# Mathematical Methods in Chemical and Biological Engineering

DOI link for Mathematical Methods in Chemical and Biological Engineering

Mathematical Methods in Chemical and Biological Engineering book

# Mathematical Methods in Chemical and Biological Engineering

DOI link for Mathematical Methods in Chemical and Biological Engineering

Mathematical Methods in Chemical and Biological Engineering book

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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.

**Architecture of Mathematical Models**

Introduction

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

References

Ordinary Differential Equations and Applications

Introduction

Review of Solution of Ordinary Differential Equations

The Laplace Transform Technique

Matrix Method of Solution of Simultaneous ODEs

Concluding Comments

Exercise Problems

References

Special Functions and Solutions of Ordinary Differential Equations with Variable Coefficients

Introduction

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

References

Partial Differential Equations

Introduction

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

Greenâ€™s Function

Concluding Comments

Exercise Problems

References

Integral Transforms

Introduction

Definition of an Integral Transform

Fourier Transform

Laplace Transform

Application to Engineering Problems

Concluding Comments

Exercise Problems

References

Approximate Methods of Solution of Model Equations

Introduction

Order Symbols

Asymptotic Expansion

Perturbation Methods

Concluding Comments

Exercise Problems

References

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