## 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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#### Review: Visual Complex Analysis

User Review - James Van alstine - GoodreadsVery unique take on complex analysis. This is a great read for a physicist. That is, it is seriously lacking in mathematical rigor. I would recommend this to anyone who wants to develop an intuitive ... Read full review

#### Review: Visual Complex Analysis

User Review - Ronald Lett - GoodreadsA beautiful exposition of the geometry behind complex analysis and topology! Assuming you have already been exposed to complex calculus, the great connections made in this text with modern geometry, topology and algebra will solidify your work with complex numbers as a geometrical language. 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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### Common terms and phrases

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 h-lines harmonic hyperbolic geometry hyperbolic plane illustrated image points infinitely infinitesimal infinity inside integral interior intersection length line-segment 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 half-plane vanish verify vertical winding number yields