METHODS OF APPLIED MATHEMATICS FOR ENGINEERS …

1 METHODS OF APPLIED MATHEMATICS FORENGINEERS AND SCIENTISTSB ased on course notes from more than twenty years of teaching engi-neering and physical sciences at Michigan Technological University,Tomas B. Co s engineering MATHEMATICS textbook is rich with examples,applications, and exercises. Professor Co uses analytical approaches tosolve smaller problems to provide mathematical insight and under-standing, and numerical METHODS for large and complex problems. Thebook emphasizes applying matrices with strong attention to matrixstructure and computational issues such as sparsity and on vector calculus and integral theorems are used to buildcoordinate-free physical models, with special emphasis on orthogonalcoordinates. Chapters on ordinary differential equations and partialdifferential equations cover both analytical and numerical on analytical solutions include similarity transform METHODS ,direct formulas for series solutions, bifurcation analysis, Lagrange-Charpit formulas, and shocks/rarefaction.

2 Topics on numerical meth-ods include stability analysis, differential algebraic equations, high-order finite-difference formulas, and Delaunay meshes. MATLAB implementations of the METHODS and concepts are fully B. Co is an associate professor of chemical engineering atMichigan Technological University. After completing his PhD in chem-ical engineering at the University of Massachusetts at Amherst, he wasa postdoctoral researcher at Lehigh University, a visiting researcherat Honeywell Corp., and a visiting professor at Korea has been teaching APPLIED MATHEMATICS to graduate and advancedundergraduate students at Michigan Tech for more than twentyyears. His research areas include advanced process control, includ-ing plantwide control, nonlinear control, and fuzzy logic.

3 His journalpublications span broad areas in such journals asIEEE Transactionsin Automatic Control,Automatica,AIChE Journal,Computers inChemical Engineering,andChemical Engineering nominated twice for the Distinguished Teaching Award atMichigan Tech and is a member of the Michigan TechnologicalUniversity Academy of Teaching in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B. CoFrontmatterMore in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B. CoFrontmatterMore informationMethods of APPLIED MATHEMATICS forEngineers and ScientistsTomas B.

4 CoMichigan Technological in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B. CoFrontmatterMore informationcambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, S ao Paulo, Delhi, Mexico CityCambridge University Press32 Avenue of the Americas, New York, NY 10013-2473, on this title: Tomas B. Co 2013 This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University published 2013 Printed in the United States of AmericaA catalog record for this publication is available from the British of Congress Cataloging in Publication DataCo, Tomas B.

5 , 1959 METHODS of APPLIED MATHEMATICS for ENGINEERS and scientists / Tomas B. Co.,Michigan Technological cmIncludes bibliographical references and 978-1-107-00412-2 (hardback)1. Matrices. 2. Differential equations Numerical solutions. I. 434 dc23 2012043979 ISBN 978-1-107-00412-2 HardbackAdditional resources for this publication at University Press has no responsibility for the persistence or accuracy ofURLs for external or third-party Internet websites referred to in this publicationand does not guarantee that any content on such websites is, or will remain, accurateor in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B.

6 CoFrontmatterMore informationContentsPrefacepagexiI MATRIX THEORY1 Matrix Definitions and Fundamental Matrix Properties of Matrix Block Matrix Matrix Sparse Exercises412 Solution of Multiple Gauss-Jordan LU Direct Matrix Iterative Solution Least-Squares QR Conjugate Gradient Newton s Enhanced Newton METHODS via Line Exercises863 Matrix Matrix Eigenvalues and Properties of Eigenvalues and Schur Triangularization and Normal Jordan Canonical Functions of Square in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B. CoFrontmatterMore Stability of Matrix Singular Value Polar Matrix Exercises138II VECTORS AND TENSORS4 Vector and Tensor Algebra and Notations and Fundamental Vector Algebra Based on Orthonormal Basis Tensor Matrix Representation of Vectors and Differential Operations for Vector Functions of One Application to Position Differential Operations for Vector Curvilinear Coordinate System.

7 Cylindrical and Orthogonal Curvilinear Exercises1965 Vector Integral Green s Divergence Stokes Theorem and Path Leibnitz Derivative Exercises225 III ORDINARY DIFFERENTIAL EQUATIONS6 Analytical Solutions of Ordinary Differential First-Order Ordinary Differential Separable Forms via Similarity Exact Differential Equations via Integrating Second-Order Ordinary Differential Multiple Differential Decoupled System Descriptions via Laplace Transform Exercises2637 Numerical Solution of Initial and Boundary Value Euler Runge Kutta Multistep Difference Equations and Boundary Value Differential Algebraic in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B.

8 CoFrontmatterMore informationContentsvii8 Qualitative Analysis of Ordinary Differential Existence and Autonomous Systems and Equilibrium Integral Curves, Phase Space, Flows, and Lyapunov and Asymptotic Phase-Plane Analysis of Linear Second-OrderAutonomous Linearization Around Equilibrium Method of Lyapunov Limit Bifurcation Exercises3409 Series Solutions of Linear Ordinary Differential Power Series Legendre Bessel Properties and Identities of Bessel Functions andModified Bessel Exercises371IV PARTIAL DIFFERENTIAL EQUATIONS10 First-Order Partial Differential Equations and the Method The Method of Alternate Forms and General The Lagrange-Charpit Classification Based on Principal Hyperbolic Systems of Exercises39911 Linear Partial Differential Linear Partial Differential Reducible Linear Partial Differential Method of Separation of

9 Nonhomogeneous Partial Differential Similarity Exercises44312 Integral Transform General Integral Fourier Solution of PDEs Using Fourier Laplace Solution of PDEs Using Laplace Method of in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B. CoFrontmatterMore informationviiiContents13 Finite Difference Finite Difference Time-Independent Time-Dependent Stability Exercises51914 Method of Finite The Weak Triangular Finite Assembly of Finite Mesh Summary of Finite Element Axisymmetric Time-Dependent Exercises552 BibliographyB-1 IndexI-1 AAdditional Details and Fortification for Chapter Matrix Classes and Special Motivation for Matrix Operations from Solution of Taylor Series Proofs for Lemma and Theorems of Chapter Positive Definite Matrices586 BAdditional Details and Fortification for Chapter Gauss Jordan Elimination SVD to Determine Gauss-Jordan Boolean Matrices and Reducible Reduction of Matrix Block LU Matrix

10 Splitting: Diakoptic Method and SchurComplement Linear Vector Algebra: Fundamental Determination of Linear Independence of Gram-Schmidt Proofs for Lemma and Theorems in Chapter Conjugate Gradient GMRES Enhanced-Newton Using Double-Dogleg Nonlinear Least Squares via Levenberg-Marquardt639 CAdditional Details and Fortification for Chapter Proofs of Lemmas and Theorems of Chapter QR Method for Eigenvalue Calculations for the Jordan in this web service Cambridge University PressCambridge University Press978-1-107-00412-2 - METHODS of APPLIED MATHEMATICS for ENGINEERS and ScientistsTomas B. CoFrontmatterMore Schur Triangularization and Sylvester s Matrix Danilevskii Method for Characteristic Polynomial660 DAdditional Details and Fortification for Chapter Proofs of Identities of Differential Derivation of Formulas in Cylindrical Derivation of Formulas in Spherical Coordinates669 EAdditional Details and Fortification for Chapter Line Surface Volume Gauss-Legendre Proofs of Integral Theorems691 FAdditional Details and Fortification for Chapter Supplemental METHODS for Solving First-Order Singular Finite Series Solution ofdx/dt=Ax+b(t)