Complex Variables and ApplicationsThis text, and accompanying disk, provides coverage of complex variables. It uses examples and exercise sets, with clear explanations of problem-solving techniqes and material on the further theory of functions. |
Contents
Complex Numbers | 1 |
Algebraic Properties | 2 |
Moduli and Conjugates | 6 |
Copyright | |
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analytic function angle antiderivative b₁ C₁ calculus Cauchy-Goursat theorem Cauchy-Riemann equations circle coefficients complex variable constant continuous converges corresponding cosh curve D₂ defined denote disk domain of definition essential singular point EXAMPLE Exercise exists expression f(zo FIGURE finite number follows function f(z ƒ is analytic half plane harmonic conjugate harmonic function Hence imaginary improper integrals inequality infinity integral formula integrand iv(x Laurent series lim f(z line segment linear fractional transformation Maclaurin series mapping neighborhood Note nth roots obtained P(ro polygon polynomial positive number positively oriented power series R₁ real axis real numbers region residue Riemann surface satisfies series representation shown in Fig simple closed contour singular point sinh smooth arc strip Taylor series theorem in Sec upper half vector verify write xy plane z₁ zero πί