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Produktbild: Brown, J: Complex Variables and Applications

Brown, J: Complex Variables and Applications

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

10.01.2008

Verlag

McGraw Hill Academic

Seitenzahl

468

Maße (L/B/H)

23.6/16.5/2 cm

Gewicht

771 g

Auflage

8 Rev ed

Sprache

Englisch

ISBN

978-0-07-305194-9

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

10.01.2008

Verlag

McGraw Hill Academic

Seitenzahl

468

Maße (L/B/H)

23.6/16.5/2 cm

Gewicht

771 g

Auflage

8 Rev ed

Sprache

Englisch

ISBN

978-0-07-305194-9

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  • Produktbild: Brown, J: Complex Variables and Applications
  • 1 Complex Numbers
    Sums and Products
    Basic Algebraic Properties
    Further Properties
    Vectors and Moduli
    Complex Conjugates
    Exponential Form
    Products and Powers in Exponential Form
    Arguments of Products and Quotients
    Roots of Complex Numbers
    Examples
    Regions in the Complex Plane
    2 Analytic Functions
    Functions of a Complex Variable
    Mappings
    Mappings by the Exponential Function
    Limits
    Theorems on Limits
    Limits Involving the Point at Infinity
    Continuity
    Derivatives
    Differentiation Formulas
    Cauchy-Riemann Equations
    Sufficient Conditions for Differentiability
    Polar Coordinates
    Analytic Functions
    Examples
    Harmonic Functions
    Uniquely Determined Analytic Functions
    Reflection Principle
    3 Elementary Functions
    The Exponential Function
    The Logarithmic Function
    Branches and Derivatives of Logarithms
    Some Identities Involving Logarithms
    Complex Exponents
    Trigonometric Functions
    Hyperbolic Functions
    Inverse Trigonometric and Hyperbolic Functions
    4 Integrals
    Derivatives of Functions w(t)
    Definite Integrals of Functions w(t)
    Contours
    Contour Integrals
    Some Examples
    Examples with Branch Cuts
    Upper Bounds for Moduli of Contour Integrals
    Antiderivatives
    Proof of the Theorem
    Cauchy-Goursat Theorem
    Proof of the Theorem
    Simply Connected Domains
    Multiply Connected Domains
    Cauchy Integral Formula
    An Extension of the Cauchy Integral Formula
    Some Consequences of the Extension
    Liouville's Theorem and the Fundamental Theorem of Algebra
    Maximum Modulus Principle
    5 Series
    Convergence of Sequences
    Convergence of Series
    Taylor Series
    Proof of Taylor's Theorem
    Examples
    Laurent Series
    Proof of Laurent's Theorem
    Examples
    Absolute and Uniform Convergence of Power Series
    Continuity of Sums of Power Series
    Integration and Differentiation of Power Series
    Uniqueness of Series Representations
    Multiplication and Division of Power Series
    6 Residues and Poles
    Isolated Singular Points
    Residues
    Cauchy's Residue Theorem
    Residue at Infinity
    The Three Types of Isolated Singular Points
    Residues at Poles
    Examples
    Zeros of Analytic Functions
    Zeros and Poles
    Behavior of Functions Near Isolated Singular Points
    7 Applications of Residues
    Evaluation of Improper Integrals
    Example
    Improper Integrals from Fourier Analysis
    Jordan's Lemma
    Indented Paths
    An Indentation Around a Branch Point
    Integration Along a Branch Cut
    Definite Integrals Involving Sines and Cosines
    Argument Principle
    Rouché's Theorem
    Inverse Laplace Transforms
    Examples
    8 Mapping by Elementary Functions
    Linear Transformations
    The Transformation w = 1/z
    Mappings by 1/z
    Linear Fractional Transformations
    An Implicit Form
    Mappings of the Upper Half Plane
    The Transformation w = sin z
    Mappings by z2 and Branches of z1/2
    Square Roots of Polynomials
    Riemann Surfaces
    Surfaces for Related Functions
    9 Conformal Mapping
    Preservation of Angles
    Scale Factors
    Local Inverses
    Harmonic Conjugates
    Transformations of Harmonic Functions
    Transformations of Boundary Conditions
    10 Applications of Conformal Mapping
    Steady Temperatures
    Steady Temperatures in a Half Plane
    A Related Problem
    Temperatures in a Quadrant
    Electrostatic Potential
    Potential in a Cylindrical Space
    Two-Dimensional Fluid Flow
    The Stream Function
    Flows Around a Corner and Around a Cylinder
    11 The Schwarz-Christoffel Transformation
    Mapping the Real Axis onto a Polygon
    Schwarz-Christoffel Transformation
    Triangles and Rectangles
    Degenerate Polygons
    Fluid Flow in a Channel Through a Slit
    Flow in a Channel with an Offset
    Electrostatic Potential about an Edge of a Conducting Plate
    12 Integral Formulas of the Poisson Type
    Poisson Integral Formula
    Dirichlet Problem for a Disk
    Related Boundary Value Problems
    Schwarz Integral Formula
    Dirichlet Problem for a Half Plane
    Neumann Problems
    Appendixes
    Bibliography
    Table of Transformations of Regions
    Index