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ISBN 10: 0367240149
ISBN 13: 9780367240141
Author: Norman W Loney
This book uses worked examples to showcase several mathematical methods that are essential to solving real-world process engineering problems. The third edition includes additional examples related to process control, Bessel Functions, and contemporary areas such as drug delivery. The author 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, incorporates examples related to biomedical engineering applications, and expands the problem sets of numerous chapters.
1.Differential Equations
Introduction
ODE
Model Development
References
2.First-Order Ordinary Differential Equations
Linear Equations
Additional Information on Linear Equations
Nonlinear Equations
Problem Setup
Problems
References
3.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
4.Sturm–Liouville Problems
Introduction
Classification of Sturm–Liouville Problems
Eigenfunction Expansion
Problems
References
5.Fourier Series and Integrals
Introduction
Fourier Coefficients
Arbitrary Interval
Cosine and Sine Series
Convergence of Fourier Series
Fourier Integrals
Problems
References
6.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
7.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
8.Dimensional Analysis and Scaling of Boundary Value Problems
Introduction
Classical Approach to Dimensional Analysis
Finding the Πs
Scaling Boundary Value Problems
Problems
References
9.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
10.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
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Tags: Norman W Loney, Mathematical, Methods
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