process engineering problems

Summary

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.


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.

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