Complex variables and applications
These classic textbooks, specializing in the techniques and applications of advanced mathematics to physical science and engineering, have endured as perennial standards for more than 60 years. The latest editions preserve the hallmark features that made Brown and Churchill a household name in advanced mathematics education-clear and concise exposition, interesting examples, and accessible level-while adding new enhancements, improved organization, and more modern examples and applications to serve another generation of students.
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Functions of a Complex Variable
Mappings by the Exponential Function
Theorems on Limits
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analytic function analytic throughout antiderivative argz boundary branch calculus Cauchy Cauchy integral formula Cauchy-Goursat theorem Cauchy-Riemann equations coefficients complex plane complex variable constant converges corresponding cosh coshz cosz defined denote disk domain of definition evaluate EXAMPLE Exercise exists expression f(zo FIGURE finite number follows function f(z half plane harmonic conjugate harmonic function Hence imaginary inequality integral formula integrand isolated singular point iv(x Laurent series lim f(z limit line segment linear fractional transformation logz Maclaurin series mapping multiple-valued nonzero complex number nonzero point Note nth roots obtained pN(z polynomial positive integer positive number positively oriented circle power series proof radius real axis real numbers real variable region residue result roots satisfied shown in Fig simple closed contour sinh sinhz sinz square statement Suppose Taylor series Taylor's theorem theorem in Sec transformation upper half vector verify write