Complex Analysis for Mathematics and Engineering,9780763714253

Complex Analysis for Mathematics and Engineering

by ;
Edition: 4th
ISBN13: 9780763714253
ISBN10: 0763714259
Format: Paperback
Pub. Date: 2000-08-01
Publisher(s): Jones & Bartlett
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Summary

The new Fifth Edition of Complex Analysis for Mathematics and Engineering presents a comprehensive, student-friendly introduction to Complex Analysis concepts. Its clear, concise writing style and numerous applications make the foundations of the subject matter easily accessible to students. Believing that mathematicians, engineers, and scientists should be exposed to a careful presentation of mathematics, the authors devote attention to important topics, such as ensuring that required assumptions are met before using a theorem, confirming that algebraic operations are valid, and checking that formulas are not blindly applied. A new chapter on z-transforms and applications provides students with a current look at Digital Filter Design and Signal Processing.

Table of Contents

Complex Numbers
1(48)
The Origin of Complex Numbers
1(5)
The Algebra of Complex Numbers
6(10)
The Geometry of Complex Numbers
16(6)
The Geometry of Complex Numbers, Continued
22(9)
The Algebra of Complex Numbers, Revisited
31(8)
The Topology of Complex Numbers
39(10)
Complex Functions
49(44)
Functions of a Complex Variable
49(4)
Transformations and Linear Mappings
53(9)
The Mappings w = zn and w = z1/n
62(7)
Limits and Continuity
69(9)
Branches of Functions
78(6)
The Reciprocal Transformation w = 1/z
84(9)
Analytic and Harmonic Functions
93(32)
Differentiable and Analytic Functions
93(8)
The Cauchy-Riemann Equations
101(13)
Harmonic Functions
114(11)
Sequences, Julia and Mandelbrot Sets, and Power Series
125(36)
Sequences and Series
125(9)
Julia and Mandelbrot Sets
134(10)
Geometric Series and Convergence Theorems
144(7)
Power Series Functions
151(10)
Elementary Functions
161(40)
The Complex Exponential Function
161(8)
The Complex Logarithm
169(7)
Complex Exponents
176(6)
Trigonometric and Hyperbolic Functions
182(12)
Inverse Trigonometric and Hyperbolic Functions
194(7)
Complex Integration
201(60)
Complex Integrals
201(4)
Contours and Contour Integrals
205(17)
The Cauchy-Goursat Theorem
222(16)
The Fundamental Theorems of Integration
238(5)
Integral Representations for Analytic Functions
243(8)
The Theorems of Morera and Liouville and Applications
251(10)
Taylor and Laurent Series
261(46)
Uniform Convergence
261(7)
Taylor Series Representations
268(12)
Laurent Series Representations
280(10)
Singularities, Zeros, and Poles
290(8)
Applications of Taylor and Laurent Series
298(9)
Residue Theory
307(48)
The Residue Theorem
307(3)
Calculation of Residues
310(7)
Trigonometric Integrals
317(5)
Improper Integrals of Rational Functions
322(6)
Improper Integrals Involving Trigonometric Functions
328(4)
Indented Contour Integrals
332(7)
Integrands with Branch Points
339(4)
The Argument Principle and Rouche's Theorem
343(12)
Conformal Mapping
355(32)
Basic Properties of Conformal Mappings
355(7)
Bilinear Transformations
362(10)
Mappings Involving Elementary Functions
372(8)
Mapping by Trigonometric Functions
380(7)
Applications of Harmonic Functions
387(96)
Preliminaries
387(2)
Invariance of Laplace's Equation and the Dirichlet Problem
389(12)
Poisson's Integral Formula for the Upper Half-Plane
401(5)
Two-Dimensional Mathematical Models
406(4)
Steady State Temperatures
410(14)
Two-Dimensional Electrostatics
424(8)
Two-Dimensional Fluid Flow
432(12)
The Joukowski Airfoil
444(10)
The Schwarz-Christoffel Transformation
454(11)
Image of a Fluid Flow
465(3)
Sources and Sinks
468(15)
Fourier Series and the Laplace Transform
483(68)
Fourier Series
483(10)
The Dirichlet Problem for the Unit Disk
493(7)
Vibrations in Mechanical Systems
500(6)
The Fourier Transform
506(6)
The Laplace Transform
512(9)
Laplace Transforms of Derivatives and Integrals
521(4)
Shifting Theorems and the Step Function
525(5)
Multiplication and Division by t
530(4)
Inverting the Laplace Transform
534(9)
Convolution
543(8)
Answers 551(38)
Index 589

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