rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Linear algebra to differential equations
  title info:
    title: MATHnetBASE
  name:
    name part: Vasundhara Devi, J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Deo, Sadashiv G.
    name part: 1933-
    role:
      role term: author.
  name:
    name part: Khandeparkar, Ramakrishna
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2021
    edition: First edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: "Linear Algebra to Differential Equations concentrates on the essential topics necessary for all engineering students in general and computer science branch students, in particular. Specifically, the topics dealt will help the reader in applying linear algebra as a tool. The advent of high-speed computers has paved the way for studying large systems of linear equations as well as large systems of linear differential equations. Along with the standard numerical methods, methods that curb the progress of error are given for solving linear systems of equations. The topics of linear algebra and differential equations are linked by Kronecker products and calculus of matrices. These topics are useful in dealing with linear systems of differential equations and matrix differential equations. Differential equations are treated in terms of vector and matrix differential systems, as they naturally arise while formulating practical problems. The essential concepts dealing with the solutions and their stability are briefly presented to motivate the reader towards further investigation. This book caters to the needs of Engineering students in general and in particular, to students of Computer Science & Engineering, Artificial Intelligence, Machine Learning and Robotics. Further, the book provides a quick and complete overview of linear algebra and introduces linear differential systems, serving the basic requirements of scientists and researchers in applied fields. Features Provides complete basic knowledge of the subject Exposes the necessary topics lucidly Introduces the abstraction and at the same time is down to earth Highlights numerical methods and approaches that are more useful Essential techniques like SVD and PCA are given Applications (both classical and novel) bring out similarities in various disciplines: Illustrative examples for every concept: A brief overview of techniques that hopefully serves the present and future needs of students and scientists"--
  table of contents: 1. Vectors and Matrices. 1.1. Introduction. 1.2. Scalars and Vectors. 1.3. Introduction to Matrices. 1.4. Types of Matrices. 1.5. Elementary Operations and Elementary Matrices. 1.6. Determinants. 1.7. Inverse of a Matrix. 1.8. Partitioning of Matrices. 1.9. Advanced Topics: Pseudo Inverse and Congruent Inverse. 1.10. Conclusion. 2. Linear System of Equations. 2.1. Introduction. 2.2. Linear System of Equations. 2.3. Rank of a Matrix. 2.4. Echelon Form and Normal Form. 2.4. Echelon Form and Normal Form. 2.5. Solutions of a Linear System of Equations. 2.6. Cayley Hamilton Theorem. 2.7. Eigen Values and Eigen Vectors. 2.8. Singular Values and Singular Vectors. 2.9. Quadratic Forms. 2.10. Conclusion. 3. Vector Spaces. 3.1. Introduction. 3.2. Vector Space and a Subspace. 3.3. Linear Independence, Basis and Dimension. 3.4. Change of Basis -- Matrix. 3.5. Linear Transformations. 3.6. Matrices of Linear Transformations. 3.7. Inner Product Space. 3.8. Gram-Schmidt Orthogonalization. 3.9. Linking Linear Algebra to Differential Equations. 3.10. Conclusion. 4. Numerical Methods in Linear Algebra. 4.1. Introduction. 4.2. Elements of Computation and Errors. 4.3. Direct Methods for Solving a Linear System of Equations. 4.4. Iterative Methods. 4.5. Householder Transformation. 4.6. Tridiagonalization of a Symmetric Matrix by Plane Rotation. 4.7. QR Decomposition. 4.8. Eigen Values: Bounds and Power Method. 4.9. Krylov Subspace Methods. 4.10. Conclusion. 5. Applications. 5.1. Introduction. 5.2. Finding Curves through Given Points. 5.3. Markov Chains. 5.4. Leontief's Models. 5.5. Cryptology. 5.6. Application to Computer Graphics. 5.7. Application to Computer Graphics. 5.8. Bioinformatics. 5.9. Principal Component Analysis (PCA). 5.10. Big Data. 5.11. Conclusion. 6. Kronecker Product. 6.1. Introduction. 6.2. Primary Matrices. 6.3. Kronecker Products. 6.4. Further Properties of Kronecker products. 6.5. Kronecker product of two linear transformations. 6.6. Kronecker Product and Vector Ope…
  note: J. Vasundhara Devi, Sadashiv G. Deo, Ramakrishna Khandeparkar.
  subject:
    topic: Algebras, Linear
  subject:
    topic: Differential equations
  subject:
    topic: MATHEMATICS / General
  subject:
    topic: MATHEMATICS / Algebra / General
  subject:
    topic: MATHEMATICS / Applied
  classification: QA184.2
  classification: 512/.5
  identifier: 9781351014953
  identifier: 1351014951
  identifier: 9781351014939
  identifier: 1351014935
  identifier: 9781351014946
  identifier: 1351014943
  identifier: 9781351014922
  identifier: 1351014927
  identifier: 9780815361466
  identifier: 9781032067988
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCoLC-P
    record creation date: 210607
    record change date: 20220613175835.1
    record identifier: in00004581236
    language of cataloging:
      language term: eng