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1. Complex Analysis -- From MathWorld
complex analysis. The study of complex numbers, their derivatives, manipulation, and other properties. complex analysis is an extremely
http://mathworld.wolfram.com/ComplexAnalysis.html

Extractions: Complex Analysis The study of complex numbers , their derivatives , manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems. Contour integration , for example, provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration. The most fundamental result of complex analysis is the Cauchy-Riemann equations , which give the conditions a function must satisfy in order for a complex generalization of the derivative , the so-called complex derivative , to exist. When the

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

Extractions: 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>>

3. Complex Analysis : Paul Scott : Title Page
complex analysis Paul Scott, University of Adelaide. Contains notes and interactive quizzes on the University course. complex analysis PDF VERSION.

complex analysis Home Page in Japan. Bers embedding. Japanese version is here. Welcome to our site! You are our 54503 th guest. (Since
http://www.cajpn.org/index_E.htm

5. Complex Analysis
A set of Mathematica notebooks on many topics.
http://www.ecs.fullerton.edu./~mathews/c2000/

?. complex analysis Home Page. English version is here. Bers embedding !
http://www.cajpn.org/

7. Math 132
Math 132, Spring 2000 (Section 1). complex analysis for Applications. pdf; Week 2 Complex analytic functions, harmonic functions, Möbius transforms.
http://www.math.ucla.edu/~tao/132.1.00w/

Extractions: Week 1: Complex arithmetic, complex sets, limits, differentiation, Cauchy-Riemann equations. [ pdf pdf pdf Week 4: Complex powers, inverse trig functions, review for first midterm. [ pdf Week 5: Contour integration, Fundamental theorem of calculus, Cauchy theorems and applications. [ pdf Week 6: Power series, Taylor series, Laurent series. [ pdf Week 7: No lecture notes this week. Week 8: Zeroes, singularities, the point at infinity. [ pdf Week 9: The residue theorem; trig integrals, rational integrals; trig-rational integrals. [ pdf Week 10: Principal value integrals; integrals with branch cuts; argument principle; Rouche's theorem [

8. Présentation
Research presentation at Jussieu.
http://www.math.jussieu.fr/projets/ac/Reseau/presentation.htm

Extractions: You can download the .tex .dvi or .ps file. ANALYSE COMPLEXE ET GEOMETRIE ANALYTIQUE (Complex Analysis and Analytic Geometry) ANACOGA 1. Research topic Complex Analysis and Analytic Geometry belong closely together and are one of the few fields in the center of pure mathematics with many applications to other areas of pure mathematics (algebraic geometry, differential geometry, dynamical systems, P.D.E., topology, number theory, etc.) and applied Mathematics (theoritical physics, geophysics, mathematical economy, tomography). The most deep results in all branches of mathematics use complex variables. There exist many results in applied mathematics which could not be discovered without the utilization of complex analysis. A first phase of development in this area lasted until about 1965, when for the first time several powerful quantative theories of the Cauchy-Riemann equations were developed (L -theories of Hörmander and J.J. Kohn/L. Nirenberg, Cauchy-Fantappié kernels of H.Grauert and G. Henkin and others) and the concepts of currents, plurisubharmonicity, q -convexity, etc. had been well established. The time between 1965 and 1989 was dominated by developing many refinements of these theories together with the theory of residues, and the foundations of CR-manifolds. Furthermore, the new methods made it possible to go on studying the strong links between geometry and analysis. First important areas of this programme were so-to-speak used as testing fields.

9. Complex Analysis Book
complex analysis, by TW Gamelin. Publication Information. First printing 2001 Publisher SpringerVerlag, New York, Inc. Textbook
http://www.math.ucla.edu/~twg/CA.book.html

Extractions: The Springer web site for the book has more information, including links to pdf files for Chapters IV and IX of the book. List of errata, compiled April 2004: ( .pdf List of changes made from first to second printing: ( .pdf There were two "major" gaffes in the first printing, which were corrected for the second printing as follows: Page 282: Exercises 3-5 in Section X.2 were replaced by substitute Exercises 3 and 4 in the list of changes. Also, Exercise 2 on page 282 was expanded, so that the combined changes fit exactly the same number of lines as in the original version. Page 406: The "potential theory" proof of the Riemann mapping theorem is incomplete. The function used in the proof is not a barrier, according to the definition given in the book. Something nontrivial must be done (Bouligand's lemma) to construct a barrier. The replacement in the second printing refers to Tsuji's book for the Bouligand lemma. Another good source is the book "Complex Potential Theory" by T.J. Ransford. I'll post soon a complete proof on this web site. There are various kinds of changes made for the second printing: Some of the changes are rather trivial (font, spelling, minor grammatical infringements, and so on).

10. The Past
Topology Math 213b. Advanced complex analysis 2000 AMS Colloquium Lectures, Washington, DC. Math 213a. complex analysis Math 101.
http://abel.math.harvard.edu/~ctm/past.html

Extractions: Namboodiri Lectures, Chicago, IL. Math 275. Algebra and Dynamics Math 212a. Real Analysis Math 99r. Geometric Topology FS 21e. Dynamics, Geometry and Randomness Math 122. Algebra Math 112. Real Analysis Math 123. Algebra Math 275. Topics in Conformal Dynamics Math 131. Topology Math 213b. Advanced Complex Analysis AMS Colloquium Lectures, Washington, DC. Math 213a. Complex Analysis Math 101. Sets, Groups and Knots Math 275. Complex dynamics and hyperbolic geometry Advanced Real Analysis Math 101. Sets, Maps and Symmetry Groups Math 212a. Real Analysis Math 275. Riemann surfaces, dynamics and geometry Math 113. Complex Analysis Math 191. Probability Theory Math 277. Discrete groups and ergodic theory Math 241. Complex Manifolds Math 205. Complex Analysis Math 205. Complex Analysis Math 290. Math 206. Banach Algebras Math 241. Complex Manifolds

complex analysis Home Page in Japan. Bers embedding. Japanese version is here. (Since April 25, 1998, last updated in 05/07/01). Links
http://www.math.kyoto-u.ac.jp/complex/index_E.html

12. Complex Analysis - Wikipedia, The Free Encyclopedia
http://en.wikipedia.org/wiki/Complex_analysis

Extractions: Complex analysis is the branch of mathematics investigating holomorphic functions , i.e. functions which are defined in some region of the complex plane , take complex values, and are differentiable as complex functions. Complex differentiability has much stronger consequences than usual (real) differentiability . For instance, every holomorphic function is representable as power series in every open disc in its domain of definition, and is therefore analytic . In particular, holomorphic functions are infinitely differentiable, a fact that is far from true for real differentiable functions. Most elementary functions, such as all polynomials , the exponential function , and the trigonometric functions , are holomorphic. See also holomorphic sheaves and vector bundles edit One central tool in complex analysis is the path integral . The integral around a closed path of a function which is holomorphic everywhere inside the area bounded by the closed path is always zero; this is the Cauchy integral theorem . The values of a holomorphic function inside a disk can be computed by a certain path integral on the disk's boundary ( Cauchy's integral formula ). Path integrals in the complex plane are often used to determine complicated real integrals, and here the theory of

13. Basic Complex Analysis, 
Contents Basic complex analysis, 1998. Jerrold E. Marsden and Michael Hoffman WH Freeman, Third Edition, November 1998. INTERNET SUPPLEMENT, 1998 (pdf).
http://www.cds.caltech.edu/~marsden/books/node7.html

14. Complex Analysis
Link Mathematics home page. Jones and Bartlett Home Mathematics complex analysis. Subdisciplines. complex analysis. Numerical Analysis. Engineering Math.
http://math.jbpub.com/complex/

15. Complex Analysis For Mathematics And Engineering, Fourth Edition
Link Mathematics home page. Jones and Bartlett Home Mathematics complex analysis complex analysis for Mathematics and Engineering, Fourth Edition.
http://math.jbpub.com/catalog/0763714259/

16. Complex Analysis
complex analysis. Let us now investigate another ``trick for solving Poisson s equation (actually it only solves Laplace s equation).
http://farside.ph.utexas.edu/teaching/em1/lectures/node58.html

Extractions: Next: Separation of variables Up: Applications of Maxwell's equations Previous: The classical image problem Let us now investigate another ``trick'' for solving Poisson's equation (actually it only solves Laplace's equation). Unfortunately, this method can only be applied in two dimensions. The complex variable is conventionally written However, we now have a slight problem. If is a ``well defined'' function (we shall leave it to the mathematicians to specify exactly what being well defined entails: suffice to say that most functions we can think of are well defined) then it should not matter from which direction in the complex plane we approach when taking the limit in Eq. (4.141). There are, of course, many different directions we could approach

17. SC_36 Complex Analysis
complex analysis. The ChinaJapan Joint Satellite Conference. Topics Applied complex analysis;; Complex Dynamical Systems; Hyperbolic Geometry and Klein Groups;;
http://www.icm2002.org.cn/satellite/satel_36.htm

18. Resources For Teaching Complex Analysis
an active classroom learning atmosphere that replicates what I do in my calculus classes and that gives meaning to the various concepts from complex analysis.
http://faculty.gvsu.edu/fishbacp/complex/complex.htm

Extractions: Created using F(z) for Windows This web site contains resources for individuals teaching an introductory, undergraduate course in complex variables. Over the years I've tried to create a series of activities, F(z) files, and Maple worksheets that can be used to create an active classroom learning atmosphere that replicates what I do in my calculus classes and that gives meaning to the various concepts from complex analysis. [Activities] [ F(z) Programs] [Links to other sites] [Bibliography] You'll need the free Adobe Acrobat Reader to view most of these activities. Euler's Identity, the Complex Exponential, and the Polar Form, Revisited This is a brief activity in which students derive Euler's identity using Taylor series. They then plot a partial sum of the resulting series for as a vector using the tip to tail method of vector addition. A "spraling in" of the vectors illustrates the convergence of the series. Adapted from Visual Complex Analysis Mapping Properties of Complex-valued Functions In this activity students use F(z) and work in small groups to investigate mapping properties of various functions. Each group is given a particular function and a particular set of domains and is asked a series of questions that focus on mapping properties and that seek to compare and contrast properties of the function with its real counterpart. Each group then presents its findings to the rest of the class in the computer lab.

19. Advanced Course In Operator Theory And Complex Analysis -- Index