1. Complex Analysis Textbook for an introductory course in complex analysis by George Cain. Chapters in PDF.Category Science Math Publications Online Texts......complex analysis. by George Cain. (c)Copyright 1999, 2001 by George Cain. All rightsreserved. This is a textbook for an introductory course in complex analysis. http://www.math.gatech.edu/~cain/winter99/complex.html

Complex Analysis by George Cain This is a textbook for an introductory course in complex analysis. It has been used for our undergraduate complex analysis course here at Georgia Tech and at a few other places that I know of. I owe a special debt of gratitude to Professor Matthias Beck of SUNY Binghamton who used the book in his class at Binghamton and found many errors and made many good suggestions for changes and additions to the book. I thank him very much. I have corrected the errors and made some changes. More extensive revisons will come later. The notes are available as Adobe Acrobat documents. If you do not have an Adobe Acrobat Reader, you may down-load a copy, free of charge, from Adobe Title page and Table of Contents Table of Contents Chapter One Complex Numbers 1.1 Introduction 1.2 Geometry 1.3 Polar coordinates Chapter Two Complex Functions 2.1 Functions of a real variable 2.2 Functions of a complex variable 2.3 Derivatives Chapter Three Elementary Functions 3.1 Introduction

2. Mathematics Archives - Topics In Mathematics - Complex Analysis KEYWORDS Lecture Notes, complex analysis, Functional Analysis. Poles and Zeros http://archives.math.utk.edu/topics/complexAnalysis.html

Topics in Mathematics Complex Analysis AMS's Materials Organized by Mathematical Subject Classification - Functions of a Complex Variable ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification - Potential Theory ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification - Several Complex Variables and Analytic Spaces ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases CA-TEACH Mailing List Archive ADD. KEYWORDS: Mailing List, News, Pedagogy Circle Packing ADD. KEYWORDS: Bibliography, Software, Manuscripts Communications in the Analytic Theory of Continued Fractions ADD. KEYWORDS: Printed Journal SOURCE: Lyle Cochran, Whitworth College A Complex Function Viewer Complex Numbers Made Easy... ADD. KEYWORDS: Addition, Multiplication, Division, Arg, Norm, Trigonometric functions, Inverse trigonometric functions, Exponential, Logarithm Complex Plot Home ADD. KEYWORDS:

3. Complex Analysis Mathematica 4.0 Notebooks to accompany the textbook by John Mathews and Russell HowellCategory Science Math Analysis Complex Variable......complex analysis Mathematica 4.0 Notebooks (c) John H. Mathews, and RussellW. Howell, 2000 Complimentary software to accompany our textbook CONTENTS. http://www.ecs.fullerton.edu/~mathews/c2000/

COMPLEX ANALYSIS: Mathematica 4.0 Notebooks (c) John H. Mathews, and Russell W. Howell, 2000 Complimentary software to accompany our textbook: CONTENTS CHAPTER 1 COMPLEX NUMBERS Section 1.1 The Origin of Complex Numbers Section 1.2 The Algebra of Complex Numbers Section 1.3 The Geometry of Complex Numbers Section 1.4 The Geometry of Complex Numbers, Continued Section 1.5 The Algebra of Complex Numbers, Revisited Section 1.6 The Topology of Complex Numbers Get Chapter 1 CHAPTER 2 COMPLEX FUNCTIONS Section 2.1 Functions of a Complex Variable Section 2.2 Transformations and Linear Mappings Section 2.3 The Mappings w = z n and w = z 1/n Section 2.4 Limits and Continuity Section 2.5 Branches of Functions Section 2.6 The Reciprocal Transformation w = 1/z Get Chapter 2 CHAPTER 3 ANALYTIC and HARMONIC FUNCTIONS Section 3.1 Differentiable Functions Section 3.2 The Cauchy-Riemann Equations Section 3.3 Analytic Functions and Harmonic Functions Get Chapter 3 CHAPTER 4 Section 4.1 Definitions and Basic Theorems for Sequences and Series Section 4.2

4. "Visual Complex Analysis" Home Page Visual complex analysis "I can only describe this book as amazing it is not an exaggeration to say that there are gems in every section even familiar facts are frequently explained in refreshingly new ways in this wonderful book. http://www.usfca.edu/vca

Visual Complex Analysis Tristan Needham Oxford University Press "I can only describe this book as amazing... it is not an exaggeration to say that there are gems in every section ... even familiar facts are frequently explained in refreshingly new ways in this wonderful book. ... many of these exercises are so absorbingly interesting that it is difficult to leave them alone. ... If your budget limits you to buying only one mathematics book in a year then make sure that this is the one that you buy." MATHEMATICAL GAZETTE "The pictures in this note were produced directly in PostScript. ... 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 different tools." Bill Casselman , NOTICES OF THE AMS "Too many textbooks neglect the historical foundations; this book is rich with history. The author has taken full advantage of modern computer graphics to provide a variety of lovely and helpful pictures... There is a rich bibliography at the end of the book spanning the gamut of both historical and modern references." "For the more mathematically inclined who also have an interest in keeping one foot in physical reality, I highly recommend Tristan Needham

5. Complex Analysis Home Page complex analysis Home Page in Japan Japanese version is here. (Since April 25, 1998, last updated in 05/07/01) Back to the home page of Math. http://www.kusm.kyoto-u.ac.jp/complex/index_E.html

Complex Analysis Home Page in Japan Bers embedding Japanese version is here (Since April 25, 1998, last updated in 05/07/01) Links (June 04, 1999) Seminars (June 02, 1999) Preprints (Feb. 28, 1999) Reference Room (in Japanese) (April 2, 1998) Complex Analysis Mailing List (in Japanese) (April 22, 1999) Gallery (Nov. 13, 1999) Several Complex Variables Home Page in Japan Back to the home page of Math. Dept. sugawa@kusm.kyoto-u.ac.jp

6. Complex Analysis Home Page complex analysis Home Page in Japan Japanese version is here. Welcome to our site! You are our th guest. (Since April 25, 1998, last updated in 28 Nov 2002) http://www.cajpn.org/index_E.htm

Complex Analysis Home Page in Japan Bers embedding Japanese version is here Welcome to our site! You are our -th guest. (Since April 25, 1998, last updated in 02 Mar 2003) Links (28 Nov 2002) Seminars (30 Jun 2002) Preprints (16 Jul 2002) Reference Room (in Japanese) (30 Sep 2001) Complex Analysis Mailing List (in Japanese) (30 Sep 2001) Gallery (03 Jul 2002) Several Complex Variables Home Page in Japan Maintenance group: www@cajpn.org

7. Graphics For Complex Analysis -- Douglas N. Arnold GRAPHICS FOR complex analysis. Douglas N. Arnold. http://www.ima.umn.edu/~arnold/complex.html

(animated GIF version) GRAPHICS FOR COMPLEX ANALYSIS Douglas N. Arnold This is a collection of graphical demonstrations of concepts in complex analysis which I developed for a course I gave on that subject during the spring semester of 1997. (For graphical demonstrations of calculus concepts see my page on Graphics for the calculus classroom .) Please send any feedback concerning this page to me by email The most common method of visualizing a complex map is to show the image under the map of a set of curves, e.g., a set of line segments of constant real and/or imaginary part (a Cartesian grid), or a set of concentric circles and spokes (a polar grid). A weakness of this approach is that it can be difficult or impossible to infer which points of the original curves are mapped to which points of the final images. The graphics on this page use two techniques to overcome this problem. First, most are animated so that the original curves are continuously deformed into the image curves, and the eye can follow which points move where. Second, I use colors to distinguish different points and curves. Viewing instructions.

8. Graphics For Complex Analysis Douglas N. Arnold GRAPHICS FOR complex analysis This is a collection of graphical demonstrations of concepts in complex analysis which I developed for a course I gave on that subject during the spring semester of 1997. http://www.math.psu.edu/dna/complex-j.html

9. Complex Analysis complex analysis. complex analysis Explorations with F(Z) page. ComplexAnalysis Mathematica 4.1 Notebooks. Maple Power Tools complex analysis. http://www.ecs.fullerton.edu/~mathews/

Dr. John H. Mathews, Ph. D. Professor of Mathematics California State University Fullerton Department of Mathematics P. O. Box 34080 Fullerton, California 92634-9480 Office: McCarthy Hall - MH-182B Phone: (714) 278-3196 Dept: (714) 278-3631 FAX: (714) 278-3972 e-mail: mathews@fullerton.edu Teaching Spring Semester 2003 Math 130 A Short Course in Calculus, Spring 2003 Math 310 Differential Equations, Spring 2003 Complex Analysis Complex Analysis: for Mathematics and Engineering Typos (1st printing) for Complex Analysis: for Math. and Engr. Typos (2nd printing) for Complex Analysis: for Math. and Engr Complex Analysis: Mathematica 4.1 Notebooks ... Etc. Dr. John H. Mathews, Ph. D. Department of Mathematics California State University Fullerton Fullerton, CA 92834 USA Phone: (714) - 278-3196 Dept: (714) - 278-3631 FAX: (714) - 278-3972 e-mail: mathews@fullerton.edu Return to the CSUF Math. Dept. home page. Revised 2/11/03

10. Websites Related To "Visual Complex Analysis" Websites related to Visual complex analysis . Plotting Transformations.Graphics for complex analysis Douglas N. Arnold Penn State http://www.usfca.edu/vca/websites.html

Websites related to "Visual Complex Analysis" Plotting Functions of a Complex Variable George Abdo and Paul Godfrey Florida Institute of Technology Includes Conformal Maps requiring Möbius and Schwartz-Christoffel Transformations. Graphics for Complex Analysis Douglas N. Arnold Penn State A nice collection of animated GIFs illustrating complex mappings. Also available in the form of controllable Java applets Understanding Complex Function Graphs Tom Banchoff and Davide Cervone Brown University and The Geometry Center This is a paper published in the Communications in Visual Mathematics . It makes imaginative use of MPEG movies as an aid to visualizing complex graphs in four dimensions. Complex Function Grapher Andrew Bennett Kansas State University, Manhattan This mathlet graphs the modular surface of a complex function and adds color to represent the argument. Complex Function Visualization Frank Farris Santa Clara University Examples of Prof. Farris's mathematically illuminating approach to visualizing complex mappings by means of colour.

11. COMPLEX ANALYSIS: F(Z) Files Math Archives Homepage complex analysis F(Z) Files complex analysisMaple Worksheets complex analysis Mathematica Notebooks. Prof. http://archives.math.utk.edu/software/msdos/complex.variables/complex_analysis/.

COMPLEX ANALYSIS: F(Z) Files COMPLEX ANALYSIS: Maple Worksheets COMPLEX ANALYSIS: Mathematica Notebooks Prof. John H. Mathews Department of Mathematics California State University Fullerton Fullerton, CA 92634 E-mail: mathews@fullerton.edu Prof. Russell W. Howell Westmont College Santa Barbara, CA 93108 E-mail: howell@westmont.edu Complimentary software to accompany the textbook: 3rd Ed, 1997, ISBN: 0-7637-0270-6 Jones and Bartlett Publishers, Inc. You need to use F(Z) - The Complex Variables Program, Maple or Mathematica to run these files. Chapter Headings: Complex Numbers Complex Functions Analytic and Harmonic Functions Sequences, Series, and Julia and Mandelbrot Sets Elementary Function Complex Integration Taylor and Laurent Series Residue Theory Conformal Mapping Applications of Harmonic Functions Fourier Series and the Laplace Transform You can copy this software for courses using the text mentioned above at your institution.

12. The Math Forum - Math Library - Complex Analysis 30 Functions of a complex variable Complex variables studies the effect of assuming differentiability of functions defined on complex numbers. of Riemann surfaces into R^3. Global complex analysis is differential topology; lowdim manifolds which are groups http://mathforum.com/library/topics/complex_a

Browse and Search the Library Home Math Topics Analysis : Complex Analysis Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Resources for the Teaching of Complex Analysis - Paul Fishback The page includes: sample F(z) for Windows files (downloadable: for each example, an F(z) file is listed along with an MS WORD document describing the F(z) file and its creation in greater detail; a TI-86 program that approximates contour integrals using Gluchoff's average value interpretation; directions for subscribing to CA-TEACH - an unmoderated internet mailing list devoted to the discussion of teaching complex analysis; a brief list of other sites related to the teaching of complex variables; and a list of readings related to the inclusion of technology in a complex variables course. more>> All Sites - 16 items found, showing 1 to 16 1997 Linear Analysis Pages - Jonathan Borwein Mathematics 419, Linear Analysis (Simon Fraser University). Course information, assignments, extras for enrichment. Classical and applied analysis, special function theory, general analytic knowledge (cardinality, irrationality, complex analysis, continued ...more>> 3D-Filmstrip - Richard Palais 3D Filmstrip is a mathematical visualization program available via ftp for computers running version 7 or later of MacOS, the Macintosh Operating System. It has algorithms for displaying mathematical objects from many different "categories" (plane and

13. Complex Analysis Course notes by Harold V. McIntosh in HTML.Category Science Math Publications Online Texts......next contents Next Contents. complex analysis. Harold V. McIntoshDepartamento de Aplicación de Microcomputadoras, Instituto de http://delta.cs.cinvestav.mx/~mcintosh/comun/complex/complex.html

Next: Contents Complex Analysis Harold V. McIntosh April 5, 2001 Abstract: Contents Complex number arithmetic complex numbers in the real plane via the Argand diagram polar and cartesian coordinates ... Weierstrass function restraints on periodic functions the differential equation for the Jacobi functions sn, cn, and dn Mapping theorems ... About this document ... Microcomputadoras

14. Complex Analysis Home Page In Japan Is Moved. The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.kusm.kyoto-u.ac.jp/complex/

Ê£ÁDzòÀϳØHome Page¤Ï5/7¤ò¤â¤Á¤Þ¤·¤ÆÆȼ«¥É¥á¥¤¥ó¤Ë°Üž¤·¤Þ¤·¤¿¡£¿·¤·¤¤URL¤Ï http://www.cajpn.org/

15. Complex Analysis Home Page In Japan The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.cajpn.org/

Complex Analysis Home Page English version is here Bers embedding ¡ÊSince 25 April 1998, ºÇ½ª Æü 02 Mar 2003¡Ë (28 Nov 2002) (02 Mar 2003) (16 Jul 2002) (30 Sep 2001) (30 Sep 2001) Gallery (03 Jul 2002) (02 Mar 2003¡Ë (09 May 2002¡Ë www@cajpn.org

16. The Math Forum - Math Library - Complex Analysis This page contains sites relating to complex analysis. Browse and Searchthe Library Home Math Topics Analysis complex analysis. http://mathforum.org/library/topics/complex_a/

Browse and Search the Library Home Math Topics Analysis : Complex Analysis Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Resources for the Teaching of Complex Analysis - Paul Fishback The page includes: sample F(z) for Windows files (downloadable: for each example, an F(z) file is listed along with an MS WORD document describing the F(z) file and its creation in greater detail; a TI-86 program that approximates contour integrals using Gluchoff's average value interpretation; directions for subscribing to CA-TEACH - an unmoderated internet mailing list devoted to the discussion of teaching complex analysis; a brief list of other sites related to the teaching of complex variables; and a list of readings related to the inclusion of technology in a complex variables course. more>> All Sites - 16 items found, showing 1 to 16 1997 Linear Analysis Pages - Jonathan Borwein Mathematics 419, Linear Analysis (Simon Fraser University). Course information, assignments, extras for enrichment. Classical and applied analysis, special function theory, general analytic knowledge (cardinality, irrationality, complex analysis, continued ...more>> 3D-Filmstrip - Richard Palais 3D Filmstrip is a mathematical visualization program available via ftp for computers running version 7 or later of MacOS, the Macintosh Operating System. It has algorithms for displaying mathematical objects from many different "categories" (plane and

17. MATH 502, Spring '97 Course notes and old exams in PDF, PS, DVI, and TeX for a first course in Complex and Functional Analysis.Category Science Math Analysis Complex Variable...... Homework. Part I complex analysis. ISBN 0387-90328-3. Other recommendedtexts complex analysis; by Lars V. Alfors; McGraw-Hill, 1966. http://www.math.psu.edu/dna/502.s97/

18. Maple PowerTools - Complex Analysis PowerTool Set of Maple lessons for an undergraduate coursein complex analysis or Complex Variables. http://www.mapleapps.com/powertools/complex/complex.shtml

19. Maple Application Center Maple Online Tour. complex analysis, Details, View Document, DownloadWorksheet, Download Code. Complex Numbers and the Lagrangian, A set http://www.mapleapps.com/List.asp?CategoryID=5&Category=Complex Analysis

20. Complex Analysis complex analysis. Exercises. Traditional texts for this course includeAhlfors' complex analysis and Lang's book of the same title. http://www.math.umn.edu/~garrett/m/complex/

Complex Analysis Notes home garrett@math.umn.edu Hartogs' theorem that separate analyticity implies joint analyticity ... Exercises Traditional texts for this course include Ahlfors' Complex Analysis and Lang's book of the same title. Also useful is the second half of Rudin's Real and Complex Analysis A weakness in the later parts of all these sources is in the treatment of algebraic functions, and of solutions to ordinary differential equations with regular singular points. And some so-called 'special functions' such as the gamma function deserve fuller treatment, especially with an eye to applications in other parts of mathematics. And the ultra-classical aspects of elliptic functions and modular forms deserve a quick and decisive treatment in this context, since all the crucial techniques at this level do really belong to 'complex analysis', as opposed to 'number theory' or anything else. And the connection between the Riemann Hypothesis on the zeta function and error terms in the Prime Number Theorem is hard to ignore, motivating as it did a great deal of work in classical complex analysis. home garrett@math.umn.edu

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