Complex Variables and ApplicationsMcGraw-Hill Higher Education, 2004 - 458페이지 From the publisher: Complex Variables and Applications provides a one-term introduction to the theory and application of functions of a complex variable. Its primary objective is to develop those parts of the theory that are prominent in the applications of the subject. Numerous applications to the physical sciences and engineering are provided throughout, including those suitable for reference and self-study. |
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analytic function angle antiderivative b₁ c₁ calculus Cauchy-Goursat theorem Cauchy-Riemann equations constant continuous converges corresponding cosh curve defined denote Dirichlet problem disk domain of definition EXAMPLE Exercise expression f is analytic FIGURE finite number follows function f half plane harmonic conjugate harmonic function Hence improper integrals inequality integral formula integrand interior isolated singular iv(x Laurent series lim f(z line segment linear fractional transformation Maclaurin series mapping neighborhood Note nth roots obtained P(ro partial derivatives point 20 polygon polynomial positive number R₁ real axis real numbers region residue Riemann surface satisfies series representation shown in Fig simple closed contour singular point sinh strip Taylor series theorem in Sec upper half vector verify w₁ write x₁ xy plane z₁ zero πί