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: Mathematical Analysis
    sub title: Foundations and Advanced Techniques for Functions of Several Variables
  name:
    name part: Giaquinta, Mariano.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Modica, Giuseppe.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 405 p. 66 illus. online resource.
  abstract: Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations. Other books published by the authors – all of which provide the reader with a strong foundation in modern-day analysis – include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . Th…
  table of contents: Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index.
  note: by Mariano Giaquinta, Giuseppe Modica.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817683108
  identifier: http://dx.doi.org/10.1007/978-0-8176-8310-8
  record info:
    record creation date: 111102
    record change date: 20151125231529.0
    record identifier: 978-0-8176-8310-8