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viii Create Quick Response Code In Java Using Barcode generator for Java Control to generate, create Denso QR Bar Code image in Java applications. QRCode Scanner In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Complex Variables Demysti ed
Barcode Creation In Java Using Barcode generation for Java Control to generate, create bar code image in Java applications. Bar Code Reader In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. The Derivative and Analytic Functions The Derivative De ned Leibniz Notation Rules for Differentiation Derivatives of Some Elementary Functions The Product and Quotient Rules The CauchyRiemann Equations The Polar Representation Some Consequences of the CauchyRiemann Equations Harmonic Functions The Re ection Principle Summary Quiz Elementary Functions Complex Polynomials The Complex Exponential Trigonometric Functions The Hyperbolic Functions Complex Exponents Derivatives of Some Elementary Functions Branches Summary Quiz Sequences and Series Sequences In nite Series Convergence Convergence Tests Uniformly Converging Series Power Series Taylor and Maclaurin Series Theorems on Power Series Some Common Series 41 42 43 45 47 48 51 57 59 61 63 64 64 65 65 70 75 78 84 85 88 89 89 91 91 94 94 96 97 97 98 98 100 Denso QR Bar Code Drawer In C# Using Barcode creation for Visual Studio .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications. QR Creator In .NET Using Barcode printer for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications. Contents
Creating QR Code In Visual Studio .NET Using Barcode drawer for .NET framework Control to generate, create QR image in .NET applications. Painting QR Code In Visual Basic .NET Using Barcode maker for .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications. Laurent Series Types of Singularities Entire Functions Meromorphic Functions Summary Quiz CHAPTER 6 Complex Integration Complex Functions w(t) Properties of Complex Integrals Contours in the Complex Plane Complex Line Integrals The CauchyGoursat Theorem Summary Quiz Residue Theory Theorems Related to Cauchy s Integral Formula The Cauchy s Integral Formula as a Sampling Function Some Properties of Analytic Functions The Residue Theorem Evaluation of Real, De nite Integrals Integral of a Rational Function Summary Quiz More Complex Integration and the Laplace Transform Contour Integration Continued The Laplace Transform The Bromvich Inversion Integral Summary Quiz Mapping and Transformations Linear Transformations The Transformation zn Conformal Mapping UPCA Creator In Java Using Barcode drawer for Java Control to generate, create GS1  12 image in Java applications. Paint Code 128A In Java Using Barcode generation for Java Control to generate, create USS Code 128 image in Java applications. 109 111 112 112 114 114 117 117 119 121 124 127 133 134 135 135 143 144 148 151 155 161 161 163 163 167 179 181 181 183 184 188 190 Draw Matrix Barcode In Java Using Barcode printer for Java Control to generate, create Matrix Barcode image in Java applications. Print Linear In Java Using Barcode generation for Java Control to generate, create Linear Barcode image in Java applications. Complex Variables Demysti ed
Printing EAN / UCC  14 In Java Using Barcode drawer for Java Control to generate, create UPC Case Code image in Java applications. EAN13 Drawer In None Using Barcode drawer for Microsoft Word Control to generate, create EAN 13 image in Word applications. The Mapping 1/z Mapping of In nite Strips Rules of Thumb M bius Transformations Fixed Points Summary Quiz 190 192 194 195 201 202 202 203 203 204 207 207 209 209 219 224 224 225 230 230 231 231 234 244 247 247 249 255 261 267 269 Encoding DataMatrix In None Using Barcode creation for Office Excel Control to generate, create DataMatrix image in Office Excel applications. Bar Code Maker In .NET Framework Using Barcode drawer for VS .NET Control to generate, create bar code image in .NET applications. The SchwarzChristoffel Transformation The Riemann Mapping Theorem The SchwarzChristoffel Transformation Summary Quiz The Gamma and Zeta Functions The Gamma Function More Properties of the Gamma Function Contour Integral Representation and Stirling s Formula The Beta Function The Riemann Zeta Function Summary Quiz Boundary Value Problems Laplace s Equation and Harmonic Functions Solving Boundary Value Problems Using Conformal Mapping Green s Functions Summary Quiz Final Exam Quiz Solutions Final Exam Solutions Bibliography Index Barcode Creator In Java Using Barcode maker for BIRT Control to generate, create barcode image in Eclipse BIRT applications. Bar Code Encoder In C#.NET Using Barcode generator for Visual Studio .NET Control to generate, create barcode image in VS .NET applications. PREFACE
Decoding ECC200 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Painting Code 128 Code Set B In VS .NET Using Barcode creator for .NET framework Control to generate, create Code 128B image in Visual Studio .NET applications. Complex variables, and its more advanced version, complex analysis, is one of the most fascinating areas in pure and applied mathematics It all started when mathematicians were mystified by equations that could only be solved if you could take the square roots of negative numbers This seemed bizarre, and back then nobody could imagine that something as strange as this could have any application in the real world Thus the term imaginary number was born and the area seemed so odd it became known as complex These terms have stuck around even though the theory of complex variables has found a home as a fundamental part of mathematics and has a wide range of physical applications In mathematics, it turns out that complex variables are actually an extension of the real variables A student planning on becoming a professional pure or applied mathematician should definitely have a thorough grasp of complex analysis Perhaps the most surprising thing about complex variables is the wide range of applications it touches in physics and engineering In many of these applications, complex variables proves to be a useful tool For example, because of Euler s identity, a formula we use over and over again in this book, electromagnetic fields are easier to deal with using complex variables Other areas where complex variables plays a role include fluid dynamics, the study of temperature, electrostatics, and in the evaluation of many real integrals of functions of a real variable In quantum theory, we meet the most surprising revelation about complex variables It turns out they are not so imaginary at all Instead, they appear to be as real as real numbers and even play a fundamental role in the working of physical systems at the microscopic level In the limited space of this book, we won t be able to cover the physical applications of complex variables Our purpose here is to build a solid foundation to get you started on the subject This book is filled with a large number of solved

