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: Real Analysis and Applications
  name:
    name part: Botelho, Fabio Silva.
    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: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 567 p. online resource.
  abstract: This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.
  table of contents: Chapter 01- Real Numbers -- Chapter 02- Metric Spaces -- Chapter 03- Real Sequences and Series -- Chapter 04- Real Function Limits -- Chapter 05- Continuous Functions -- Chapter 06- Derivatives -- Chapter 07- The Riemann Integral -- Chapter 08- Differential Analysis in Rn -- Chapter 09- Integration in Rn -- Chapter 10- Topics on Vector Calculus and Vector Analysis.
  note: by Fabio Silva Botelho.
  subject:
    topic: Functions of real variables
  subject:
    topic: Measure theory
  subject:
    topic: Sequences (Mathematics)
  subject:
    topic: Real Functions
  subject:
    topic: Measure and Integration
  subject:
    topic: Sequences, Series, Summability
  classification: QA331.5
  classification: 515.8
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319786315
  identifier: https://doi.org/10.1007/978-3-319-78631-5
  record info:
    record creation date: 180514
    record change date: 20191024214141.0
    record identifier: 978-3-319-78631-5