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: Algebraic and Differential Methods for Nonlinear Control Theory
    sub title: Elements of Commutative Algebra and Algebraic Geometry
  name:
    name part: Martínez-Guerra, Rafael.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Martínez-Fuentes, Oscar.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Montesinos-García, Juan Javier.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 196 p. 13 illus., 11 illus. in color. online resource.
  abstract: This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.
  table of contents: Mathematical Background -- Group Theory -- Rings -- Matrices and linear equations systems -- Permutations and Determinants -- Vector and Euclidean Spaces -- Linear Transformations -- Matrix Diagonalization and Jordan Canonical Form -- Differential Equations -- Differential Algebra for Nonlinear Control Theory -- Appendix -- Index.
  note: by Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García.
  subject:
    topic: Engineering mathematics
  subject:
    topic: Statistical physics
  subject:
    topic: Control engineering
  subject:
    topic: System theory
  subject:
    topic: Engineering Mathematics
  subject:
    topic: Applications of Nonlinear Dynamics and Chaos Theory
  subject:
    topic: Control and Systems Theory
  subject:
    topic: Systems Theory, Control
  classification: TA329-348
  classification: 620.00151
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Mathematical and Analytical Techniques with Applications to Engineering
  identifier: 9783030120252
  identifier: https://doi.org/10.1007/978-3-030-12025-2
  record info:
    record creation date: 190130
    record change date: 20191027151747.0
    record identifier: 978-3-030-12025-2