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Topic: Complex variable

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Complex number

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	PlanetMath: several complex variables
		While the theory of one complex variable is really a subset of the study of several complex variables, the study of several complex variables is substantially different.
		A large part of the study of several complex variables is the study of domains of holomorphic functions, namely, the domains of holomorphy.
		Several complex variables also includes the study of the zero sets of complex analytic functions and these are called complex analytic varieties.
	planetmath.org /encyclopedia/SeveralComplexVariables.html (317 words)

	complex variable analysis - HighBeam Encyclopedia
		COMPLEX VARIABLE ANALYSIS [complex variable analysis] branch of mathematics that deals with the calculus of functions of a complex variable, i.e., a variable of the form z = x + iy, where x and y are real and i = -1 (see number).
		The theory of functions of a complex variable is concerned mainly with functions that have a derivative at every point of a given domain of values for z; such functions are called analytic, regular, or holomorphic.
		Also of interest in complex variable analysis are the points in a domain, called singular points, where a function fails to have a derivative.
	www.encyclopedia.com /doc/1E1-complexv.html (516 words)

	PlanetMath: complex
		The ordered-pair notation lets us visualize complex numbers as points in the plane, but then we can also describe complex numbers with polar coordinates.
		The ordinate (vertical) axis is known as the imaginary axis, since it consists of all complex numbers with real part equal to zero.
		This is version 32 of complex, born on 2001-11-08, modified 2006-10-27.
	planetmath.org /encyclopedia/Complex.html (390 words)

	Complex Analysis -- from Wolfram MathWorld
		Complex analysis is the study of complex numbers together with 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.
		The key result in complex analysis is the Cauchy integral theorem, which is the reason that single-variable complex analysis has so many nice results.
	mathworld.wolfram.com /ComplexAnalysis.html (380 words)

	Plotting Functions of a Complex Variable
		Graphs of functions of a complex variable are also pretty but the concept is more basic and easier to understand.
		In complex plotting, instead of two real axes there are two so-called complex planes, the domain is called the z-plane and the range, the w-plane.
		Many textbooks show plots of functions of a complex variable but since they are printed in fl and white only the few points that are labeled exhibit their correspondence.
	my.fit.edu /~gabdo/intro.html (721 words)

	Complex number - Wikipedia, the free encyclopedia
		The conjugate of the complex number z corresponds to the transformation which rotates through the same angle as z but in the opposite direction, and scales in the same manner as z; this can be described by the transpose of the matrix corresponding to z.
		The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics.
		Complex numbers are used in signal analysis and other fields as a convenient description for periodically varying signals.
	en.wikipedia.org /wiki/Complex_number (3580 words)

	Amazon.com: Function Theory of One Complex Variable: Books: Robert Everist Greene,Steven G. Krantz (Site not responding. Last check: 2007-11-06)
		It departs from the tradition of teaching complex analysis as a self-contained subject and, instead, treats the subject as a natural development from calculus.
		The authors provide the ideal framework for a first-year graduate course in complex analysis—building upon ideas the student is already familiar with and simplifying the transition to advanced topics.
		They emphasize how complex analysis is a natural outgrowth of multivariable real calculus by comparing and contrasting complex variable theory with real variable theory.
	www.amazon.com /Function-Theory-One-Complex-Variable/dp/0471804681 (840 words)

	Visualizing Complex (Site not responding. Last check: 2007-11-06)
		A complex function of a complex variable therefore is an object imbedded in a FOUR dimensional space.
		A complex graph of a complex variable, as we mentioned, is imbedded in four dimensions.
		The complex function is actually a wavy surface, because it is parameterized by TWO variables, x and y.
	www.people.fas.harvard.edu /~pitkow/complex (433 words)

	Complex variable Analysis (Site not responding. Last check: 2007-11-06)
		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.
		30: Complex variables studies the effect of assuming differentiability of functions defined on complex numbers.
		32: Several complex variables is, naturally, the study of (differentiable) functions of more than one complex variable.
	www.math.niu.edu /~rusin/known-math/index/tour_cplx.html (276 words)

	Complex - Using the GNU Compiler Collection (GCC)
		ISO C99 supports complex floating data types, and as an extension GCC supports them in C89 mode and in C++, and supports complex integer data types which are not part of ISO C99.
		GCC can allocate complex automatic variables in a noncontiguous fashion; it's even possible for the real part to be in a register while the imaginary part is on the stack (or vice-versa).
		If you are using the stabs debug info format, GCC describes a noncontiguous complex variable as if it were two separate variables of noncomplex type.
	gcc.gnu.org /onlinedocs/gcc/Complex.html (322 words)

	Complex Analysis (Site not responding. Last check: 2007-11-06)
		When the School of Computation was established at the University of Puebla, it inherited a course on complex variables from an earlier curriculum.
		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)

	30: Functions of a complex variable
		Complex variables studies the effect of assuming differentiability of functions defined on complex numbers.
		Problems involving complex numbers, rather than functions, are likely to be topics in algebra; see especially 12: Fields.
		Hamilton, Hugh J.: "A primer of complex variables, with an introduction to advanced techniques", Wadsworth Publishing Co., Inc. Brooks/Cole Publishing Co., Belmont, Calif. 1966 227 pp.
	www.math.niu.edu /~rusin/known-math/index/30-XX.html (522 words)

	The Complex Variable Boundary Element Method (More)
		The Complex Variable Boundary Element Method or CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method or BIEM.
		Because of the direct link between the real variable BIEM models and the CVBEM, detailed discussions of accomodating anisotropic and dissimilar materials and time advancement techniques are not presented.
		Several application problems are solved which demonstrate the use of the CVBEM and the interpretation of the produced approximation error for subsequent reduction.
	www.hromadka.net /COMPLE1_More.html (869 words)

	MT290 Complex Variable (Term 2: Dr C M Farmer)
		This course is designed to provide an outline of the basic complex variable theory with some proofs.
		Functions of a complex variable: Continuity and differentiability of functions defined on an open set.
		Complex Analysis – J M Howie (Springer 2003).
	www.rhul.ac.uk /mathematics/bluebook/courses/MT290.htm (304 words)

	Web Directory » Web Directory » Science » Math » Analysis » Complex Variable (Site not responding. Last check: 2007-11-06)
		Complex Analysis - Mathematica 4.0 Notebooks to accompany the textbook by John Mathews and Russell Howell
		Complex and Functional Analysis - Course notes and old exams in PDF, PS, DVI, and TeX for a first course in Complex and Functional Analysis.
		Complex Variable Toolbox - MATLAB toolbox designed and developed for teaching complex variables with focus on the graphic representation of the concepts.
	www.dcpages.com /DC_ODP/?c=Science/Math/Analysis/Complex_Variable (326 words)

	Several complex variables at Texas A&M University (Site not responding. Last check: 2007-11-06)
		From the point of view of function theory, for example, a notable difference from the theory of one complex variable is that zeroes of holomorphic functions of several variables are never isolated.
		The theory of functions of several complex variables presents both a surprising rigidity and a remarkable richness.
		Emil J. Straube are particularly noted for their research on the theory of the Bergman kernel function and on the the boundary regularity theory of the inhomogeneous Cauchy-Riemann equations in pseudoconvex domains.
	www.math.tamu.edu /~harold.boas/scv.html (374 words)

	[No title]
		Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering.
		Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authors’ extensive experience in modeling complicated situations and providing analytic solutions.
		Based on graduate courses in applied mathematics, Functions of a Complex Variable: Theory and Technique is intended for applied mathematicians, scientists, engineers, and senior or graduate-level students who have advanced knowledge in calculus and are interested in such subjects as complex variable theory, function theory, mathematical methods, advanced engineering mathematics, and mathematical physics.
	www.ec-securehost.com /SIAM/CL49.html (487 words)

	Functions of a complex variable. (Site not responding. Last check: 2007-11-06)
		This short tutorial is a companion material to the course on Functions of a Complex Variables.
		It is intented to help the student, but will replace neither personal lecture notes nor a good textbook.
		Algebraic form for a function of a complex variable.
	ndp.jct.ac.il /tutorials/complex/complex.html (43 words)

	[No title]
		There is a clever way was devised to calculate with complex numbers, that automatically incorporates the rules.
		This is a basic formula used in performing complex arithmetic.
		This solution involves the exponential function for a complex variable: for complex z = x + iy, the exponential function is defined by the power series
	www.math.buffalo.edu /ugterms/Basic_Complex_Variables.html (384 words)

	complex variable analysis — Infoplease.com (Site not responding. Last check: 2007-11-06)
		The theory of functions of a complex variable is concerned mainly with functions that have a derivative at every point of a given domain of values for
		Organochlorine pesticide analysis using a robust GC column phase: the composition of sample extracts in an environmental lab can be......
		The sensitivity analysis of the FHA technique of housing market analysis: the effect of ratios and variables, and their perturbations......
	www.infoplease.com /ce6/sci/A0813103.html (310 words)

	Complex Variable Methods in Elasticity
		This graduate-level text describes the mathematical methods used in solving problems related to plane problems of elasticity, illustrates the connections between common boundary problems, and offers a series of worked problems that illustrate the techniques of complex function theory.
		Three important aspects of elasticity theory are explored in this highly regarded engineering manual: finite elastic deformations, complex variable methods for two-dimensional problems for isotropic and aeolotropic bodies, and shell theory.
		It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions.
	www.doverdirect.com /0486432300.html (133 words)

	PRB: Error F2112 Caused by COMPLEX Number Variable
		The COMPLEX or COMPLEX*8 data type is an ordered pair of single- precision real numbers.
		The first number in the pair represents the real part of a complex number, and the second number represents the imaginary part.
		For example, the complex number (7, 3.2) represents the number 7.0+3.2i.
	support.microsoft.com /kb/39068 (214 words)

	Visualizing Functions of a Complex Variable
		We can represent the complex value of the function as a vector, drawing f(x+iy) as a 2D vector plot.
		We can consider the complex function as mapping from regions in (x,y) to regions in (u,v) and show how this mapping morphs lines and pictures.
		In all the images above, the lines and picture are the left are mapped under the complex inverse function to produce the image on the right.
	www.pacifict.com /ComplexFunctions.html (567 words)

	Imaginary Exponents
		We may define imaginary exponents the same way that all sufficiently smooth real-valued functions of a real variable are generalized to the complex case--using Taylor series.
		Since these elementary operations are also defined for complex numbers, any smooth function of a real variable
		may be generalized to a function of a complex variable
	ccrma.stanford.edu /~jos/mdft/Imaginary_Exponents.html (160 words)

	Complex Variable Methods in Elasticity
		The plane strain and generalized plane stress boundary value problems of linear elasticity are the focus of this graduate-level text, which formulates and solves these problems by employing complex variable theory.
		Its five-part treatment covers functions of a complex variable, the basic equations of two-dimensional elasticity, plane and half-plane problems, regions with circular boundaries, and regions with curvilinear boundaries.
		It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples...
	store.doverpublications.com /0486432300.html (192 words)

	Functions of a Complex Variable
		A thorough treatment of the fundamental elements, concepts, and theorems pertaining to the function of a complex variable, this text offers a complete study, suitable for advanced mathematics students, physicists, and advanced engineers.
		Students of applied mathematics will particularly value the full exposition of the theory of linear differential equations, especially in regard to the functions of Legendre, Laplace, Bessel, and Lamé.
		A collection of lectures by a distinguished mathematician and teacher, this volume discusses important issues of dynamics from the viewpoint of the theory of functions of the complex variable.
	store.doverpublications.com /0486446441.html (246 words)

	Complex analysis - Wikipedia, the free encyclopedia
		Henrici P., Applied and Computational Complex Analysis (Wiley).
		Shaw, W.T., Complex Analysis with Mathematica (Cambridge, 2006).
		This page was last modified 15:45, 18 October 2006.
	en.wikipedia.org /wiki/Complex_analysis (808 words)

	MIT OpenCourseWare \| Mathematics \| 18.112 Functions of a Complex Variable, Fall 2005 \| Lecture Notes (Site not responding. Last check: 2007-11-06)
		The lecture notes were prepared by Zuoqin Wang under the guidance of Prof.
		Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable.
		The Algebra of Complex Numbers: The Geometry of the Complex Plane, The Spherical Representation
	ocw.mit.edu /OcwWeb/Mathematics/18-112Fall-2005/LectureNotes/index.htm (305 words)

	complex variable analysis. The Columbia Encyclopedia, Sixth Edition. 2001-05
		branch of mathematics that deals with the calculus of functions of a complex variable, i.e., a variable of the form z=x+iy, where x and y are real and i=[radical]-1 (see number).
		A function w=f(z) of a complex variable z is separable into two parts, w = g
		The function can also be expressed in the infinite serieswhere z
	www.bartleby.com /65/co/complexv.html (242 words)

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