Applied Mathematics and Modeling for Chemical Engineers

ISBN-10: 1118024729
ISBN-13: 9781118024720
Edition: 2nd 2012
List price: $86.50 Buy it from $80.48
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Description: This Second Edition of the go–to reference combines the classical analysis and modern applications of applied mathematics for chemical engineers. The book introduces traditional techniques for solving ordinary differential equations (ODEs), adding  More...

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Book details

List price: $86.50
Edition: 2nd
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 11/2/2012
Binding: Hardcover
Pages: 400
Size: 8.00" wide x 11.00" long x 1.25" tall
Weight: 2.772
Language: English

This Second Edition of the go–to reference combines the classical analysis and modern applications of applied mathematics for chemical engineers. The book introduces traditional techniques for solving ordinary differential equations (ODEs), adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions. It also includes analytical methods to deal with important classes of finite–difference equations. The last half discusses numerical solution techniques and partial differential equations (PDEs). The reader will then be equipped to apply mathematics in the formulation of problems in chemical engineering. Like the first edition, there are many examples provided as homework and worked examples.

Preface to the Second Edition
Formulation of Physicochemical Problems
Introduction
Illustration of the Formulation Process (Cooling of Fluids)
Combining Rate and Equilibrium Concepts (Packed Bed Adsorber)
Boundary Conditions and Sign Conventions
Models with Many Variables: Vectors and Matrices
Matrix Definition
Types of Matrices
Matrix Algebra
Useful Row Operations
Direct Elimination Methods
Iterative Methods
Summary of the Model Building Process
Model Hierarchy and its Importance in Analysis
Problems
Solution Techniques for Models Yielding Ordinary Differential Equations
Geometric Basis and Functionality
Classification of ODE
First-Order Equations
Solution Methods for Second-Order Nonlinear Equations
Linear Equations of Higher Order
Coupled Simultaneous ODE
Eigenproblems
Coupled Linear Differential Equations
Summary of Solution Methods for ODE
Problems
References
Series Solution Methods and Special Functions
Introduction to Series Methods
Properties of Infinite Series
Method of Frobenius
Summary of the Frobenius Method
Special Functions
Problems
References
Integral Functions
Introduction
The Error Function
The Gamma and Beta Functions
The Elliptic Integrals
The Exponential and Trigonometric Integrals
Problems
References
Staged-Process Models: The Calculus of Finite Differences
Introduction
Solution Methods for Linear Finite Difference Equations
Particular Solution Methods
Nonlinear Equations (Riccati Equations)
Problems
References
Approximate Solution Methods for ODE: Perturbation Methods
Perturbation Methods
The Basic Concepts
The Method of Matched Asymptotic Expansion
Matched Asymptotic Expansions for Coupled Equations
Problems
References
Numerical Solution Methods (Initial Value Problems)
Introduction
Type of Method
Stability
Stiffness
Interpolation and Quadrature
Explicit Integration Methods
Implicit Integration Methods
Predictor-Corrector Methods and Runge-Kutta Methods
Runge-Kutta Methods
Extrapolation
Step Size Control
Higher Order Integration Methods
Problems
References
Approximate Methods for Boundary Value Problems: Weighted Residuals
The Method of Weighted Residuals
Jacobi Polynomials
Lagrange Interpolation Polynomials
Orthogonal Collocation Method
Linear Boundary Value Problem: Dirichlet Boundary Condition
Linear Boundary Value Problem: Robin Boundary Condition
Nonlinear Boundary Value Problem: Dirichlet Boundary Condition
One-Point Collocation
Summary of Collocation Methods
Concluding Remarks
Problems
References
Introduction to Complex Variables and Laplace Transforms
Introduction
Elements of Complex Variables
Elementary Functions of Complex Variables
Multivalued Functions
Continuity Properties for Complex Variables: Analyticity
Integration: Cauchy���s Theorem
Cauchy���s Theory of Residues
Inversion of Laplace Transforms by Contour Integration
Laplace Transformations: Building Blocks
Practical Inversion Methods
Applications of Laplace Transforms for Solutions of ODE
Inversion Theory for Multivalued Functions: the Second Bromwich Path
Numerical Inversion Techniques
Problems
References
Solution Techniques for Models Producing PDEs
Introduction
Particular Solutions for PDES
Combination of Variables Method
Separation of Variables Method
Orthogonal Functions and Sturm-Liouville Conditions
Inhomogeneous Equations
Applications of Laplace Transforms for Solutions of PDES
Problems
References
Transform Methods for Linear PDEs
Introduction
Transforms in Finite Domain: Sturm-Liouville Transforms
Generalized Sturm-Liouville Integral Transforms
Problems
References
Approximate and Numerical Solution Methods for PDEs
Polynomial Approximation
Singular Perturbation
Finite Difference
Orthogonal Collocation for Solving PDEs
Orthogonal Collocation on Finite Elements
Problems
References
Review of Methods for Nonlinear Algebraic Equations
Derivation of the Fourier-Mellin Inversion Theorem
Table of Laplace Transforms
Numerical Integration
Nomenclature
Postface
Index

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