Complex Variables and ApplicationsFrom 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. |
Contents
Basic Algebraic Properties | 3 |
Complex Conjugates | 11 |
Products and Quotients in Exponential Form | 17 |
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analytic function angle antiderivative arctan b₁ c₁ C₂ calculus Cauchy Cauchy-Goursat theorem Cauchy-Riemann equations complex variable constant continuous converges corresponding cosh curve defined denote Dirichlet problem disk domain of definition evaluate EXAMPLE Exercise expression FIGURE finite number follows function f(z ƒ is analytic half plane harmonic conjugate harmonic function Hence improper integrals inequality integral formula integrand interior isolated singular iv(x Laurent series lemma line segment linear fractional transformation Maclaurin series mapping neighborhood Note nth roots obtained P(ro partial derivatives point z₁ polygon polynomial positive number R₁ R₂ 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 zero πί