Visual Complex Analysis

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Clarendon Press, 1998 - Mathematics - 592 pages
22 Reviews
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  - Nishant Pappireddi - Goodreads

I 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 - Goodreads

Really 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
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

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About the author (1998)


Tristan Needham is Associate Professor of Mathematics at the University of San Francisco. For part of the work in this book, he was presented with the Carl B. Allendoerfer Award by the Mathematical Association of America.

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