Applied Mathematics and Modeling for Chemical Engineers

Understand the fundamentals of applied mathematics with this up-to-date introduction
 
Applied mathematics is the use of mathematical concepts and methods in various applied or practical areas, including engineering, computer science, and more. As engineering science expands, the ability to work from mathematical principles to solve and understand equations has become an ever more critical component of engineering fields. New engineering processes and materials place ever-increasing mathematical demands on new generations of engineers, who are looking more and more to applied mathematics for an expanded toolkit.
 
Applied Mathematics and Modeling for Chemical Engineers provides this toolkit in a comprehensive and easy-to-understand introduction. Combining classical analysis of modern mathematics with more modern applications, it offers everything required to assess and solve mathematical problems in chemical engineering. Now updated to reflect contemporary best practices and novel applications, this guide promises to situate readers in a 21st century chemical engineering field in which direct knowledge of mathematics is essential.
 
Readers of the third edition of Applied Mathematics and Modeling for Chemical Engineers will also find:
* Detailed treatment of ordinary differential equations (ODEs) and partial differential equations (PDEs) and their solutions
* New material concerning approximate solution methods like perturbation techniques and elementary numerical solutions
* Two new chapters dealing with Linear Algebra and Applied Statistics
 
Applied Mathematics and Modeling for Chemical Engineers is ideal for graduate and advanced undergraduate students in chemical engineering and related fields, as well as instructors and researchers seeking a handy reference.

List of contents

Preface to the Third Edition xv
 
Part I 1
 
1 Formulation of Physicochemical Problems 3
 
1.1 Introduction 3
 
1.2 Illustration of the Formulation Process (Cooling of Fluids) 3
 
1.2.1 Model I: Plug Flow 3
 
1.2.2 Model II: Parabolic Velocity 6
 
1.3 Combining Rate and Equilibrium Concepts (Packed-Bed Adsorber) 7
 
1.4 Boundary Conditions and Sign Conventions 8
 
1.5 Summary of the Model Building Process 9
 
1.6 Model Hierarchy and its Importance in Analysis 10
 
1.6.1 Level 1 10
 
1.6.2 Level 2 11
 
1.6.3 Level 3 13
 
1.6.4 Level 4 13
 
Problems 15
 
References 20
 
2 Modeling with Linear Algebra and Matrices 21
 
2.1 Introduction 21
 
2.2 Basic Concepts of Systems of Linear Equations 21
 
2.3 Matrix Notation 22
 
2.3.1 Matrices 22
 
2.3.2 Vectors 22
 
2.3.3 Scalars 22
 
2.3.4 Matrices and Vectors with Special Structure 22
 
2.4 Matrix Algebra and Calculus Operations 24
 
2.4.1 Equality 24
 
2.4.2 Addition and Subtraction 24
 
2.4.3 Multiplication 24
 
2.4.4 Division 26
 
2.4.5 Further Algebraic Properties of Matrices 27
 
2.4.6 Basic Differential and Integral Relations for Matrices 28
 
2.5 Problem 1: Solution of N Equations in N Unknowns 29
 
2.5.1 Analytical Results 29
 
2.5.2 Computational Approach: Gauss Elimination 30
 
2.6 Problem 2: The Matrix Eigenvalue Problem 32
 
2.6.1 Problem Statement and Formal Solution 32
 
2.6.2 Computing Eigensystems: Basic Procedure 33
 
2.7 Singular Systems 34
 
2.7.1 Consistent and Inconsistent Systems 34
 
2.7.2 Solution Structure for Consistent Systems 35
 
2.7.3 Formulation and Characteristics of Non-Square Problems 36
 
2.7.4 Over-Determined Systems: Least-Squares Solution 37
 
2.7.5 Under-Determined Systems 38
 
2.8 Computational Linear Algebra 40
 
2.8.1 The LU Factorization 40
 
2.8.2 The QR Factorization 40
 
2.8.3 The SVD Factorization 40
 
2.8.4 Large-Scale Problems and Iterative Methods 41
 
Problems 42
 
References 47
 
3 Solution Techniques for Models Yielding Ordinary Differential Equations 49
 
3.1 Geometric Basis and Functionality 49
 
3.2 Classification of ODE 50
 
3.3 First-Order Equations 50
 
3.3.1 Exact Solutions 51
 
3.3.2 Equations Composed of Homogeneous Functions 52
 
3.3.3 Bernoulli's Equation 52
 
3.3.4 Riccati's Equation 52
 
3.3.5 Linear Coefficients 54
 
3.3.6 First-Order Equations of Second Degree 54
 
3.4 Solution Methods for Second-Order Nonlinear Equations 55
 
3.4.1 Derivative Substitution Method 55
 
3.4.2 Homogeneous Function Method 58
 
3.5 Linear Equations of Higher Order 59
 
3.5.1 Second-Order Unforced Equations: Complementary Solutions 60
 
3.5.2 Particular Solution Methods for Forced Equations 64
 
3.5.3 Summary of Particular Solution Methods 70
 
3.6 Coupled Simultaneous ODE 71
 
3.7 Eigenproblems 74
 
3.8 Coupled Linear Differential Equations 74
 
3.9 Summary of Solution Methods for ODE 75
 
Problems 75
 
References 87
 
4 Series Solution Methods and Special Functions 89
 
4.1 Introduction to Series Methods 89
 
4.2 Properties of Infinite Series 90
 
4.3 Method of Frobenius 91
 
4.3.1 Indicial Equation and Recurrence Relation 91
 
4.4 Summary of the Frobenius Method 98
 
4.5 Speci

About the author

Richard G. Rice, PhD is Emeritus Professor in the Department of Chemical Engineering at Louisiana State University, Baton Rouge, LA, USA.

Duong D. Do, PhD is Emeritus Professor in the School of Chemical Engineering at the University of Queensland, Australia.

James E. Maneval, PhD is Professor in the Department of Chemical Engineering at Bucknell University, Lewisburg, PA, USA.

Summary

Understand the fundamentals of applied mathematics with this up-to-date introduction

Applied mathematics is the use of mathematical concepts and methods in various applied or practical areas, including engineering, computer science, and more. As engineering science expands, the ability to work from mathematical principles to solve and understand equations has become an ever more critical component of engineering fields. New engineering processes and materials place ever-increasing mathematical demands on new generations of engineers, who are looking more and more to applied mathematics for an expanded toolkit.

Applied Mathematics and Modeling for Chemical Engineers provides this toolkit in a comprehensive and easy-to-understand introduction. Combining classical analysis of modern mathematics with more modern applications, it offers everything required to assess and solve mathematical problems in chemical engineering. Now updated to reflect contemporary best practices and novel applications, this guide promises to situate readers in a 21st century chemical engineering field in which direct knowledge of mathematics is essential.

Readers of the third edition of Applied Mathematics and Modeling for Chemical Engineers will also find:
* Detailed treatment of ordinary differential equations (ODEs) and partial differential equations (PDEs) and their solutions
* New material concerning approximate solution methods like perturbation techniques and elementary numerical solutions
* Two new chapters dealing with Linear Algebra and Applied Statistics

Applied Mathematics and Modeling for Chemical Engineers is ideal for graduate and advanced undergraduate students in chemical engineering and related fields, as well as instructors and researchers seeking a handy reference.

Product details

• Authors: Duong D Do, Duong D. Do, Do Duong D., James E Maneval, James E. Maneval, Rice, Rg Rice, Richard G Rice, Richard G. Rice, Richard G. (Louisiana State University) Do Rice, Rice Richard G.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 31.12.2022
• EAN: 9781119833857
• ISBN: 978-1-119-83385-7
• No. of pages: 432
• Subjects: Natural sciences, medicine, IT, technology > Technology > Chemical engineering; Mathematik, Maschinenbau, Angewandte Mathematik, Mathematics, Chemical Engineering, Mechanical Engineering, chemische Verfahrenstechnik, Applied mathematics, Computer-aided engineering, Computergestützte Verfahrenstechnik, Allg. Maschinenbau