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Topic: Complex analysis

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	Complex analysis - Wikipedia, the free encyclopedia
		Complex analysis is the branch of mathematics investigating functions of complex numbers, and is of enormous practical use in many branches of mathematics, including applied mathematics.
		Complex analysis is particularly concerned with analytic functions of complex variables, known as holomorphic functions.
		Complex analysis is one of the classical branches in mathematics with its roots in the 19th century and some even before.
	en.wikipedia.org /wiki/Complex_analysis (821 words)

	Category:Complex analysis - Wikipedia, the free encyclopedia
		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.
	en.wikipedia.org /wiki/Category:Complex_analysis (175 words)

	CATHOLIC ENCYCLOPEDIA: Analysis (Site not responding. Last check: 2007-10-21)
		The necessity of analysis comes from the fact that knowledge begins with the perception of the concrete and the individual, and that whatever is concrete is complex.
		The relative usefulness of analysis and synthesis in the various sciences depends on the nature of the problems to be solved, on the knowledge already at hand, on the mind's attitude, and on the stage of development of the science.
		Analysis has the advantage of adhering more strictly to the point under investigation; synthesis is in danger of going astray, since from the same principle many different conclusions may be drawn, and a multitude of real or possible events are governed by the same law.
	www.newadvent.org /cathen/01450a.htm (1274 words)

	Présentation
		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 goal of the project is to develop research on fundamental problems in complex analysis and partially or totally complex analytic geometry; these problems concern a rather large part of the quoted domains, but are, generally, closely related together.
		Complex Monge-Ampère equation and canonical bundle of a complex manifold.
	www.math.jussieu.fr /projets/ac/Reseau/presentation.htm (2291 words)

	Calculus:Complex analysis - Wikibooks, collection of open-content textbooks
		Complex analysis is the study of functions of complex variables.
		Complex analysis is a widely used and powerful tool in certain areas of electrical engineering, and others.
		A function of a complex variable is a function that can take on complex values, as well as strictly real ones.
	en.wikibooks.org /wiki/Calculus:Complex_analysis (1219 words)

	MA21510 - COMPLEX ANALYSIS
		Complex analysis is the study of complex valued functions of a complex variable.
		The important role of complex variables in aplied mathematics, for instance, is partly due to the use of the theory of residues in the evaluation of certain real integrals and the application of conformal mapping in hydrodynamics and problems in potential theory.
		The aim of the module is to study the theoretical foundations of complex variable theory and to develop skills in the application of this theory to particular problems.
	www.aber.ac.uk /modules/2003/MA21510.html (201 words)

	Complex-Analysis
		Complex Analysis is the study of complex numbers, their derivatives, manipulation, and other properties.
		the singularities of the function in regions of the complex plane near and between the limits of integration.
		When the complex derivative is defined "everywhere," the function is said to be analytic.
	www.adwan.net /Complex-Analysis.html (480 words)

	Graphics Archive - Special Topics:Complex Analysis (Site not responding. Last check: 2007-10-21)
		Complex number originally were developed as a means of solving algebraic equations that did not have roots in the real numbers (such as x^2 = -3).
		The set of complex numbers can be identified 2-dimensional plane of points, R^2, where the point (x,y) is the complex number x + iy (where i is one of the solutions to the equation x^2 = -1); this is called the complex plane, C.
		The geometry of the complex plane is both beautiful and intricate.
	www.geom.uiuc.edu /graphics/pix/Special_Topics/Complex_Analysis (131 words)

	Complex Analysis (Site not responding. Last check: 2007-10-21)
		Complex Analysis is perhaps one of the most beautiful parts of mathematics, a place of magic and wonder, where everything seems possible.
		Complex Analysis studies complex valued functions of a complex variable, specifically those functions f(z) which are differentiable in the sense that
		Complex analysis also plays an essential role in understanding many topics which are absolutely central to mathematics and its applications, such as Fourier series and integrals, Laplace transforms, Special Function Theory (Bessel, Hermite, Legendre, etc., functions).
	www.math.fau.edu /Schonbek/htmdocs/canf7.html (378 words)

	Complex Analysis -- from Mathematica Information Center
		The objectives are to teach a standard undergraduate course in the area of complex analysis.
		It strikes a balance between the pure and applied aspects of complex analysis.
		Sufficient applications are included to illustrate how complex analysis is used in science and engineering.
	library.wolfram.com /infocenter/Courseware/4307 (226 words)

	Complex variable Analysis (Site not responding. Last check: 2007-10-21)
		Complex variables are often accepted in other parts of analysis when this causes no essential change in the theory; but here we focus on those aspects of analytic behaviour unique to complex functions.
		32: Several complex variables is, naturally, the study of (differentiable) functions of more than one complex variable.
		In particular, study of the related spaces tends to resemble algebraic geometry, except that tools of analysis are used in addition to algebraic constructs.
	www.math.niu.edu /~rusin/known-math/index/tour_cplx.html (276 words)

	30: Functions of a complex variable
		Complex variables studies the effect of assuming differentiability of functions defined on complex numbers.
		Fascinatingly, the effect is markedly different than for real functions; these functions are much more rigidly constrained, and in particular it is possible to make very definite comments about their global behaviour, convergence, and so on.
		Problems involving complex numbers, rather than functions, are likely to be topics in algebra; see especially 12: Fields.
	www.math.niu.edu /~rusin/known-math/index/30-XX.html (522 words)

	Amazon.com: Complex Analysis: Books: Lars Ahlfors (Site not responding. Last check: 2007-10-21)
		Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory.
		The topics presented in the book is the classic need-to-know materials for undergraduates (complex functions, analytic functions as mappings, complex integration, series and products, etc), plus other topics which undergraduate complex analysis course usually omits: Weirstrass theory, Picard's theorem and zeta function (from complex analysis point of view).
		This is a classic complex analysis text, a pleasure to read and covering all the usual topics.
	www.amazon.com /exec/obidos/tg/detail/-/0070006571?v=glance (1470 words)

	Complex Analysis - Cambridge University Press (Site not responding. Last check: 2007-10-21)
		Price is not yet set (C) This textbook is an introduction to the classical theory of functions of a complex variable.
		He emphasizes geometrical considerations, and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions.
		It should be an ideal text for either a first course in complex analysis or more advanced study.
	www.cambridge.org /us/catalogue/catalogue.asp?isbn=0521809371 (141 words)

	Amazon.com: Real and Complex Analysis (Higher Mathematics Series): Books: Walter Rudin (Site not responding. Last check: 2007-10-21)
		This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level.
		The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized.
		The tenth chapter, on basic complex analysis, essentially covers an entire undergraduate course on the subject, with added results based on a solid knowledge of topology on the plane.
	www.amazon.com /exec/obidos/tg/detail/-/0070542341?v=glance (2402 words)

	Course Guidance/What is complex analysis?
		The reason for this change can be roughly explained: In order for a function f from the complex numbers (x+iy) to the complex numbers (u+iv), to be differentiable, of course four partial derivatives (du/dx, du/dy, dv/dx, dv/dy) must exist.
		Because multiplication by i (or any other complex number) must commute (more or less) with the process of taking derivatives at a point, these four partials have to "match up when rotated".
		One difficulty of reasoning about functions from the complex plane to the complex plane is that their graphs should be drawn on a four-dimensional space (two for the domain, and two for the range), but that's impossible.
	www.math.jhu.edu /mathcourses/guidance/complex.html (300 words)

	The Math Forum - Math Library - Complex Analysis (Site not responding. Last check: 2007-10-21)
		The theme of the journal is the field of complex systems, the generation of complex behaviour from the interaction of multiple parallel processes.
		The FoCM's primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer.
		A collection of graphical demonstrations using Java of concepts in complex analysis developed for a course at McAllister.
	mathforum.org /library/topics/complex_a (741 words)

	European School on Complex Analysis
		This course is organized by the Universities of Coimbra and Aveiro with the same goals as the ones organized under the programme Socrates, and is open to all young mathematicians interested in Complex Analysis and its applications.
		There will be an Workshop on "Applications and Generalizations of Complex Analysis" on the 23th and 24th of March.
		Riemann Mapping Theorem is one of the fundamental results of single variable complex analysis.
	www.mat.uc.pt /~ajplb/7.htm (616 words)

	The Math Forum - Math Library - Analysis
		An extensive collection of analysis resources, including class notes, discussion boards, and homework assignments, with questions and answers from analysis labs, and techniques of proofs.
		There are interactive demonstrations of several central themes in the study of analysis (sequences, continuity, definition of derivative, convergence and open sets).
		Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering.
	mathforum.org /library/topics/analysis (1989 words)

	Complex Analysis
		In the meantime, a requirement has arisen for the inclusion of complex analysis in a course on Mathematical Methods related to solid state physics (band gaps, Bloch's theorem,...).
		There are so many books on complex variable theory in existence that there hardly seems room for still another; nevertheless written material is needed for the entertainment of the students.
		Consequently these notes cover some of the why's and wherefore's of complex variables; ranging from the role of the cross ratio and the Schwartz derivative to topics such as the Mandelbrot Set, Elliptic Curves, and spectral densities.
	delta.cs.cinvestav.mx /~mcintosh/comun/complex/complex.html (202 words)

	Real and Complex Analysis
		Geared toward upper-level undergraduates and graduate students, this applications-oriented approach assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space.
		Contents include functions of a complex variable, basic equations of two-dimensional elasticity, plane and half-plane problems, regions with circular boundaries, and regions with curvilinear boundaries.
		Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods.
	store.doverpublications.com /by-subject-science-and-mathematics-mathematics-real-and-complex-analysis.html (647 words)

	Manageability - Simplicity Trumps Complex Analysis
		The realities of an urban environment in particular with a persons relationships with their neighbors is much more complex considering the diversity.
		However to dismiss the rural areas not being sophisticated in their analysis may be off the mark.
		The unbiased block recognized this and feeling that the flaws of the inumbment were something that they could live with; decided that simple solutions and decisiveness trumped complex and compromised solutions.
	www.manageability.org /blog/stuff/simplicity-trumps-complex-analysis (1217 words)

	Resources for Teaching Complex Analysis
		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.
		Under this identification, the derivative may be thought of locally as a linear transformation, and the tangent line approximation from calculus becomes an affine transformation.
		The "amplitwist" principle is the complex analog of the calculus idea of local linearity or linearization.
	faculty.gvsu.edu /fishbacp/complex/complex.htm (1519 words)

	Complex analysis
		(14,19,22), strongly suggest that there should be a simpler analysis leading to the same conclusions.
		That simpler analysis is the subject of this section.
		The great utility of the complex representation is that it allows us to encode complicated trigonometric manipulations, such as those of the previous section, into familiar algebraic manipulations.
	people.ccmr.cornell.edu /~muchomas/P214/Notes/SHM/node15.html (415 words)

	Complex Analysis - Cambridge University Press (Site not responding. Last check: 2007-10-21)
		Price is not yet set (C) In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, develops material on classical non-Euclidean geometry.
		He shows how it can be developed in a natural way from the invariant geometry of the complex disk.
		The climax of the book is an introduction to several complex variables from the geometric viewpoint.
	www.cambridge.org /us/catalogue/catalogue.asp?isbn=0883850354 (151 words)

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