Applied Numerical Methods for Chemical Engineers

Applied Numerical Methods for Chemical Engineers

1st Edition - May 22, 2022

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  • Authors: Navid Mostoufi, Alkis Constantinides
  • Paperback ISBN: 9780128229613
  • eBook ISBN: 9780128229347

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Description

Applied Numerical Methods for Chemical Engineers emphasizes the derivation of a variety of numerical methods and their application to the solution of engineering problems, with special attention to problems in the chemical engineering field. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, differentiation and integration, ordinary differential equations, boundary value problems, partial differential equations, and linear and nonlinear regression analysis. MATLAB is adopted as the calculation environment throughout the book because of its ability to perform all the calculations in matrix form, its large library of built-in functions, its strong structural language, and its rich graphical visualization tools. Through this book, students and other users will learn about the basic features, advantages and disadvantages of various numerical methods, learn and practice many useful m-files developed for different numerical methods in addition to the MATLAB built-in solvers, develop and set up mathematical models for problems commonly encountered in chemical engineering, and solve chemical engineering related problems through examples and after-chapter problems with MATLAB by creating application m-files.

Key Features

  • Clearly and concisely develops a variety of numerical methods and applies them to the solution of chemical engineering problems. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, linear and nonlinear regression analysis, differentiation and integration, ordinary differential equations, boundary value problems, and partial differential equations
  • Includes systematic development of the calculus of finite differences and its application to the integration of differential equations, and a detailed discussion of nonlinear regression analysis, with powerful programs for implementing multivariable nonlinear regression and statistical analysis of the results
  • Makes extensive use of MATLAB and Excel, with most of the methods discussed implemented into general MATLAB functions. All the MATLAB-language scripts developed are listed in the text and included in the book’s companion website
  • Includes numerous real-world examples and homework problems drawn from the field of chemical and biochemical engineering

Readership

Chemical and biochemical engineering students taking numerical methods courses specific to chemical engineering at junior level and above. Practicing chemical and biochemical engineers looking to strengthen their knowledge of numerical methods

Table of Contents

  • Cover image
  • Title page
  • Table of Contents
  • Copyright
  • Dedication
  • Preface
  • Chapter 1. Nonlinear equations
  • Abstract
  • Chapter Outline
  • Motivation
  • 1.1 Introduction
  • 1.2 Types of roots and their approximation
  • 1.3 The method of successive substitution
  • 1.4 The Wegstein method
  • 1.5 The bisection method
  • 1.6 The method of linear interpolation
  • 1.7 The Newton-Raphson method
  • 1.8 Synthetic division algorithm
  • 1.9 The eigenvalue method
  • 1.10 Newton’s method for solving system of nonlinear equations
  • 1.11 Homotopy method
  • 1.12 Using the built-in MATLAB and Excel functions
  • 1.13 Summary
  • Problems
  • References
  • Chapter 2. Simultaneous linear algebraic equations
  • Abstract
  • Chapter Outline
  • Motivation
  • 2.1 Introduction
  • 2.2 Review of selected matrix and vector operations
  • 2.3 Consistency of equations and existence of solutions
  • 2.4 Cramer’s rule
  • 2.5 Gauss elimination method
  • Calculation of determinants by the Gauss method
  • 2.6 Gauss-Jordan Reduction Method
  • 2.7 Gauss-Seidel substitution method
  • 2.8 Jacobi method
  • 2.9 Homogeneous algebraic equations and the characteristic-value problem
  • 2.10 Using built-in MATLAB® and Excel functions
  • 2.11 Summary
  • Problems
  • References
  • Chapter 3. Finite difference methods and interpolation
  • Abstract
  • Chapter Outline
  • Motivation
  • 3.1 Introduction
  • 3.2 Symbolic operators
  • 3.3 Backward finite differences
  • 3.4 Forward finite differences
  • 3.5 Central finite differences
  • 3.6 Interpolating polynomials
  • 3.7 Interpolation of equally spaced points
  • 3.8 Interpolation of unequally spaced points
  • 3.9 Using built-in MATLAB® functions
  • 3.10 Summary
  • Problems
  • References
  • Chapter 4. Differentiation and integration
  • Abstract
  • Chapter Outline
  • Motivation
  • 4.1 Introduction
  • 4.2 Differentiation by backward finite differences
  • 4.3 Differentiation by forward finite differences
  • 4.4 Differentiation by central finite differences
  • 4.5 Spline differentiation
  • 4.6 Integration formulas
  • 4.7 Newton-Cotes formulas of integration
  • 4.8 Gauss quadrature
  • 4.9 Spline integration
  • 4.10 Multiple integrals
  • 4.11 Using built-in MATLAB® functions
  • 4.12 Summary
  • Problems
  • References
  • Chapter 5. Ordinary differential equations: initial value problems
  • Abstract:
  • Chapter Outline
  • Motivation
  • 5.1 Introduction
  • 5.2 Classifications of ordinary differential equations
  • 5.3 Transformation to canonical form
  • 5.4 Linear ordinary differential equations
  • 5.5 Nonlinear ordinary differential equations
  • 5.6 Using built-in MATLAB® functions
  • 5.7 Difference equations and their solutions
  • 5.8 Propagation, stability, and convergence
  • 5.9 Step size control
  • 5.10 Stiff differential equations
  • 5.11 Summary
  • Problems
  • References
  • Chapter 6. Ordinary differential equations: boundary value problems
  • Abstract
  • Chapter Outline
  • Motivation
  • 6.1 Introduction
  • 6.2 The shooting method
  • 6.3 The finite-difference method
  • 6.4 Collocation methods
  • 6.5 Using built-in MATLAB® functions
  • 6.6 Summary
  • Problems
  • References
  • Chapter 7. Partial differential equations
  • Abstract
  • Chapter Outline
  • Motivation
  • 7.1 Introduction
  • 7.2 Classification of partial differential equations
  • 7.3 Initial and boundary conditions
  • 7.4 Solution of partial differential equations using finite differences
  • 7.5 Using built-in MATLAB® functions
  • 7.6 Stability analysis
  • 7.7 Summary
  • Problems
  • References
  • Chapter 8. Linear and nonlinear regression analysis
  • Abstract
  • Chapter Outline
  • Motivation
  • 8.1 Process analysis, mathematical modeling, and regression analysis
  • 8.2 Review of statistical terminology used in regression analysis
  • 8.3 Linear regression analysis
  • 8.4 Nonlinear regression analysis
  • 8.5 Analysis of variance and other statistical tests of the regression results
  • 8.6 Using built-in MATLAB® and Excel functions
  • 8.7 Summary
  • Problems
  • References
  • Appendix. Orthogonal Polynomials
  • Index

Product details

  • No. of pages: 504
  • Language: English
  • Copyright: © Academic Press 2022
  • Published: May 22, 2022
  • Imprint: Academic Press
  • Paperback ISBN: 9780128229613
  • eBook ISBN: 9780128229347

About the Authors

Navid Mostoufi

Navid Mostoufi is Professor of Chemical Engineering at the University of Tehran. He has taught advanced mathematics and fluid mechanics courses for over 16 years. His research interests include process modeling, simulation and optimization, and fluidization. He holds a Ph.D. in Fluidization from Canada’s Ecole Polytechnique de Montréal. Professor Mostoufi has more than 270 publications in major international journals and conferences and is co-author of the textbook “Numerical Methods for Chemical Engineers with MATLAB Applications”, published by Pearson/Prentice Hall in 1999 and “Coupled CFD-DEM Modeling: Formulation, Implementation and Application to Multiphase Flows”, published by Wiley in 2016. He is the Founder and Editor-in-Chief of Chemical Product and Process Modeling (http://www.degruyter.com/view/j/cppm) published by Walter de Gruyter GmbH, Germany and winner of University of Tehran’s International Award, 2015. He is also the University of Tehran’s distinguished researcher, 2013. Prof. Mostoufi is now the secretary of the Iranian Association of Chemical Engineers.

Affiliations and Expertise

Professor, School of Chemical Engineering, University of Tehran, Iran

Alkis Constantinides

Alkis Constantinides was Emeritus Professor of Chemical and Biochemical Engineering at Rutgers University, with nearly forty years of academic and industrial experience. He was the author of the textbook Applied Numerical Methods with Personal Computers and the co-author of the textbook Numerical Methods for Chemical Engineers with MATLAB Applications.

Affiliations and Expertise

Rutgers, The State University of New Jersey (deceased)

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