Mathematical Methods in Chemical and Biological Engineering: 1st Edition (Hardback) book cover

Mathematical Methods in Chemical and Biological Engineering

1st Edition

By Binay Kanti Dutta

CRC Press

694 pages | 20 Color Illus. | 182 B/W Illus.

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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.


"… 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

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

View a List of Solved Examples.

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / Industrial & Technical