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VISUAL COMPLEX ANALYSIS

Front Cover
21 Reviews
Oxford University 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  - Joecolelife - Goodreads

i am not a philisopher like some reviewers here...this book is really wonderful and even better. the subject is very clearly explained in a very educational manner. the illustrations are phenomenal ... Read full review

Review: Visual Complex Analysis

User Review  - Edwin - Goodreads

This book is a gem. If you want a feel for complex analysis and want to experience the motivation behind some fuzzy concepts that are introduced in terse texts, then this book is for you. This book will show you the beauty that is complex analysis. Read full review

All 12 reviews »

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Selected pages

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

Other editions - View all

Visual complex analysis
Visual complex analysis
Tristan Needham
Snippet view - 1997
Visual complex analysis
Visual complex analysis
Tristan Needham
Snippet view - 1997

Common terms and phrases

algebraic amplitwist analytic function analytic mapping angle arbitrary Argument Principle branch point Chapter complex function complex inversion complex numbers complex plane complex potential conformal mapping consider constant contour convergence critical point curvature curve deduce defined derivative dipole direct motion disc of convergence distance ellipse equal equation Euclidean Euclidean geometry example exercise fact Figure fixed points flow flux formula geometric given h,line harmonic hyperbolic geometry hyperbolic plane illustrated image points infinitesimal infinity inside integral interior intersection length line,segment linear Mobius transformation multiplication n,gon non,Euclidean obtain one,to,one origin orthogonal pole Polya vector field polynomial power series preimages pseudosphere quaternion radius real axis real number reflection region result Riemann Riemann sphere round segment simple loop singularity sphere square stereographic projection streamlines surface symmetric tangent triangle unit circle unit disc upper half,plane vanish verify vertical winding number yields

Popular passages

Page 573 - Note sur le probleme des deux corps et sur une integration nouvelle dans le probleme des trois corps.‎
Appears in 5 books from 1912-2001

References to this book

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References from web pages

Visual Complex Analysis
A review of "Visual Complex Analysis" by Tristan Needham, Oxford University Press, 1997, $55.00. Written for www.amazon.com. Arun Kumar (kumar@tri.sbc.com) ...
www.kahany.com/ writing/ 0998vca.html

"Visual Complex Analysis" Home Page
There are other possibilities—one very fine recent example of mathematical graphics at a high level is Needham’s Visual Complex Analysis, which used quite ...
www.usfca.edu/ vca/

Visual Complex Analysis - Needham
Visual Complex Analysis - Needham Science Book Reviews.
www.physicsforums.com/ showthread.php?t=118926

JSTOR: Visual Complex Analysis
Visual complex analysis, by Tristan Needham. Pp. 592. $32.95. 1997. ISBN 0 19 853447 7 (Oxford: Clarendon Press). When some reviewers say a book is good ...
links.jstor.org/ sici?sici=0025-5572(199903)2%3A83%3A496%3C182%3AVCA%3E2.0.CO%3B2-J

Tristan Needham - Wikipedia, the free encyclopedia
Visual Complex Analysis. The Clarendon Press, Oxford University Press, New York, 1997. ... 570: "Visual complex analysis will show you the field of complex ...
en.wikipedia.org/ wiki/ Tristan_Needham

Needham T. Visual Complex Analysis (Oxford, 1997)(O)(T)(C)(612s ...
Please wait, ожидайте 28 секунд [ Скачать m_mathematics/mc_calculus/mcc_complex variable/Needham T. Visual Complex Analysis (Oxford, ...
lib.org.by/ info/ M_Mathematics/ MC_Calculus/ MCc_Complex%20variable/ Needham%20T.%20Visual%20Complex%20Analysis%20(Oxfor...

Geometry.Net - pure_and_applied_math: Complex Analysis
I was delighted when I came across Visual complex analysis. In October 1997 Visual complex analysis received First Prize in the National Jesuit Book ...
www5.geometry.net/ detail/ pure_and_applied_math/ complex_analysis_page_no_2.html

Complex Analysis
Visual Complex Analysis ~ Tristan Needham Oxford University Press Tristan Needham. Schaum's Outline of Complex Variables (Schaum's Outline) ~ Murray R. ...
www.mathinfale.co.uk/ cat149202.html

INTERACTIVE VISUALIZATION IN COMPLEX ANALYSIS ABSTRACT
Needham's recent text "Visual Complex Analysis" clearly demonstrates the power of a ... book “Visual Complex Analysis” by T. Needham [13] has much further ...
www.math.uoc.gr/ ~ictm2/ Proceedings/ pap286.pdf

Prijzen Vergelijken: Visual analysis
Visual Complex Analysis - .... Visual Complex Analysis (Needham, Tristan) · Stepniak daniel - Audio-Visual Coverage Of Courts (A Comparative Analysis) ...
www.glandigovalue.com/ Prijzen_Vergelijken.asp?sSearch=Visual%20analysis

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.

Bibliographic information

QR code for VISUAL COMPLEX ANALYSIS
TitleVISUAL COMPLEX ANALYSIS
AuthorNeedham Tristan
Editionillustrated, reprint
PublisherOxford University Press, 1998
ISBN0198534469, 9780198534464
Length592 pages
Subjects › 

Mathematics / Applied
Mathematics / Mathematical Analysis
Technology & Engineering / Mechanical
  
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