Complex Variables and Applications
Contents - Complex Numbers; Analytic Functions; Elementary Functions; Integrals; Series; Residues and Poles; Applications of Residues; Mapping by Elementary Functions; Conformal Mapping; Applications of Conformal Mapping; The Schwarz - Christoffel Transformation; Integral Formulas of the Poisson Type.
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analytic function angle antiderivative arctan Boundary Value Problems calculus Cauchy Cauchy-Goursat theorem Cauchy-Riemann equations coefficients complex variable constant continuous converges corresponding cosh counterclockwise curve defined denote Dirichlet problem disk domain of definition evaluate EXAMPLE Exercise exists expression FIGURE finite number flow follows function f(z half plane harmonic conjugate harmonic function Hence imaginary improper integrals inequality integral formula integrand inverse iv(x Laurent series lemma limit line segment linear fractional transformation Maclaurin series mapping multiple-valued nonzero complex number Note nth roots obtained origin parametric representation partial derivatives point z0 pole of order polygon polynomial positive number power series quadrant real axis real numbers region residue result Riemann surface roots satisfies series representation shown in Fig simple closed contour sinh square strip Suppose Taylor series temperature theorem in Sec upper half vector verify write written xy plane zero