A First Course In Complex Analysis With Applications
The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.
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Chapter 2 Complex Functions and Mappings
Chapter 3 Analytic Functions
Chapter 4 Elementary Functions
Chapter 5 Integration in the Complex Plane
Chapter 6 Series and Residues
Chapter 7 Conformal Mappings
Answers to Selected OddNumbered Problems
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A First Course in Complex Analysis with Applications
Dennis G. Zill,Patrick Shanahan
Vista previa restringida - 2003
analytic function angle Answers to selected arg(w arg(Z boundary conditions branch Cauchy-Goursat theorem Cauchy-Riemann equations color in Figure complex exponential function complex function complex logarithm complex mapping complex plane complex power conformal mapping deﬁned Deﬁnition derivative Dirichlet problem disk evaluate Example f is analytic Figure for Problem ﬁnd Find the image ﬁow ﬁrst ﬂow follows function f harmonic hyperbolic functions inﬁnite integral formula isin Laurent series level curves line segment linear fractional transformation linear mapping loge magniﬁcation modulus multiple-valued function nth root obtain odd-numbered problems begin parametrization point Z0 polygonal region polynomial power series principal value proof radius of convergence real and imaginary real axis real functions real number satisﬁes Section selected odd-numbered problems shown in black shown in color shown in Figure simple closed contour sinz Solution solve Theorem unit circle upper half-plane vector ﬁeld velocity ﬁeld Z-plane zero