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

Marsden, Jerrold E.
Contributor(s): Hoffman, Michael J.
Material type: materialTypeLabelBook; Format: print Publisher: New York : W.H. Freeman, cop. 1999Edition: 3rd ed.Description: VIII, 516 p. : il. ; 25 cm.ISBN: 071672877X.Subject(s): Functions of complex variables | Funciones de variables complejas
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Manuales (7 días) 02. BIBLIOTECA CAMPUS PUERTO REAL
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Enhanced descriptions from Syndetics:

Basic Complex Analysis skillfully combines a clear exposition of core theory with a rich variety of applications.  Designed for undergraduates in mathematics, the physical sciences, and engineering who have completed two years of calculus and are taking complex analysis for the first time. .

Referencias bibliográficas. - Índice.

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)

Author notes provided by Syndetics

JERROLD E. MARSDEN, University of California, Berkeley
MICHAEL J. HOFFMAN, California State University, Los Angeles

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Other editions of this work

Basic complex analysis / by Marsden, Jerrold E
Student guide to accompany for Basic Complex Analysis by Marsden, Jerrold E.

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