Applied Linear Analysis for Chemical Engineers : : A Multi-scale Approach with Mathematica® / / Vemuri Balakotaiah, Ram R. Ratnakar.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1
• VerfasserIn: Balakotaiah, Vemuri,; R. Ratnakar, Ram,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2023
• Year of Publication: 2022
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XXII, 762 p.)

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. Some unique features include: Use of symbolic software for illustrating and enhancing the impact of physical parameter changes on solutions. Multi-scale analysis of engineering problems with physical interpretation of time and length scales in terms of eigenvalues and eigenvectors/eigenfunctions. Discussion of compartment models for various finite dimensional problems. Evaluation and illustration of functions of matrices (and use of symbolic manipulation) to solve multi-component diffusion-convection-reaction problems. Illustration of the techniques and interpretation of solutions to several classical engineering problems. Emphasis on the connection between discrete (matrix algebra) and continuum. Physical interpretation of adjoint operator and adjoint systems. Use of complex analysis and algebra in the solution of practical engineering problems.

Table of Contents

Frontmatter -- Preface -- Introduction -- Contents -- Part I: Applied matrix algebra -- 1 Matrices and linear algebraic equations -- 2 Determinants -- 3 Vectors and vector expansions -- 4 Solution of linear equations by eigenvector expansions -- 5 Solution of linear equations containing a square matrix -- 6 Generalized eigenvectors and canonical forms -- 7 Quadratic forms, positive definite matrices and other applications -- Part II: Abstract vector space concepts -- Introduction -- 8 Vector space over a field -- 9 Linear transformations -- 10 Normed and inner product vector spaces -- 11 Applications of finite-dimensional linear algebra -- Part III: Linear ordinary differential equations-initial value problems, complex variables and laplace transform -- 12 The linear initial value problem -- 13 Linear systems with periodic coefficients -- 14 Analytic solutions, adjoints and integrating factors -- 15 Introduction to the theory of functions of a complex variable -- 16 Series solutions and special functions -- 17 Laplace transforms -- Part IV: Linear ordinary differential equations-boundary value problems -- 18 Two-point boundary value problems -- 19 The nonhomogeneous BVP and Green’s function -- 20 Eigenvalue problems for differential operators -- 21 Sturm–Liouville theory and eigenfunction expansions -- 22 Introduction to the solution of linear integral equations -- Part V: Fourier transforms and solution of boundary and initial-boundary value problems -- 23 Finite Fourier transforms -- 24 Fourier transforms on infinite intervals -- 25 Fourier transforms in cylindrical and spherical geometries -- Part VI: Formulation and solution of some classical chemical engineering problems -- Introduction -- 26 The classical Graetz–Nusselt problem -- 27 Friction factors for steady-state laminar flow in ducts -- 28 Multicomponent diffusion and reaction -- 29 Packed-bed chromatography -- 30 Stability of transport and reaction processes -- Bibliography -- Index