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 userfriendly 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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Review: Visual Complex Analysis
User Review  Nishant Pappireddi  GoodreadsI got this book because I was promised geometrically intuitive explanations of the results in a standard Complex Analysis course, and I was not disappointed! Almost every result the author stated was ... Read full review
Review: Visual Complex Analysis
User Review  Amar Pai  GoodreadsReally great book... the closest I've come to actually 'getting' complex analysis. Basic operations like complex multiplication are clearly explained in terms of vector diagrams. Hyperbolic geometry ... Read full review
Contents
Geometry and Complex Arithmetic  1 
Eulers Formula  10 
Transformations and Euclidean Geometry  30 
Copyright  
111 other sections not shown
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algebraic amplitwist analytic function analytic mapping angle arbitrary Argument Principle branch point called Chapter complex function complex inversion complex numbers complex plane complex potential conformal mapping consider constant contour convergence corresponding critical point curvature curve deduce defined derivative dipole direct motion disc of convergence distance equal equation Euclidean Euclidean geometry example exercise fact Figure fixed points flow flux formula geometric given hlines harmonic hyperbolic geometry hyperbolic plane illustrated image points infinitely infinitesimal infinity inside integral interior intersection length linesegment linear Mobius transformation multiplication obtain orbit origin orthogonal P6lya vector field particle Poincare pole polynomial power series preimages pseudosphere radius real axis real number reflection region result Riemann sphere round segment simple loop singularity sourceless square stereographic projection streamlines surface symmetric tangent temperature triangle unit circle unit disc upper halfplane vanish verify vertical winding number yields