Complex Variables and ApplicationsThis text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text. |
Contents
Complex Numbers | 1 |
Analytic Functions | 35 |
Elementary Functions | 89 |
Copyright | |
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analytic function analytic throughout antiderivative b₁ boundary c₁ C₂ calculus Cauchy-Goursat theorem Cauchy-Riemann equations coefficients constant continuous converges corresponding cosh defined denote disk domain of definition essential singular point evaluate EXAMPLE Exercise expression FIGURE finite number follows function f(z ƒ is analytic half plane harmonic conjugate Hence improper integrals inequality integrand integration formula isolated singular point iv(x Izzo Laurent series Laurent series representation limit line segment linear fractional transformation Maclaurin series mapping Note obtained partial derivatives pole of order polynomial positive integer positive number positively oriented circle power series proof R₁ real axis real numbers region Res est F(s residue result Riemann surface shown in Fig simple closed contour simple pole sinh Suppose Taylor series theorem in Sec upper half verify write z₁ πί