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
  name:
    name part: Chillingworth, H. R.
    role:
      role term: creator
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    place:
      place term: Oxford
    place:
      place term: New York
    publisher: Pergamon Press
    date issued: [1973]
    date issued: 1973
    edition: [1st ed.].
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (ix, 269 pages) : illustrations
  abstract: Complex Variables covers topics ranging from complex numbers to point sets in the complex plane, elementary functions, straight lines and circles, simple and conformal transformations, and zeros and singularities. Cauchy's theorem, Taylor's theorem, Laurent's theorem, contour integration, and miscellaneous theorems are also discussed. This volume consists of 14 chapters, the first of which introduces the theory of complex numbers and their development either from an algebraic or from a geometrical viewpoint. Emphasis is on the complex plane, modulus, amplitude, number pairs, complex conjugates.
  table of contents: Front Cover; Complex Variables; Copyright Page; Table of Contents; INTRODUCTION; CHAPTER 1. COMPLEX NUMBERS; 1.1. The Complex Plane; 1.2. Modulus; 1.3. Amplitude; 1.4. Number Pairs; 1.5. Addition; 1.6. Scalar Multiplication; 1.7. Subtraction; 1.8. Multiplication; 1.9. Division; 1.10. An Alternative Notation; 1.11. An Algebraic Approach; 1.12. Complex Numbers as an Extension of the Real Number Field; 1.13. Complex Conjugates; 1.14. The Triangle Inequality; 1.15. De Moivre's Theorem; Exercises; CHAPTER 2. POINT SETS IN THE COMPLEX PLANE. SEQUENCES. LIMITS.
  table of contents: 2.1. Point Sets: Finite, Countable, and Non-countable Sets. Real Intervals2.2. Bounded and Unbounded Sets on the Real Line; 2.3. The Bolzano-Weierstrass Property; 2.4. Bounded and Unbounded Sets in the Complex Plane; 2.5. Neighbourhoods. Open Sets; 2.6. Limit Points; 2.7. Closed Sets; 2.8. Boundary Points; 2.9. Closure; 2.10. Sequences; 2.11. Convergence; 2.12. Divergence; 2.13. Boundedness of Convergent Sequences; 2.14. A Test for Convergence; 2.15. Cauchy Sequences of Real Numbers; 2.16. Cauchy Sequences of Complex Numbers; 2.17. Non-decreasing Real Sequences; Exercises.
  table of contents: CHAPTER 3. INFINITE SERIES. TESTS FOR CONVERGENCE3.1. The Sum of an Infinite Series; 3.2. Summability; 3.3. Testing for Convergence or Divergence; 3.4. The Comparison Test; 3.5. d'Alembert's Ratio Test; 3.6. Upper and Lower Limits; 3.7. Cauchy's Root Test; 3.8. The Integral Test; 3.9. Series with Negative or Complex Terms; 3.10. Absolute Convergence; 3.11. Other Tests; 3.12. Multiplication of Series; Exercises; CHAPTER 4. FUNCTIONS OF A COMPLEX VARIABLE; 4.1. The Definition of a Function; 4.2. Continuity; 4.3. Differentiability; 4.4. The Cauchy-Riemann Equations.
  table of contents: 4.5. The Cauchy-Riemann Equations. Sufficiency4.6. Analytic Functions; 4.7. Laplace's Equation; 4.8. Orthogonal Families of Curves; Exercises; CHAPTER 5. ELEMENTARY FUNCTIONS; 5.1. Polynomials; 5.2. Rational Functions; 5.3. The Exponential Function; 5.4. Sine and Cosine; 5.5. The Link between the Exponential and Trigonometric Functions; 5.6. de Moivre's Theorem; 5.7. Hyperbolic Functions; 5.8. The Logarithmic Function; 5.9. More General Power Functions; 5.10. The Expression of a Regular Function as a Series; 5.11. Differentiability of Power Series.
  table of contents: 5.12. Repeated Differentiation of an Infinite Series5.13. Inverse Functions; Exercises; CHAPTER 6. STRAIGHT LINE AND CIRCLE; 6.1. The Standard Equation of a Straight Line; 6.2. Other Forms of the Equation; 6.3. The Circle; Exercises; CHAPTER 7. SIMPLE TRANSFORMATIONS; 7.1. Translation; 7.2. Reflection; 7.3. Rotation; 7.4. Magnification; 7.5. Glide Reflection; 7.6. Shear; 7.7. Inversion; 7.8. The Point at Infinity; Exercises; CHAPTER 8. CONFORMAL TRANSFORMATIONS; 8.1. Regular Transformations; 8.2. The Bilinear Transformation; 8.3. Straight Lines and Circles; 8.4. The Mapping of a Domain.
  note: by H.R. Chillingworth.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (page 255).
  subject:
    topic: Functions of complex variables
  subject:
    topic: Fonctions d'une variable complexe
  subject:
    topic: MATHEMATICS
    topic: Calculus
  subject:
    topic: MATHEMATICS
    topic: Mathematical Analysis
  subject:
    topic: Functions of complex variables
  subject:
    topic: Komplexe Variable
  subject:
    topic: Complexe variabelen
  subject:
    topic: Functions
    topic: of
    topic: complex
    topic: variables
  classification: QA331 .C49 1973
  classification: 515/.9
  classification: 31.42
  classification: 32-XX
  related item:
    title info:
      title: Complex variables
    name:
      name part: Chillingworth, H.R.
    origin info:
      publisher: Oxford, New York, Pergamon Press [1973]
      edition: [1st ed.].
    identifier: (DLC) 72086178
    identifier: (OCoLC)605059
  related item:
    title info:
      title: Commonwealth and international library
      part name: Mathematical topics
  identifier: 9781483139951
  identifier: 1483139956
  identifier: 0080169384
  identifier: 9780080169385
  identifier: 0080169392
  identifier: 9780080169392
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCLCE
    record creation date: 101107
    record change date: 20260326184030.9
    record identifier: in00005746341
    language of cataloging:
      language term: eng