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: Complex variables
    sub title: a physical approach with applications
  name:
    name part: Krantz, Steven G. (Steven George)
    name part: 1951-
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: ProQuest (Firm)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2019
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  table of contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface to the Second Edition for the Instructor; Preface to the Second Edition for the Student; Preface to the First Edition; 1: Basic Ideas; 1.1 Complex Arithmetic; 1.1.1 The Real Numbers; 1.1.2 The Complex Numbers; 1.1.3 Complex Conjugate; Exercises; 1.2 Algebraic and Geometric Properties; 1.2.1 Modulus of a Complex Number; 1.2.2 The Topology of the Complex Plane; 1.2.3 The Complex Numbers as a Field; 1.2.4 The Fundamental Theorem of Algebra; Exercises; 2: The Exponential and Applications
  table of contents: 2.1 The Exponential Function2.1.1 Laws of Exponentiation; 2.1.2 The Polar Form of a Complex Number; Exercises; 2.1.3 Roots of Complex Numbers; 2.1.4 The Argument of a Complex Number; 2.1.5 Fundamental Inequalities; Exercises; 3: Holomorphic and Harmonic Functions; 3.1 Holomorphic Functions; 3.1.1 Continuously Differentiable and Ck Functions; 3.1.2 The Cauchy-Riemann Equations; 3.1.3 Derivatives; 3.1.4 Definition of Holomorphic Function; 3.1.5 Examples of Holomorphic Functions; 3.1.6 The Complex Derivative; 3.1.7 Alternative Terminology for Holomorphic Functions; Exercises
  table of contents: 3.2 Holomorphic and Harmonic Functions3.2.1 Harmonic Functions; 3.2.2 Holomorphic and Harmonic Functions; Exercises; 3.3 Complex Differentiability; 3.3.1 Conformality; Exercises; 4: The Cauchy Theory; 4.1 Real and Complex Line Integrals; 4.1.1 Curves; 4.1.2 Closed Curves; 4.1.3 Differentiable and Ck Curves; 4.1.4 Integrals on Curves; 4.1.5 The Fundamental Theorem of Calculus along Curves; 4.1.6 The Complex Line Integral; 4.1.7 Properties of Integrals; Exercises; 4.2 The Cauchy Integral Theorem; 4.2.1 The Cauchy Integral Theorem, Basic Form; 4.2.2 More General Forms of the Cauchy Theorem
  table of contents: 4.2.3 Deformability of Curves4.2.4 Cauchy Integral Formula, Basic Form; 4.2.5 More General Versions of the Cauchy Formula; Exercises; 4.3 Variants of the Cauchy Formula; 4.4 The Limitations of the Cauchy Formula; Exercises; 5: Applications of the Cauchy Theory; 5.1 The Derivatives of a Holomorphic Function; 5.1.1 A Formula for the Derivative; 5.1.2 The Cauchy Estimates; 5.1.3 Entire Functions and Liouville's Theorem; 5.1.4 The Fundamental Theorem of Algebra; 5.1.5 Sequences of Holomorphic Functions and Their Derivatives; 5.1.6 The Power Series Representation of a Holomorphic Function
  table of contents: 5.1.7 Table of Elementary Power SeriesExercises; 5.2 The Zeros of a Holomorphic Function; 5.2.1 The Zero Set of a Holomorphic Function; 5.2.2 Discrete Sets and Zero Sets; 5.2.3 Uniqueness of Analytic Continuation; Exercises; 6: Isolated Singularities; 6.1 Behavior Near an Isolated Singularity; 6.1.1 Isolated Singularities; 6.1.2 A Holomorphic Function on a Punctured Domain; 6.1.3 Classification of Singularities; 6.1.4 Removable Singularities, Poles, and Essential Singularities; 6.1.5 The Riemann Removable Singularities Theorem; 6.1.6 The Casorati-Weierstrass Theorem; 6.1.7 Concluding Remarks
  note: Steven G. Krantz.
  note: Electronic resource.
  note: Includes bibliographical references and index.
  subject:
    topic: Functions of complex variables
  subject:
    topic: Functions of complex variables
    genre: Textbooks
  subject:
    topic: Numbers, Complex
    genre: Textbooks
  subject:
    topic: Mathematical analysis
    genre: Textbooks
  classification: QA331.7 .K732 2019
  classification: 515/.9
  related item:
    identifier: (DLC) 2018061709
  related item:
    title info:
      title: Textbooks in mathematics (Boca Raton, Fla.)
  identifier: 9780429275166
  identifier: 0429275161
  identifier: 9780415000352
  identifier: 0415000351
  identifier: 9780367222673
  identifier: 0367222671
  identifier: 9781000000351
  identifier: 1000000354
  identifier: 9781000013719
  identifier: 1000013715
  identifier: 9781000007183
  identifier: 1000007189
  identifier: 9780429275166 Taylor & Francis
  identifier: https://ebookcentral.proquest.com/lib/tamucs/detail.action
  record info:
    record content source: NhCcYBP
    record creation date: 190419
    record change date: 20221130134220.6
    record identifier: in00004060251