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Basic complex analysis / Jerrold E. Marsden, Michael J. Hoffman

Main Author Marsden, Jerrold E. Coauthor Hoffman, Michael J. Country Estados Unidos. Edition 2nd ed Publication New York : W. H. Freeman, cop. 1987 Description XII, 604 p. : il. ; 25 cm ISBN 0-7167-1814-6 CDU 517.53
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Holdings
Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca Geral da Universidade do Minho
BGUM 517.53 - M Available 131566
Monografia Biblioteca da UMinho no Campus de Azurém
BPG 517.53 - M Não requisitável | Not for loan 193833
Monografia Biblioteca da UMinho no Campus de Azurém
BPG2 517.53 - M Available 193835
Monografia Biblioteca da UMinho no Campus de Azurém
BPG2 517.53 - M Available 193836
Total holds: 0

Table of contents provided by Syndetics

  • Preface (p. vii)
  • 1 Analytic Functions (p. 1)
  • 1.1 Introduction to Complex Numbers (p. 1)
  • 1.2 Properties of Complex Numbers (p. 12)
  • 1.3 Some Elementary Functions (p. 25)
  • 1.4 Continuous Functions (p. 41)
  • 1.5 Basic Properties of Analytic Functions (p. 60)
  • 1.6 Differentiation of the Elementary Functions (p. 81)
  • 2 Cauchy's Theorem (p. 95)
  • 2.1 Contour Integrals (p. 95)
  • 2.2 Cauchy's Theorem--A First Look (p. 111)
  • 2.3 A Closer Look at Cauchy's Theorem (p. 123)
  • 2.4 Cauchy's Integral Formula (p. 144)
  • 2.5 Maximum Modulus Theorem and Harmonic Functions (p. 164)
  • 3 Series Representation of Analytic Functions (p. 183)
  • 3.1 Convergent Series of Analytic Functions (p. 184)
  • 3.2 Power Series and Taylor's Theorem (p. 203)
  • 3.3 Laurent Series and Classification of Singularities (p. 222)
  • 4 Calculus of Residues (p. 243)
  • 4.1 Calculation of Residues (p. 243)
  • 4.2 Residue Theorem (p. 256)
  • 4.3 Evaluation of Definite Integrals (p. 269)
  • 4.4 Evaluation of Infinite Series and Partial-Fraction Expansions (p. 304)
  • 5 Conformal Mappings (p. 319)
  • 5.1 Basic Theory of Conformal Mappings (p. 319)
  • 5.2 Fractional Linear and Schwarz-Christoffel Transformations (p. 327)
  • 5.3 Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics (p. 345)
  • 6 Further Development of the Theory (p. 365)
  • 6.1 Analytic Continuation and Elementary Riemann Surfaces (p. 365)
  • 6.2 Rouche's Theorem and Principle of the Argument (p. 384)
  • 6.3 Mapping Properties of Analytic Functions (p. 398)
  • 7 Asymptotic Methods (p. 409)
  • 7.1 Infinite Products and the Gamma Function (p. 409)
  • 7.2 Asymptotic Expansions and the Method of Steepest Descent (p. 427)
  • 7.3 Stirling's Formula and Bessel Functions (p. 446)
  • 8 Laplace Transform and Applications (p. 457)
  • 8.1 Basic Properties of Laplace Transforms (p. 457)
  • 8.2 Complex Inversion Formula (p. 471)
  • 8.3 Application of Laplace Transforms to Ordinary Differential Equations (p. 476)
  • Answers to Odd-Numbered Exercises (p. 481)
  • Index (p. 506)

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