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 
Rigidity  2 
Eulers Formula  10 
Copyright  
55 other sections not shown
Common terms and phrases
algebra amplification amplitwist analytic function analytic mapping angle 9 arbitrary branch point called Chapter complex function complex inversion complex numbers complex plane complex potential conformal mapping consider convergence coordinates corresponding critical point curvature deduce defined derivative dilative rotation dipole direct motion disc of convergence distance elliptic equal equation Euclidean Euclidean geometry example exercise fact Figure fixed points flow flux formula geometric given graph hlines harmonic hyperbolic geometry hyperbolic plane illustrated image points imaginary infinitely infinitesimal infinity inside integral length linesegment linear log(z loop matrix Mobius transformation multifunction multiplier Note obtain origin origincentred circle orthogonal particle polynomial power series preimages pseudosphere radius real axis real function real numbers reflection result Riemann sphere round simple singularity square stereographic projection streamlines surface symmetric tangent Theorem translation triangle unit circle unit disc upper halfplane vanish verify vertical winding number yields