Enables chemical engineers to use mathematics to solve common
on-the-job problems

With its clear explanations, examples, and problem sets,
Applied Mathematics and Modeling for Chemical Engineers has
enabled thousands of chemical engineers to apply mathematical
principles to successfully solve practical problems. The book
introduces traditional techniques to solve ordinary differential
equations as well as analytical methods to deal with important
classes of finite-difference equations. It then explores techniques
for solving partial differential equations from classical methods
to finite-transforms, culminating with??numerical
methods??including orthogonal collocation.

This Second Edition demonstrates how classical
mathematics solves a broad range of new applications that have
arisen since the publication of the acclaimed first edition.
Readers will find new materials and problems dealing with such
topics as:

* Brain implant drug delivery

* Carbon dioxide storage

* Chemical reactions in nanotubes

* Dissolution of pills and pharmaceutical capsules

* Honeycomb reactors used in catalytic converters

* New models of physical phenomena such as bubble
coalescence

Like the first edition, this Second Edition provides
plenty of worked examples that explain each step on the way to
finding a problem's solution. Homework problems at the end of each
chapter are designed to encourage readers to more deeply examine
the underlying logic of the mathematical techniques used to arrive
at the answers. Readers can refer to the references, also at the
end of each chapter, to explore individual topics in greater depth.
Finally, the text's appendices provide additional information on
numerical methods for solving algebraic equations as well as a
detailed explanation of numerical integration algorithms.

Applied Mathematics and Modeling for Chemical Engineers
is recommended for all students in chemical engineering as well as
professional chemical engineers who want to improve their ability
to use mathematics to solve common on-the-job problems.

RICHARD G. RICE, PhD, is Emeritus Professor at Louisiana
State University and widely published in the areas of chemical
separations and two-phase flow.

DUONG D. DO, PhD, is University Professor at the
University of Queensland, Australia, and is well-known in the area
of adsorption science.

Enables chemical engineers to use mathematics to solve common on-the-job problems

With its clear explanations, examples, and problem sets, Applied Mathematics and Modeling for Chemical Engineers has enabled thousands of chemical engineers to apply mathematical principles to successfully solve practical problems. The book introduces traditional techniques to solve ordinary differential equations as well as analytical methods to deal with important classes of finite-difference equations. It then explores techniques for solving partial differential equations from classical methods to finite-transforms, culminating with??numerical methods??including orthogonal collocation.

This Second Edition demonstrates how classical mathematics solves a broad range of new applications that have arisen since the publication of the acclaimed first edition. Readers will find new materials and problems dealing with such topics as:

• Brain implant drug delivery
• Carbon dioxide storage
• Chemical reactions in nanotubes
• Dissolution of pills and pharmaceutical capsules
• Honeycomb reactors used in catalytic converters
• New models of physical phenomena such as bubble coalescence

Like the first edition, this Second Edition provides plenty of worked examples that explain each step on the way to finding a problem's solution. Homework problems at the end of each chapter are designed to encourage readers to more deeply examine the underlying logic of the mathematical techniques used to arrive at the answers. Readers can refer to the references, also at the end of each chapter, to explore individual topics in greater depth. Finally, the text's appendices provide additional information on numerical methods for solving algebraic equations as well as a detailed explanation of numerical integration algorithms.

Applied Mathematics and Modeling for Chemical Engineers is recommended for all students in chemical engineering as well as professional chemical engineers who want to improve their ability to use mathematics to solve common on-the-job problems.

Preface to the Second Edition xi

Part I. 1

1. Formulation of Physicochemical Problems 3

1.1 Introduction 3

1.2 Illustration of the Formulation Process (Cooling of Fluids) 3

1.3 Combining Rate and Equilibrium Concepts (Packed Bed Adsorber) 7

1.4 Boundary Conditions and Sign Conventions 8

1.5 Models with Many Variables: Vectors and Matrices 10

1.6 Matrix Definition 10

1.7 Types of Matrices 11

1.8 Matrix Algebra 12

1.9 Useful Row Operations 13

1.10 Direct Elimination Methods 14

1.11 Iterative Methods 18

1.12 Summary of the Model Building Process 19

1.13 Model Hierarchy and its Importance in Analysis 19

Problems 25

2. Solution Techniques for Models Yielding Ordinary Differential Equations 31

2.1 Geometric Basis and Functionality 31

2.2 Classification of ODE 32

2.3 First-Order Equations 32

2.4 Solution Methods for Second-Order Nonlinear Equations 37

2.5 Linear Equations of Higher Order 42

2.6 Coupled Simultaneous ODE 55

2.7 Eigenproblems 59

2.8 Coupled Linear Differential Equations 59

2.9 Summary of Solution Methods for ODE 60

Problems 60

References 73

3. Series Solution Methods and Special Functions 75

3.1 Introduction to Series Methods 75

3.2 Properties of Infinite Series 76

3.3 Method of Frobenius 77

3.4 Summary of the Frobenius Method 85

3.5 Special Functions 86

Problems 93

References 95

4. Integral Functions 97

4.1 Introduction 97

4.2 The Error Function 97

4.3 The Gamma and Beta Functions 98

4.4 The Elliptic Integrals 99

4.5 The Exponential and Trigonometric Integrals 101

Problems 102

References 104

5. Staged-Process Models: The Calculus of Finite Differences 105

5.1 Introduction 105

5.2 Solution Methods for Linear Finite Difference Equations 106

5.3 Particular Solution Methods 109

5.4 Nonlinear Equations (Riccati Equations) 111

Problems 112

References 115

6. Approximate Solution Methods for ODE: Perturbation Methods 117

6.1 Perturbation Methods 117

6.2 The Basic Concepts 120

6.3 The Method of Matched Asymptotic Expansion 122

6.4 Matched Asymptotic Expansions for Coupled Equations 125

Problems 128

References 136

Part II. 137

7. Numerical Solution Methods (Initial Value Problems) 139

7.1 Introduction 139

7.2 Type of Method 142

7.3 Stability 142

7.4 Stiffness 147

7.5 Interpolation and Quadrature 149

7.6 Explicit Integration Methods 150

7.7 Implicit Integration Methods 152

7.8 Predictor-Corrector Methods and Runge-Kutta Methods 152

7.9 Runge-Kutta Methods 153

7.10 Extrapolation 155

7.11 Step Size Control 155

7.12 Higher Order Integration Methods 156

Problems 156

References 159

8. Approximate Methods for Boundary Value Problems: Weighted Residuals 161