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Complex Variables and Applications 7th Edition by James Ward Brown, Ruel Vance Churchill ISBN 978-0072872521 0072872527

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Complex Variables and Applications 7th Edition James Ward Brown Digital Instant Download

Author(s): James Ward Brown, Ruel Vance Churchill
ISBN(s): 0072872527
Edition: 7
File Details: PDF, 7.86 MB
Year: 2003
Language: english
SKU: EB-2141048 Category: Tags: ,

Complex Variables and Applications 7th Edition by James Ward Brown, Ruel Vance Churchill  – Ebook PDF Instant Download/Delivery: 978-0072872521, 0072872527
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Product details: 

ISBN 10:  0072872527

ISBN 13: 978-0072872521

Author: James Ward Brown, Ruel Vance Churchill

“Complex Variables and Applications, 8E” will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the earlier editions. The text is designed to develop the theory that is prominent in applications of the subject. You will find a special emphasis given to the application of residues and conformal mappings. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results in advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, and the separation of topics into their own sections.

Table of contents: 

1. Complex Numbers

  • Sums and Products

  • Basic Algebraic Properties

  • Further Properties

  • Moduli

  • Complex Conjugates

  • Exponential Form

  • Products and Quotients in Exponential Form

  • 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 ω(1)

  • Definite Integrals of Functions ω(1)

  • Contours

  • Contour Integrals

  • Examples

  • Upper Bounds for Moduli of Contour Integrals

  • Antiderivatives

  • Examples

  • Cauchy–Goursat Theorem

  • Proof of the Theorem

  • Simply and Multiply Connected Domains

  • Cauchy Integral Formula

  • Derivatives of Analytic Functions

  • Liouville’s Theorem and the Fundamental Theorem of Algebra

  • Maximum Modulus Principle

5. Series

  • Convergence of Sequences

  • Convergence of Series

  • Taylor Series

  • Examples

  • Laurent Series

  • 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

  • Residues

  • Cauchy’s Residue Theorem

  • Using a Single Residue

  • The Three Types of Isolated Singular Points

  • Residues at Poles

  • Examples

  • Zeros of Analytic Functions

  • Zeros and Poles

  • Behavior 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=12w = frac{1}{2}

  • Mappings by 12frac{1}{2}21​

  • Linear Fractional Transformations

  • An Implicit Form

  • Mappings of the Upper Half Plane

  • The Transformation w=sin⁡zw = sin z

  • Mappings by z2z^2z2 and Branches of 2sqrt{2}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
10.1 Steady Temperatures
10.2 Steady Temperatures in a Half Plane
10.3 A Related Problem
10.4 Temperatures in a Quadrant
10.5 Electrostatic Potential
10.6 Potential in a Cylindrical Space
10.7 Two‑Dimensional Fluid Flow
10.8 The Stream Function
10.9 Flows Around a Corner and Around a Cylinder

11. The Schwarz–Christoffel Transformation
11.1 Mapping the Real Axis onto a Polygon
11.2 Schwarz–Christoffel Transformation
11.3 Triangles and Rectangles
11.4 Degenerate Polygons
11.5 Fluid Flow in a Channel Through a Slit
11.6 Flow in a Channel with an Offset
11.7 Electrostatic Potential about an Edge of a Conducting Plate

12. Integral Formulas of the Poisson Type 
12.1 Poisson Integral Formula
12.2 Dirichlet Problem for a Disk
12.3 Related Boundary Value Problems
12.4 Schwarz Integral Formula
12.5 Dirichlet Problem for a Half Plane
12.6 Neumann Problems

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Tags: James Ward Brown, Ruel Vance Churchill, Complex Variables