The Resource Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)

Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)

Label
Linear algebra and linear operators in engineering with applications in Mathematica
Title
Linear algebra and linear operators in engineering with applications in Mathematica
Statement of responsibility
H. Ted Davis, Kendall T. Thomson
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert sp
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Davis, H. Ted
Dewey number
  • 512.5
  • 512.502466
  • 512/.5 21
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA184
LC item number
.D38 2000
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Thomson, Kendall T
Series statement
Process systems engineering
Series volume
v. 3
http://library.link/vocab/subjectName
  • Algebras, Linear
  • Linear operators
  • Mathematica (Computer program language)
Label
Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Linear Algebra and Linear Operators in Engineering; Copyright Page; Contents; Preface; Chapter 1. Determinants; 1.1. Synopsis; 1.2. Matrices; 1.3. Definition of a Determinant; 1.4. Elementary Properties of Determinants; 1.5. Cofactor Expansions; 1.6. Cramer's Rule for Linear Equations; 1.7. Minors and Rank of Matrices; Problems; Further Reading; Chapter 2. Vectors and Matrices; 2.1. Synopsis; 2.2. Addition and Multiplication; 2.3. The Inverse Matrix; 2.4. Transpose and Adjoint; 2.5. Partitioning Matrices; 2.6. Linear Vector Spaces; Problems; Further Reading
  • Chapter 3. Solution of Linear and Nonlinear Systems3.1. Synopsis; 3.2. Simple Gauss Elimination; 3.3. Gauss Elimination with Pivoting; 3.4. Computing the Inverse of a Matrix; 3.5. LU-Decomposition; 3.6. Band Matrices; 3.7. Iterative Methods for Solving Ax = b; 3.8. Nonhnear Equations; Problems; Further Reading; Chapter 4. General Theory of Solvability of Linear Algebraic Equations; 4.1. Synopsis; 4.2. Sylvester's Theorem and the Determinants of Matrix Products; 4.3. Gauss-Jordan Transformation of a Matrix; 4.4. General Solvability Theorem for Ax = b
  • 4.5. Linear Dependence of a Vector Set and the Rank of Its Matrix4.6. The Fredholm Alternative Theorem; Problems; Further Reading; Chapter 5. The Eigenproblem; 5.1. Synopsis; 5.2. Linear Operators in a Normed Linear Vector Space; 5.3. Basis Sets in a Normed Linear Vector Space; 5.4. Eigenvalue Analysis; 5.5. Some Special Properties of Eigenvalues; 5.6. Calculation of Eigenvalues; Problems; Further Reading; Chapter 6. Perfect Matrices; 6.1. Synopsis; 6.2. Implications of the Spectral Resolution Theorem; 6.3. Diagonalization by a Similarity Transformation
  • 6.4. Matrices with Distinct Eigenvalues6.5. Unitary and Orthogonal Matrices; 6.6. Semidiagonalization Theorem; 6.7. Self-Adjoint Matrices; 6.8. Normal Matrices; 6.9. Miscellanea; 6.10. The Initial Value Problem; 6.11. Perturbation Theory; Problems; Further Reading; Chapter 7. Imperfect or Defective Matrices; 7.1. Synopsis; 7.2. Rank of the Characteristic Matrix; 7.3. Jordan Block Diagonal Matrices; 7.4. The Jordan Canonical Form; 7.5. Determination of Generalized Eigenvectors; 7.6. Dyadic Form of an Imperfect Matrix; 7.7. Schmidt's Normal Form of an Arbitrary Square Matrix
  • 7.8. The Initial Value ProblemProblems; Further Reading; Chapter 8. Infinite-Dimensional Linear Vector Spaces; 8.1. Synopsis; 8.2. Infinite-Dimensional Spaces; 8.3. Riemann and Lebesgue Integration; 8.4. Inner Product Spaces; 8.5. Hilbert Spaces; 8.6. Basis Vectors; 8.7. Linear Operators; 8.8. Solutions to Problems Involving ke-term Dyadics; 8.9. Perfect Operators; Problems; Further Reading; Chapter 9. Linear Integral Operators in a Hilbert Space; 9.1. Synopsis; 9.2. Solvability Theorems; 9.3. Completely Continuous and Hilbert-Schmidt Operators; 9.4. Volterra Equations
  • 9.5. Spectral Theory of Integral Operators
Dimensions
unknown
Extent
1 online resource (561 p.)
Form of item
online
Isbn
9781281053800
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)1000000000383736
  • (EBL)313688
  • (OCoLC)476103260
  • (SSID)ssj0000192586
  • (PQKBManifestationID)11196881
  • (PQKBTitleCode)TC0000192586
  • (PQKBWorkID)10218018
  • (PQKB)11764152
  • (MiAaPQ)EBC313688
  • (EXLCZ)991000000000383736
Label
Linear algebra and linear operators in engineering with applications in Mathematica, H. Ted Davis, Kendall T. Thomson, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Linear Algebra and Linear Operators in Engineering; Copyright Page; Contents; Preface; Chapter 1. Determinants; 1.1. Synopsis; 1.2. Matrices; 1.3. Definition of a Determinant; 1.4. Elementary Properties of Determinants; 1.5. Cofactor Expansions; 1.6. Cramer's Rule for Linear Equations; 1.7. Minors and Rank of Matrices; Problems; Further Reading; Chapter 2. Vectors and Matrices; 2.1. Synopsis; 2.2. Addition and Multiplication; 2.3. The Inverse Matrix; 2.4. Transpose and Adjoint; 2.5. Partitioning Matrices; 2.6. Linear Vector Spaces; Problems; Further Reading
  • Chapter 3. Solution of Linear and Nonlinear Systems3.1. Synopsis; 3.2. Simple Gauss Elimination; 3.3. Gauss Elimination with Pivoting; 3.4. Computing the Inverse of a Matrix; 3.5. LU-Decomposition; 3.6. Band Matrices; 3.7. Iterative Methods for Solving Ax = b; 3.8. Nonhnear Equations; Problems; Further Reading; Chapter 4. General Theory of Solvability of Linear Algebraic Equations; 4.1. Synopsis; 4.2. Sylvester's Theorem and the Determinants of Matrix Products; 4.3. Gauss-Jordan Transformation of a Matrix; 4.4. General Solvability Theorem for Ax = b
  • 4.5. Linear Dependence of a Vector Set and the Rank of Its Matrix4.6. The Fredholm Alternative Theorem; Problems; Further Reading; Chapter 5. The Eigenproblem; 5.1. Synopsis; 5.2. Linear Operators in a Normed Linear Vector Space; 5.3. Basis Sets in a Normed Linear Vector Space; 5.4. Eigenvalue Analysis; 5.5. Some Special Properties of Eigenvalues; 5.6. Calculation of Eigenvalues; Problems; Further Reading; Chapter 6. Perfect Matrices; 6.1. Synopsis; 6.2. Implications of the Spectral Resolution Theorem; 6.3. Diagonalization by a Similarity Transformation
  • 6.4. Matrices with Distinct Eigenvalues6.5. Unitary and Orthogonal Matrices; 6.6. Semidiagonalization Theorem; 6.7. Self-Adjoint Matrices; 6.8. Normal Matrices; 6.9. Miscellanea; 6.10. The Initial Value Problem; 6.11. Perturbation Theory; Problems; Further Reading; Chapter 7. Imperfect or Defective Matrices; 7.1. Synopsis; 7.2. Rank of the Characteristic Matrix; 7.3. Jordan Block Diagonal Matrices; 7.4. The Jordan Canonical Form; 7.5. Determination of Generalized Eigenvectors; 7.6. Dyadic Form of an Imperfect Matrix; 7.7. Schmidt's Normal Form of an Arbitrary Square Matrix
  • 7.8. The Initial Value ProblemProblems; Further Reading; Chapter 8. Infinite-Dimensional Linear Vector Spaces; 8.1. Synopsis; 8.2. Infinite-Dimensional Spaces; 8.3. Riemann and Lebesgue Integration; 8.4. Inner Product Spaces; 8.5. Hilbert Spaces; 8.6. Basis Vectors; 8.7. Linear Operators; 8.8. Solutions to Problems Involving ke-term Dyadics; 8.9. Perfect Operators; Problems; Further Reading; Chapter 9. Linear Integral Operators in a Hilbert Space; 9.1. Synopsis; 9.2. Solvability Theorems; 9.3. Completely Continuous and Hilbert-Schmidt Operators; 9.4. Volterra Equations
  • 9.5. Spectral Theory of Integral Operators
Dimensions
unknown
Extent
1 online resource (561 p.)
Form of item
online
Isbn
9781281053800
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)1000000000383736
  • (EBL)313688
  • (OCoLC)476103260
  • (SSID)ssj0000192586
  • (PQKBManifestationID)11196881
  • (PQKBTitleCode)TC0000192586
  • (PQKBWorkID)10218018
  • (PQKB)11764152
  • (MiAaPQ)EBC313688
  • (EXLCZ)991000000000383736

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