# 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 The Exponential Function 14 Transformations and Euclidean Geometry 30 Exercises 45 Complex Functions as Transformations 55 Power Series 64 XI 74
 A Topological Argument Principle 350 The Generalized Argument Principle 363 Exercises 369 Cauchys Theorem 377 The Complex Integral 383 Conjugation 395 The Exponential Mapping 401 Parametric Evaluation 409

 Cosine and Sine 84 Multifunctions 90 The Logarithm Function 98 Exercises 111 Möbius Transformations and Inversion 122 Complex Inversion 124 The Riemann Sphere 139 Basic Results 148 Möbius Transformations as Matrices 156 Vll Visualization and Classification 162 VIIl Decomposition into 2 or 4 Reflections 172 Exercises 181 The Amplitwist Concept 189 Some Simple Examples 199 The CauchyRiemann Equations 207 Further Geometry of Differentiation 216 Ill Visual Differentiation of logz 222 Visual Differentiation of the Power Function 229 NonEuclidean Geometry 267 Winding Numbers and Topology 338 Polynomials and the Argument Principle 344
 The General Formula of Contour Integration 418 Cauchys Formula and its Applications 427 387 433 Physics and Topology 450 Vector Fields and Complex Integration 472 Flows and Harmonic Functions 508 Conformal Invariance of the Laplacian 515 Flow Around an Obstacle 527 The Physics of Riemanns Mapping Theorem 540 Dirichlets Problem 554 Exercises 570 79 575 Index 579 102 581 267 583 450 584 414 587 560 588 328 589 494 590 Copyright

### References to this book

 CRC Concise Encyclopedia of Mathematics, Second EditionEric W. WeissteinNo preview available - 2002
 Shape Analysis and Classification: Theory and PracticeNo preview available - 2010
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