# Visual Complex Analysis

Clarendon Press, 1998 - Mathematics - 592 pages
This 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 - Goodreads

Very 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

### Contents

 Geometry and Complex Arithmetic 1 Eulers Formula 10 Transformations and Euclidean Geometry 30 Exercises 45 Complex Functions as Transformations 55 Power Series 64 The Exponential Function 79 Multifunctions 90
 Winding Numbers and Topology 338 Polynomials and the Argument Principle 344 Rouches Theorem 353 The Generalized Argument Principle 363 Exercises 369 Cauchys Theorem 377 The Complex Integral 383 Conjugation 392

 The togarithm Function 98 Exercises 111 Mobius Transformations and Inversion 122 Three Illustrative Applications of Inversion 136 Basic Results 148 Mobius Transformations as Matrices 156 Visualization and Classification 162 Decomposition into 2 or 4 Reflections 172 Exercises 181 The Amplitwist Concept 189 Critical Points 204 Exercises 211 An Intimation of Rigidity 219 Polynomials Power Series and Rational Func 226 VIM Geometric Solution of E E 232 Celestial Mechanics 241 Analytic Continuation 247 Exercises 258 NonEuclidean Geometry 267 Spherical Geometry 278 Hyperbolic Geometry 293 Exercises 328
 The Exponential Mapping 401 Parametric Evaluation 409 The General Formula of Contour Integration 418 Cauchys Formula and Its Applications 427 Calculus of Residues 434 Annular taurent Series 442 Physics and Topology 450 Winding Numbers and Vector Fields 456 Flows on Closed Surfaces 462 Exercises 468 Complex Integration in Terms of Vector Fields 481 The Complex Potential 494 Exercises 505 Conformal Invariance 513 The Complex Curvature Revisited 520 Flow Around an Obstacle 527 The Physics of Riemanns Mapping Theorem 540 Dirichlets Problem 554 VIM Exercises 570 Index 579 Copyright