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: Introduction to Mathematical Analysis
  name:
    name part: Kriz, Igor.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Pultr, Aleš.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 510 p. 1 illus. in color. online resource.
  abstract: The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today.
  table of contents: Preface -- Introduction -- Part 1. A Rigorous Approach to Advanced Calculus -- 1. Preliminaries -- 2. Metric and Topological Spaces I -- 3. Multivariable Differential Calculus -- 4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral -- 5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration -- 6. Systems of Ordinary Differential Equations -- 7. System of Linear Differential Equations -- 8. Line Integrals and Green's Theorem -- Part 2. Analysis and Geometry -- 9. An Introduction to Complex Analysis -- 10. Metric and Topological Spaces II -- 11. Multilinear Algebra -- 12. Smooth Manifolds, Differential Forms and Stokes' Theorem -- 13. Calculus of Variations and the Geodesic Equation -- 14. Tensor Calculus and Riemannian Geometry -- 15. Hilbert Spaces I: Definitions and Basic Properties -- 16. Hilbert Spaces II: Examples and Applications -- Appendix A. Linear Algebra I: Vector Spaces -- Appendix B. Linear Algebra II: More about Matrices -- Bibliography -- Index of Symbols -- Index. .
  note: by Igor Kriz, Aleš Pultr.
  subject:
    topic: Mathematics
  subject:
    topic: Matrix theory
  subject:
    topic: Algebra
  subject:
    topic: Functions of complex variables
  subject:
    topic: Measure theory
  subject:
    topic: Differential equations
  subject:
    topic: Functions of real variables
  subject:
    topic: Sequences (Mathematics)
  subject:
    topic: Mathematics
  subject:
    topic: Real Functions
  subject:
    topic: Linear and Multilinear Algebras, Matrix Theory
  subject:
    topic: Measure and Integration
  subject:
    topic: Functions of a Complex Variable
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Sequences, Series, Summability
  classification: QA331.5
  classification: 515.8
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783034806367
  identifier: http://dx.doi.org/10.1007/978-3-0348-0636-7
  record info:
    record creation date: 130725
    record change date: 20151107111015.0
    record identifier: 978-3-0348-0636-7