Mathematical Methods in Chemical and Biological Engineering  book cover
1st Edition

Mathematical Methods in Chemical and Biological Engineering

ISBN 9781482210385
Published October 20, 2016 by CRC Press
694 Pages 20 Color & 182 B/W Illustrations

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Book Description

Mathematical Methods in Chemical and Biological Engineering describes basic to moderately advanced mathematical techniques useful for shaping the model-based analysis of chemical and biological engineering systems. Covering an ideal balance of basic mathematical principles and applications to physico-chemical problems, this book presents examples drawn from recent scientific and technical literature on chemical engineering, biological and biomedical engineering, food processing, and a variety of diffusional problems to demonstrate the real-world value of the mathematical methods. Emphasis is placed on the background and physical understanding of the problems to prepare students for future challenging and innovative applications.

Table of Contents

Architecture of Mathematical Models
Classification of Mathematical Models in Chemical and Biological Engineering
Models Resulting in Algebraic Equations: Lumped-Parameter, Steady-State Models
Models Resulting in Ordinary Differential Equations: Initial Value Problems
Models Resulting in Ordinary Differential Equations: Boundary Value Problems
Models Resulting in Partial Differential Equations
Model Equations in Non-Dimensional Form
Concluding Comments
Exercise Problems

Ordinary Differential Equations and Applications
Review of Solution of Ordinary Differential Equations
The Laplace Transform Technique
Matrix Method of Solution of Simultaneous ODEs
Concluding Comments
Exercise Problems

Special Functions and Solutions of Ordinary Differential Equations with Variable Coefficients
The Gamma Function
The Beta Function
The Error Function
The Gamma Distribution
Series Solution of Linear Second-Order ODEs with Variable Coefficients
Series Solution of Linear Second-Order ODEs Leading to Special Functions
Legendre Differential Equation and the Legendre Functions
Hypergeometric Functions
Concluding Comments
Exercise Problems

Partial Differential Equations
Common Second Order PDEs in Science and Engineering
Boundary Value Problems
Types of Boundary Conditions
Techniques of Analytical Solution of a Second Order PDE
Examples: Use of the Technique of Separation of Variables
Solution of Non-Homogeneous PDEs
Similarity Solution
Moving Boundary Problems
Principle of Superposition
Green’s Function
Concluding Comments
Exercise Problems

Integral Transforms
Definition of an Integral Transform
Fourier Transform
Laplace Transform
Application to Engineering Problems
Concluding Comments
Exercise Problems

Approximate Methods of Solution of Model Equations
Order Symbols
Asymptotic Expansion
Perturbation Methods
Concluding Comments
Exercise Problems

Answers to Selected Exercise Problems
Appendix A: Topics in Matrices
Appendix B: Fourier Series Expansion and Fourier Integral Theorem
Appendix C: Review of Complex Variables
Appendix D: Selected Formulas and Identities; Dirac Delta Function and Heaviside Function
Appendix E: Brief Table of Inverse Laplace Transforms
Appendix F: Some Detailed Derivations

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Binay Kanti Dutta is a former chairman of the West Bengal Pollution Control Board, Kolkata, India. He has been involved in research and teaching in chemical engineering since 1970. He has taught at the Regional Engineering College (now the National Institute of Technology), Durgapur, India; the University of Calcutta, Kolkata, India; the University of Alberta, Edmonton, Canada; the Universiti Teknologi Petronas, Perak, Malaysia; and the Petroleum Institute, Abu Dhabi, United Arab Emirates. He has also worked as a visiting scientist at the National Institute of Standards and Technology, Boulder, Colorado, USA; the Stevens Institute of Technology, Hoboken, New Jersey, USA; and the Environmental Protection Agency, Cincinnati, Ohio, USA. He is a former head of the Chemical Engineering Department and a former director of the Academic Staff College at the University of Calcutta. Professor Dutta has published extensively on transport processes, mathematical modeling, membranes separation, reaction engineering, and environmental engineering, and holds a number of US, European, and Malaysian patents. He is the author of Heat Transfer—Principles and Applications and Principles of Mass Transfer and Separation Processes. He also served as the 2005 president of the Indian Institute of Chemical Engineers.


"… gives both professionals and the less experienced a variety and a hierarchy of useful tools that should enable all users to make wise choices faster."
—From the Foreword by Edward L. Cussler Jr., Distinguished Institute Professor, University of Minnesota, Minneapolis, USA, and Past President, American Institute of Chemical Engineers

"This book will excite [both students and] researchers in chemical, environmental, and biological engineering fields to appreciate the power of mathematical modeling. … a landmark book due to the diverse examples of daily life as well as practical engineering problems."
—Ajay K. Ray, Professor and Chair, Western University, London, Ontario, Canada