Applied Mathematics And Modeling For Chemical Engineers – Richard G. Rice, Duong D. Do – 1st Edition

Part I.
1. Formulation of Physicochemical Problems
1.1 Introduction 
1.2 Illustration of the Formulation Process (Cooling of Fluids) 
1.3 Combining Rate and Equilibrium Concepts (Packed Bed Adsorber) 
1.4 Boundary Conditions and Sign Conventions 
1.5 Models with Many Variables: Vectors and Matrices 
1.6 Matrix Definition 
1.7 Types of Matrices 
1.8 Matrix Algebra 
1.9 Useful Row Operations 
1.10 Direct Elimination Methods 
1.11 Iterative Methods 
1.12 Summary of the Model Building Process 
1.13 Model Hierarchy and its Importance in Analysis 
Problems 

2. Solution Techniques for Models Yielding Ordinary Differential Equations 
2.1 Geometric Basis and Functionality 
2.2 Classification of ODE 
2.3 First-Order Equations 
2.4 Solution Methods for Second-Order Nonlinear Equations 
2.5 Linear Equations of Higher Order 
2.6 Coupled Simultaneous ODE 
2.7 Eigenproblems 
2.8 Coupled Linear Differential Equations 
2.9 Summary of Solution Methods for ODE 
Problems 
References 

3. Series Solution Methods and Special Functions 
3.1 Introduction to Series Methods 
3.2 Properties of Infinite Series 
3.3 Method of Frobenius 
3.4 Summary of the Frobenius Method 
3.5 Special Functions 
Problems 
References 

4. Integral Functions 
4.1 Introduction 
4.2 The Error Function 
4.3 The Gamma and Beta Functions 
4.4 The Elliptic Integrals 
4.5 The Exponential and Trigonometric Integrals 
Problems 
References 

5. Staged-Process Models: The Calculus of Finite Differences 
5.1 Introduction 
5.2 Solution Methods for Linear Finite Difference Equations 
5.3 Particular Solution Methods 
5.4 Nonlinear Equations (Riccati Equations) 
Problems 
References 

6. Approximate Solution Methods for ODE: Perturbation Methods
6.1 Perturbation Methods 
6.2 The Basic Concepts 
6.3 The Method of Matched Asymptotic Expansion 
6.4 Matched Asymptotic Expansions for Coupled Equations 
Problems 
References 

Part II.
7. Numerical Solution Methods (Initial Value Problems)
7.1 Introduction 
7.2 Type of Method 
7.3 Stability 
7.4 Stiffness 
7.5 Interpolation and Quadrature 
7.6 Explicit Integration Methods 
7.7 Implicit Integration Methods 
7.8 Predictor-Corrector Methods and Runge-Kutta Methods 
7.9 Runge-Kutta Methods 
7.10 Extrapolation 
7.11 Step Size Control 
7.12 Higher Order Integration Methods 
Problems 
References 

8. Approximate Methods for Boundary Value Problems: Weighted Residuals
8.1 The Method of Weighted Residuals 161
8.2 Jacobi Polynomials 179
8.3 Lagrange Interpolation Polynomials 172
8.4 Orthogonal Collocation Method 172
8.5 Linear Boundary Value Problem: Dirichlet Boundary Condition 175
8.6 Linear Boundary Value Problem: Robin Boundary Condition 177
8.7 Nonlinear Boundary Value Problem: Dirichlet Boundary Condition 179
8.8 One-Point Collocation 181
8.9 Summary of Collocation Methods 182
8.10 Concluding Remarks 183
Problem 184

9. Introduction to Complex Variables and Laplace Transforms
9.1 Introducton 193
9.2 Elements of Complex Variables 193
9.3 Elementary Functions of Complex Variables 194
9.4 Multivalued Functions 195
9.5 Continuity Properties for Complex Variables: Analyticity 196
9.6 Integration: Cauchy’s Theorem 198
9.7 Cauchy’s Theory of Residues 201
9.8 Inversion of Laplace Transforms by Contour Integration 202
9.9 Laplace Transformations: Building Blocks 204
9.10 Practical Inversion Methods 209
9.11 Applications of Laplace Transforms for Solutions of ODE 211
9.12 Inversion Theory for Multivalued Functions: the Second Bromwich Path 215
9.13 Numerical Inversion Techniques 218
Problems 221
References 225

10. Solution Techniques for Models Producing PDEs
10.1 Introduction 227
10.2 Particular Solutions for PDES 231
10.3 Combination of Variables Method 233
10.4 Separation of Variables Method 238
10.5 Orthogonal Functions and Sturm-Liouville Conditions 241
10.6 Inhomogeneous Equations 245
10.7 Applications of Laplace Transforms for Solutions of PDES 248
Problems 254
References 271

11. Transform Methods for Linear PDEs
11.1 Introduction 273
11.2 Transforms in Finite Domain: Sturm-Liouville Transforms 273
11.3 Generalized Sturm-Liouville Integral Transforms 289
Problems 297
References 301

12. Approximate and Numerical Solution Methods for PDEs
12.1 Polynomial Approximation 303
12.2 Singular Perturbation 310
12.3 Finite Difference 315
12.4 Orthogonal Collocation for Solving PDEs 324
12.5 Orthogonal Collocation on Finite Elements 330