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. |
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algebraic amplification amplitwist analytic function analytic mapping angle arbitrary Argument Principle C₁ Cauchy's Theorem centred Chapter complex function complex inversion complex number complex plane complex potential conformal mapping consider constant contour convergence critical point curvature curve deduce defined derivative dipole direct motion elliptic equal equation Euclidean Euclidean geometry example exercise fact Figure fixed points flow flux formula h-lines harmonic hyperbolic geometry hyperbolic plane illustrated infinitesimal infinity inside integral interior intersection Laurent series line-segment linear matrix Möbius transformation multiplicity obtain origin orthogonal Poincaré disc pole Pólya vector field polynomial power series preimages pseudosphere radius real axis reflection region result Riemann sphere rotation round simple loop sourceless square stereographic projection streamlines surface symmetric tangent tractrix triangle unit circle unit disc upper half-plane vanish verify vertical winding number yields