Applied Linear Analysis for Chemical Engineers : A Multi-Scale Approach with Mathematica®.

Format:

Book

Author/Creator:

Balakotaiah, Vemuri.

Series:

De Gruyter Textbook Series

Language:

English

Subjects (All):

Chemical engineering.

Differential equations.

Physical Description:

1 online resource (788 pages)

Edition:

2nd ed.

Place of Publication:

Berlin/Boston : Walter de Gruyter GmbH, 2025.

Summary:

This textbook gives a unified treatment of the solution of various linear equations that arise in science and engineering with examples.It is based on a course taught by the first author for over thirty years.

Contents:

Intro

Preface

Introduction

Contents

Part I: Applied matrix algebra

1 Matrices and linear algebraic equations

1.1 Simultaneous linear equations

1.2 Review of basic matrix operations

1.2.1 Matrix addition and subtraction

1.2.2 Matrix multiplication

1.2.3 Special matrices

1.3 Elementary row operations and row echelon form of a matrix

1.3.1 Representation of elementary row operations

1.4 Rank of a matrix and condition for existence of solutions

1.4.1 The homogeneous system Au=0

1.4.2 The inhomogeneous system Au=b

1.5 Gaussian elimination and LU decomposition

1.5.1 Lower and upper triangular systems

1.5.2 Gaussian elimination

1.5.3 LU decomposition/factorization

1.6 Inverse of a square matrix

1.6.1 Properties of inverse

1.6.2 Calculation of inverse

1.7 Vector-matrix formulation of some chemical engineering problems

1.7.1 Batch reactor: evolution equations with multiple reactions

1.7.2 Continuous-flow stirred tank reactor (CSTR): transient and steady-state models with multiple reactions

1.7.3 Two interacting tank system: transient model for mixing with in- and outflows

1.7.4 Models for transient diffusion, convection and diffusion-convection (compartment models)

1.8 Application of elementary matrix concepts

1.9 Application of computer algebra and symbolic manipulation

1.9.1 Example 1: mass transfer disguised matrix for a five species system

1.9.2 Example 2: mass transfer disguised matrix for a ten species system

2 Determinants

2.1 Definition of determinant

2.2 Properties of the determinant

2.3 Computation of determinant by pivotal condensation

2.4 Minors, cofactors and Laplace's expansion

2.4.1 Classical adjoint and inverse matrices

2.5 Determinant of the product of two matrices

2.6 Rank of a matrix defined in terms of determinants.

2.7 Solution of Au=0 and Au=b by Cramer's rule

2.8 Differentiation of a determinant

2.9 Applications of determinants

3 Vectors and vector expansions

3.1 Linear dependence, basis and dimension

3.2 Dot or scalar product of vectors

3.3 Linear algebraic equations

3.4 Applications of vectors and vector expansions

3.4.1 Stoichiometry

3.4.2 Dimensional analysis

3.5 Application of computer algebra and symbolic manipulation

3.5.1 Determination of independent reactions

4 Solution of linear equations by eigenvector expansions

4.1 The matrix eigenvalue problem

4.2 Left eigenvectors and the adjoint eigenvalue problem (eigenrows)

4.3 Properties of eigenvectors/eigenrows

4.4 Orthogonal and biorthogonal expansions

4.4.1 Vector expansions

4.4.2 Orthogonal expansions

4.4.3 Biorthogonal expansions

4.5 Solution of linear equations using eigenvector expansions

4.5.1 Solution of linear algebraic equations Au=b

4.5.2 (Fredholm alternative): solution of linear algebraic equations Au=b when A is singular

4.5.3 Linear coupled first-order differential equations with constant coefficients

4.5.4 Linear coupled inhomogeneous equations

4.5.5 A second-order vector initial value problem

4.5.6 Multicomponent diffusion and reaction in a catalyst pore

4.6 Diagonalization of matrices and similarity transforms

4.6.1 Examples of similarity transforms

4.6.2 Canonical form

4.6.3 Similarity transform when AT=A

5 Solution of linear equations containing a square matrix

5.1 Cayley-Hamilton theorem

5.2 Functions of matrices

5.3 Formal solutions of linear differential equations containing a square matrix

5.4 Sylvester's theorem

5.5 Spectral theorem

5.6 Projection operators and vector projections

5.6.1 Standard basis and projection in R2

5.6.2 Nonorthogonal projections.

5.6.3 Geometric interpretation with real and negative eigenvalues

5.6.4 Geometrical interpretation with complex eigenvalues with negative real part

5.6.5 Geometrical interpretation with one zero eigenvalue

5.6.6 Physical and geometrical interpretation of transient behavior of interacting tank systems for various initial conditions

6 Generalized eigenvectors and canonical forms

6.1 Repeated eigenvalues and generalized eigenvectors

6.1.1 Linearly independent solutions of dudt=Au with repeated eigenvalues

6.1.2 Examples of repeated EVs and GEVs

6.2 Jordan canonical forms

6.3 Multiple eigenvalues and generalized eigenvectors

6.4 Determination of f(A) when A has repeated eigenvalues

6.5 Application of Jordan canonical form to differential equations

7 Quadratic forms, positive definite matrices and other applications

7.1 Quadratic forms

7.2 Positive definite matrices

7.3 Rayleigh quotient

7.4 Maxima/minima for a function of several variables

7.5 Linear difference equations

7.6 Generalized inverse and least square solutions

Part II: Abstract vector space concepts

8 Vector space over a field

8.1 Definition of a field

8.2 Definition of an abstract vector or linear space:

8.2.1 Subspaces

8.2.2 Bases and dimension

8.2.3 Coordinates

9 Linear transformations

9.1 Definition of a linear transformation

9.2 Matrix representation of a linear transformation

9.2.1 Change of basis

9.2.2 Kernel and range of a linear transformation

9.2.3 Relation to linear equations

9.2.4 Isomorphism

9.2.5 Inverse of a linear transformation

10 Normed and inner product vector spaces

10.1 Definition of normed linear spaces

10.2 Inner product vector spaces

10.2.1 Gram-Schmidt orthogonalization procedure

10.3 Linear functionals and adjoints.

11 Applications of finite-dimensional linear algebra

11.1 Weighted dot/inner product in R n

11.2 Application of weighted inner product to interacting tank systems

11.3 Application of weighted inner product to monomolecular kinetics

Part III: Linear ordinary differential equations-initial value problems, complex variables and Laplace transform

12 The linear initial value problem

12.1 The vector initial value problem

12.2 The n-th order initial value problem

12.2.1 The n-th order inhomogeneous equation

12.3 Linear IVPs with constant coefficients

13 Linear systems with periodic coefficients

13.1 Scalar equation with a periodic coefficient

13.2 Vector equation with periodic coefficient matrix

14 Analytic solutions, adjoints and integrating factors

14.1 Analytic solutions

14.2 Adjoints and integrating factors

14.2.1 First-order equation

14.2.2 Second-order equation

14.3 Relationship between solutions of Lu=0 and Lv=0

14.4 Vector initial value problem

15 Introduction to the theory of functions of a complex variable

15.1 Complex valued functions

15.1.1 Algebraic operations with complex numbers

15.1.2 Polar form of complex numbers

15.1.3 Roots of complex numbers

15.1.4 Complex-valued functions

15.2 Limits, continuity and differentiation

15.2.1 Limits

15.2.2 Continuity

15.2.3 Derivative

15.2.4 The Cauchy-Riemann equations

15.2.5 Some elementary functions of a complex variable

15.2.6 Zeros and singular points of complex-valued functions

15.3 Complex integration, Cauchy's theorem and integral formulas

15.3.1 Simply and multiply connected domains

15.3.2 Contour integrals and traversal of a closed path

15.3.3 Cauchy's theorem

15.3.4 Cauchy's integral formulas

15.4 Infinite series: Taylor's and Laurent's series

15.4.1 Taylor's series.

15.4.2 Practical methods of obtaining power series

15.4.3 Laurent series

15.5 The residue theorem and integration by the method of residues

15.5.1 Other methods for evaluating residues

15.5.2 Residue theorem

16 Series solutions and special functions

16.1 Series solution of a first-order ODE

16.2 Ordinary and regular singular points

16.3 Series solutions of second-order ODEs

16.4 Special functions defined by second-order ODEs

16.4.1 Airy equation

16.4.2 Bessel equation

16.4.3 Modified Bessel equation

16.4.4 Spherical Bessel equation

16.4.5 Legendre equation

16.4.6 Associated Legendre equation

16.4.7 Hermite's equation

16.4.8 Laguerre's equation

16.4.9 Chebyshev's equation

17 Laplace transforms

17.1 Definition of Laplace transform

17.2 Properties of Laplace transform

17.2.1 Examples of Laplace transform

17.3 Inversion of Laplace transform

17.3.1 Bromwich's complex inversion formula

17.3.2 Computing the Bromwich's integral

17.4 Solution of linear differential equations by Laplace transform

17.4.1 Initial value problems with constant coefficients

17.4.2 Elementary derivation of Heaviside's formula

17.4.3 Two-point boundary value problems

17.4.4 Linear ODEs with variable coefficients:

17.4.5 Simultaneous ODEs with constant coefficients

17.5 Solution of linear partial differential equations by Laplace transform

17.5.1 Heat transfer in a finite slab

17.5.2 TAP reactor model

17.5.3 Dispersion of tracers in unidirectional flow

17.5.4 Unsteady-state operation of a packed-bed

17.6 Control system with delayed feedback

17.6.1 PI control with delayed feedback

Part IV: Linear ordinary differential equations-boundary value problems

18 Two-point boundary value problems

18.1 The adjoint differential operator.

18.1.1 The Lagrange identity for an n-th order linear differential operator.

Notes:

Description based on publisher supplied metadata and other sources.

Part of the metadata in this record was created by AI, based on the text of the resource.

ISBN:

3-11-159805-5

OCLC:

1564497899