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 The Cauchy-Goursat Theorem The Cauchy-Goursat theorem states that within certain domains the integral of an analytic function over a simple closed contour is zero. The deformation of contour theorem is an extension of the Cauchy-Goursat theorem to a doubly connected domain in the following sense. We can extend Theorem 6.6 to multiply connected domains with more than one "hole.'' The proof, which is left for the reader, involves the introduction of several cuts and is similar to the proof of Theorem 6.6. math.fullerton.edu /mathews/c2003/CauchyGoursatMod.html   (716 words)

 Calculus III at the Library of Math (Free Online Mathematics) Vector fields are studied cumulating in the theorems of Green, Stoke, and the divergence theorem, which are extended versions of the Fundamental Theorem of Calculus. Green's theorem elegantly yields another technique to evaluate a line integral of a vector field and is especially important when the vector field is not conservative. Green's theorem for doubly connected regions and alternate forms of Green's theorem involving the curl and div of a vector field are also detailed. libraryofmath.com /Calculus_III.html   (2498 words)

 Calculus III (Math 2415) - Line Integrals - Green's Theorem   (Site not responding. Last check: 2007-10-06) Let’s first sketch C and D for this case to make sure that the conditions of Green’s Theorem are met for C and will need the sketch of D to evaluate the double integral. Okay, a circle will satisfy the conditions of Green’s Theorem since it is closed and simple and so there really isn’t a reason to sketch it. The end result of all of this is that we could have just used Green’s Theorem on the disk from the start even though there is a hole in it.  This will be true in general for regions that have holes in them. tutorial.math.lamar.edu /AllBrowsers/2415/GreensTheorem.asp   (1149 words)

 Planimeters & Green's Theorem Green's Theorem is a higher dimensional analogue of the Fundamental Theorem of Calculus. Green first published the theorem in 1828, but it did not become well known until 1846 when it was republished by Lord Kelvin. These devices can also be explained using Green's Theorem, although it is a bit more difficult than it was for the electronic planimeter (see Tanya Leise's planimeter site). www.attewode.com /Calculus/AreaMeasurement/area.htm   (1363 words)

 Green's Theorem -- from Wolfram MathWorld Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Arfken, G. "Gauss's Theorem." §1.11 in Mathematical Methods for Physicists, 3rd ed. Kaplan, W. "Green's Theorem." §5.5 in Advanced Calculus, 4th ed. mathworld.wolfram.com /GreensTheorem.html   (128 words)

 Maths Course 3E1   (Site not responding. Last check: 2007-10-06) Recap on vector calculus, Greens theorem and divergence (Gauss') theorem [January 15th, 2003] Further recap on vector caclulus, use of diveregence theorem to derive heat equation [February 2, 2003] Lecture notes for 30th April, 2003 to end of course (on complex integration, Cauchy's theorem and related topics). www.maths.tcd.ie /~richardt/3E1   (237 words)

 TheArtShowcase-large selection unique hand made gifts - Theorems   (Site not responding. Last check: 2007-10-06) Theorem Painting is an Early American stenciling craft that was taught during the early 1800's to the young girls in New England finishing schools. The name theorem is derived from the dividing of a design into sections for painting. Tea is used to achieve the soft tan aged look while oil paint is used to fill in each section of the design. www.theartshowcase.com /theorems?start=15   (298 words)

 Greens' Theorems Greens' Second Theorem or Greens' Theorem in Symmetric Form. This is simply Stokes' theorem but with the capping surface in a coordinate plane. These theorems are used in the potential theory, witch I hopefully will cover later. hemsidor.torget.se /users/m/mauritz/math/field/green.htm   (149 words)

 User Macro Document - VolumeIntegral If the geometric units defining the object are not the desired units, then a conversion factor can be entered, for instance to convert feet to meters. The internal volume of the shape is computed using Gauss' Theorem, rather than by explicitly looking at all cells in the interior. This module uses a form of Gauss' Theorem, or Greens' Theorem in Space. www.iavsc.org /repository/express/pages/volint/volint.shtml   (612 words)

 TheArtShowcase-large selection unique hand made gifts - Theorem Painting   (Site not responding. Last check: 2007-10-06) The gentle blues of the petunia complimented by the greens of its leaves. This cute brown bear is so cheery with the red bow and floating hearts in this theorem. Theorem is wall-hanging only and is 9 X 7 www.theartshowcase.com /theorem_painting?start=15   (189 words)

 Hawkes Learning Systems It is based on a dual geometric-analytic approach to each topic of discussion. The concepts and theorems are first visualized and understood heuristically, and then are reduced to an algebra-calculus framework for computation or mathematical scrutiny. The text is unique in its presentation of the laplacian and the vector potential and can be used at several levels. www.quantsystems.com /PC_IVAtext.htm   (120 words)

 Minnesota State Community and Technical College MNTC Goal Areas Stoke's Theorem, Greens Theorem, and the Divergence Theorem. This course is a beginning study of green plants and their growth, including basic plant anatomy, morphology, physiology, taxonomy, pathology, propagation, soil science, plant nutrition, and ethnobotany. Study of issues related to human biology with reference to genetics, nutrition, health, disease, or other contemporary issues. www.minnesota.edu /programs_majors/mntc_goal_area.php   (8766 words)

 Gauss' Theorem, or Greens' Theorem in Space. This will almost be a copy of the page of Stokes' Theorem. This is the same as saying that all that the net sum of all created inside V must come out trough the surface S of V. This integral theorem is called As with Stokes' Theorem we must take caution. hemsidor.torget.se /users/m/mauritz/math/field/gauss.htm   (280 words)

 Math 621 - Spring 2005 Basic Theory: Holomorphic and harmonic functions; conformal mappings; Cauchy's Theorem and consequences; Taylor and Laurent series; singularities; residues; Dirichlet Series such as the Riemann Zeta Function and/or other topics as time permits. In addition, students should review basic concepts of basic real analysis and advanced calculus such as: limits of sequences, series, absolute and uniform convergence, compact and connected sets in the plane, uniform continuity. You are encouraged to discuss the problems with your classmates but each student should write up his or her own solutions. www.math.umass.edu /~cattani/M621S05/index.html   (285 words)

 Template for Course Syllabus In linear algebra the student will learn matrix algebra, matrix inversion, eigen pairs, diagonalizing matrices, and classes of matrices. In vector calculus the student will learn vector fields, divergence, curl, Greens Theorem, Divergence Theorem, Stokes Theorem, and how to apply these topics. In complex function theory the student will learn complex numbers and their representations, analytic functions, complex integrals, Chauchy's Theorem, Taylor Series, Laurent Series, residues, and complex integration techniques as needed for special functions, transforms, and further studies. www4.ncsu.edu /~charlton/MA502sum06.html   (986 words)

 Multivariable exhibit: The proof of Greens theorem   (Site not responding. Last check: 2007-10-06) The animation illustrates the core of the proof of Greens theorem. The circulation around a small square is the differential quotient approximation of the curl of F. If you add up all the circulations, then only the boundary circulation survives due to cancellations in the interior. Oliver Knill, Math21a, Multivariable Calculus, Fall 2005, Department of Mathematics, Faculty of Art and Sciences, Harvard University www.math.harvard.edu /archive/21a_fall_05/exhibits/green/index.html   (97 words)

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