Visual Complex AnalysisThis radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields. |
Other editions - View all
Common terms and phrases
algebra amplitwist analytic analytic function angle apply arbitrary becomes branch called centred Chapter circle clear clearly complex numbers conformal connecting consider constant construction continuation convergence corresponding curvature curves deduce defined definition derivative direction disc distance draw effect equal equation example exercise exists explain expressed fact Figure Finally fixed points flow formula function geometric given hyperbolic idea illustrated infinitesimal infinity inside integral intersection inversion length look loop mapping means Möbius transformation motion moves multiplier Note obtain origin orthogonal particular passing plane positive power series precisely preserves radius reflection region represented result rotation round sense shown simple singularity space sphere square suppose surface symmetric Theorem translation triangle vector field vertical write yields