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Topic: Stokes theorem


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  Stokes' theorem - Wikipedia, the free encyclopedia
Stokes' theorem in differential geometry is a statement about the integration of differential forms which generalizes several theorems from vector calculus.
The fundamental theorem of calculus is the 0+1 dimensional case: the boundary is then the two endpoints, with + on the right and − on the left being the orientation.
Green's theorem is immediately recognizable as the third integrand of both sides in the integral in terms of P, Q, and R cited above.
en.wikipedia.org /wiki/Stokes'_theorem   (535 words)

  
 George Gabriel Stokes
Ray MacSharry, of a memorial at Stokes' birthplace in Skreen on Saturday 10th June 1995 as part of a meeting organised at Sligo RTC by the Institutes of Physics and of Mathematics and its Applications, under the auspices of the Royal Irish Academy, as part of the Sligo 750 celebrations.
In 1798, Gabriel Stokes, son of John Stokes and Rector of Skreen, married Elizabeth, the daughter of John Haughton, the Rector of Kilrea.
Stokes' manuscript notes still exist in the University Library in Cambridge, although his writing was so bad that he eventually became one of the first people in Britain to make regular use of a typewriter.
www.cmde.dcu.ie /Stokes/GGStokes.html   (3233 words)

  
 Green's and Stokes' Theorems: Kalid's Page
Green's theorem states that the amount of circulation around a boundary is equal to the total amount of circulation of all the area inside.
Stokes' theorem states that the total amount of twisting along a surface is equal to the amount of twisting on its boundary.
Stokes' theorem states that both of these regions would have the same circulation, because they have the same boundary.
www.cs.princeton.edu /~kazad/resources/math/Stokes_and_Green/green.htm   (339 words)

  
 Stokes's Theorem   (Site not responding. Last check: 2007-11-05)
Lecture 10 moves on to the last of the three theorems of vector calculus which we will be discussing, Stokes Theorem.
Stokes theorem deals with the problem of a 3-Dimensional curve in space, and the line integral around such a curve.
Stokes Theorem reduces to Green's Theorem when the curve is a 2-D curve, i.e.
omega.albany.edu:8008 /calc3/Stokes-theorem-dir/lec10.html   (323 words)

  
 Stokes' theorem biography .ms   (Site not responding. Last check: 2007-11-05)
The theorem is to be considered as a generalisation of the fundamental theorem of calculus and indeed easily proved using this theorem.
The fundamental theorem of calculus and Green's theorem are also special cases of the general Stokes theorem.
The general form of the Stokes theorem using differential forms is more powerful than the special cases, of course, although the latter are more accessible and are often considered more convenient by practicing scientists and engineers.
www.biography.ms /Stokes%27_theorem.html   (327 words)

  
 PlanetMath: proof of general Stokes theorem
"proof of general Stokes theorem" is owned by paolini.
Cross-references: theorem, equality, properties, partition of unity, contained, neighbourhood, translations, point, open set, cube, atlas, additivity, differential form, inclusion map, support, compact, fundamental theorem of calculus, manifold, integral, term, divide
This is version 4 of proof of general Stokes theorem, born on 2003-06-16, modified 2003-06-16.
planetmath.org /encyclopedia/ProofOfGeneralStokesTheorem.html   (190 words)

  
 PlanetPhysics: Stokes' theorem   (Site not responding. Last check: 2007-11-05)
Stokes' theorem: The surface integral of the curl of a vector function is equal to the line integral of that vector function taken around the closed curve bounding that surface.
On account of its great importance in all branches of mathematical physics a number of different proofs will be given.
This is version 2 of Stokes' theorem, born on 2006-07-25, modified 2006-07-27.
planetphysics.org /encyclopedia/StokesTheorem.html   (78 words)

  
 The idea of Stokes' theorem*
The required relationship between the curve C and the surface S (Stokes' theorem) is identical to the relationship between the curve C and the region D (Green's theorem):
To define the orientation for Green's theorem, this was sufficient.
For Stokes' theorem, we cannot just say "counterclockwise," since the orientation that is counterclockwise depends on the direction from which you are looking.
www.math.umn.edu /~nykamp/m2374/readings/stokesidea   (1222 words)

  
 Worksheet XVI
Stokes, one of the most influential scientific figures of his century, was Lucasian professor of mathematics at Cambridge University from 1849 until his death in 1903.
It is another one of those delightful quirks of history that the theorem that we call Stokes’ theorem isn’t his theorem at all.
Stokes was the original discover of the principles of spectrum analysis that we now credit to Robert Bunsen and Gustav Robert Kirchhoff.
www.math.luc.edu /~ajs/courses/263fall2001/worksheets/ws16.html   (265 words)

  
 Who discovered the general case of Stokes' Theorem?
Later Stokes assigns the proof of this theorem as part of the examination for the Smith's Prize.
The general case of Stokes Theorem was the first great publication by Nicolas Bourbaki.
Stoke's theorem and Noether's are probably two of my favourite theorems.
www.physicsforums.com /showthread.php?p=958905   (542 words)

  
 PlanetMath: classical Stokes' theorem
The classical Stokes' theorem, and the other “Stokes' type” theorems are special cases of the general Stokes' theorem involving differential forms.
In fact, in the proof we present below, we appeal to the general Stokes' theorem.
This is version 3 of classical Stokes' theorem, born on 2005-08-12, modified 2005-08-14.
planetmath.org /encyclopedia/ClassicalStokesTheorem.html   (269 words)

  
 The Cauchy-Stokes decomposition theorem   (Site not responding. Last check: 2007-11-05)
Physicist and mathematician noted for his studies of the behavior of viscous fluids, particularly for his law of viscosity, which describes the motion of a solid sphere in a fluid, and for Stokes's theorem in vector analysis.
The stoke, a unit of kinematic viscosity in the cgs system, was named after him.
We read this as saying that the most general differential motion of a fluid element corresponds to a uniform translation (first term), plus a rigid rotation (second term) plus a distortion which can be resolved into a uniform expansion or contraction plus a distortion without change in volume.
grus.berkeley.edu /~jrg/ay202/node58.html   (705 words)

  
 UNL Math 107H, CalculusII, Section 005, Dunbar, 9:30-10:20 M-F
Stokes' Theorem is an analogue of the Fundamental Theorem of Calculus: the integral of circulation density equals the total circulation around the boundary of the surface.
Stokes' Theorem relates the flux integral of a curl of a vector field through a surface with the circulation of the field around the boundary:
Stokes' theorem is named after Sir George Gabriel Stokes, (1819-1903) Irish mathematician and physicist, who became a professor at Cambridge in 1849.
www.math.unl.edu /~sdunbar1/Teaching/Calculus208/Lessons/VectorCalculus/stokes.shtml   (993 words)

  
 The Theorems of Green and Stokes
Stokes' Theorem states that if S is an oriented surface with boundary curve
Problem 3: Verify Stokes' theorem for the case in which S is the portion of the upper sheet of the hyperbolic paraboloid
A curious consequence of Green's Theorem is that the area of the region R enclosed by a simple closed curve C in the plane can be computed directly from a line integral over the curve itself, without direct reference to the interior.
www.math.umd.edu /~jmr/241/lineint2.htm   (841 words)

  
 The Generalized Stokes Theorem and Differential Forms   (Site not responding. Last check: 2007-11-05)
One of the most beautiful topics is the Generalized Stokes Theorem.
Gauss' Theorem: The integral of a vector function F(x,y,z) over the surface of a closed three dimensional volume B is equal to the integral of the divergence of F(x,y,z) over the volume B. Restated in symbols this is:
Stokes' Theorem: The integral of a vector function F(x,y,z) around a directed closed curve ∂B, which is the oriented boundary of an oriented surface B is equal to the integral of the curl of F over the surface B. Restated this is
www.applet-magic.com /stokes.htm   (213 words)

  
 Stokes' Theorem (ResearchIndex)   (Site not responding. Last check: 2007-11-05)
Our Stokes' theorem (and Acker's) specialize to a version of Green's theorem which implies the Cauchy-Goursat theorem: If f is analytic in an open set containing a simple closed curve C and its interior, then # C f(z)dz = 0.
0.8: Beppo Levi's Theorem for the Vector-Valued McShane Integral and..
2 The multidimensional fundamental theorem of calculus (context) - Pfe - 1987
citeseer.ist.psu.edu /480690.html   (532 words)

  
 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-11-05)
I have been studying vector calculus, and I was interested in finding more about the principles of the divergence theorem and Stokes' theorem, which relate to flux and curl, respectively.
I never could figure out, though, why they don't just call all those kinds of theorems "The Fundamental Theorem of Calculus" and leave it at that, rather than giving them all kinds of different names like Green's theorem, Gauss's theorem, and whatever all the rest are.
Anyway, if you've seen Stokes' theorem, you've probably been told that it's the n-dimensional analogue of the Fundamental theorem of Calculus you saw in regular one-dimensional calculus.
mathforum.org /library/drmath/view/53426.html   (288 words)

  
 Earth's Geoid   (Site not responding. Last check: 2007-11-05)
It is possible to estimate the geoid at a point from gravity values by means of the Theorem of Stokes (from Heiskanen and Vening Meinesz: The Earth and Its Gravity Field, p.
We thus have obtained the theorem of Stokes, which is of fundamental importance for geodesy because it allows us to determine the geoid from gravity.
In the third place, although the applicability of Stokes' theorem seems to be impeded by the fact that the integral must be extended over the whole earth and that gravity is still unknown over great parts of it, actually, however, for great distances from the station where N
solid_earth.ou.edu /notes/geoid/earths_geoid.htm   (1677 words)

  
 World Web Math: Vector Calculus Independent Study Path Unit 4   (Site not responding. Last check: 2007-11-05)
In single variable calculus, the fundamental theorem of calculus related the integral of the derivative of a function over an interval to the values of that function on the endpoints of the interval.
Stokes' Theorem, and how to simplify certain flux or work integrals using it.
The form of the theorems, and the notation, is that of Calculus with Analytic Geometry, Second Edition, by George F. Simmons, and page references are to this volume.
web.mit.edu /wwmath/vectorc/ispath/unit8.html   (239 words)

  
 Circulation, Vorticity, and Stokes Theorem   (Site not responding. Last check: 2007-11-05)
Stokes' theorem is an integral identity that may be written:
This result implies that the circulation around a contour that contains a group of vortices is just equal to the sum of the enclosed vortex strengths.
This allows application of the Blasius theorem to find the force acting on a group of vortices.
www.desktopaero.com /appliedaero/potential/stokes.html   (264 words)

  
 Calculus III (Math 2415) - Surface Integrals - Stokes' Theorem   (Site not responding. Last check: 2007-11-05)
C.  To get the positive orientation of C think of yourself as walking along the curve.  While you are walking along the curve if your head is pointing in the same direction as the unit normal vectors while the surface is on the left then you are walking in the positive direction on C.
In this theorem note that the surface S can actually be any surface so long as its boundary curve is given by C.  This is something that can be used to our advantage to simplify the surface integral on occasion.
In both of these examples we were able to take an integral that would have been somewhat unpleasant to deal with and by the use of Stokes’ Theorem we were able to convert it into an integral that wasn’t too bad.
tutorial.math.lamar.edu /AllBrowsers/2415/StokesTheorem.asp   (597 words)

  
 Mathematics Other Homework Help
A theorem states that if d:D-->R is uniformly continuous on D iff the followin...
Green's Theorem and Stokes' Theorem - Using Green's Theorem and Stokes' Theorem respectivly, calculate the given line integrals.
green's, divergence and stokes theorems - describe in 5-15 lines th elinks and connections among Green's theorem in all forms, stokes' theorem and the divergene theorem.
www.brainmass.com /homeworkhelp/math/other/34598   (251 words)

  
 Differential Forms and Vector Calculus - Numericana
The general theorem is due to Nicolas Bourbaki...
A stunning generalization of the fundamental theorem of calculus states that the integral of a form's derivative d
Among the above formulae, the least popular is probably the one involving an irreducible nabla (as tabulated above in terms of cartesian coordinates).
home.att.net /~numericana/answer/forms.htm   (659 words)

  
 Earliest Known Uses of Some of the Words of Mathematics (S)
The theorem was attributed to Robert Simson (1687-1768) by François Joseph Servois (1768-1847) in the Gergonne's Journal, according to Jean-Victor Poncelet in Traité des propriétés projectives des figures.
STOKES'S THEOREM was attributed to George Gabriel Stokes (1819-1903) by J. Maxwell in his A Treatise on Electricity and Magnetism (1873, p.
Sturm's theorem appears in English in 1841 in the title Mathematical Dissertations, for the use of students in the modern analysis; with improvements in the practice of Sturm's Theorem, in the theory of curvature, and in the summation of infinite series by J. Young [James A. Landau].
members.aol.com /Jeff570/s.html   (13176 words)

  
 George Gabriel Stokes - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-05)
Stokes did not have a doctorate, however William Hopkins is considered to be his equivalent mentor.
Perhaps his best-known researches are those which deal with the wave theory of light.
A mechanical model, illustrating the dynamical principle of Stokes's explanation was shown.
en.wikipedia.org /wiki/George_Gabriel_Stokes   (1589 words)

  
 [No title]
Stokes’ Theorem (and some review!) A. Green’s Theorem 1.
Example: Say S is the top hemisphere of a sphere of radius 5, centered at the origin.
Set up the line integral corresponding to the LHS of Stokes’ Theorem.
www.maa.org /t_and_l/exchange/ite11/Stokes.doc   (506 words)

  
 Stokes' law - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-05)
For a theorem in differential geometry, see Stokes theorem.
In 1851, George Gabriel Stokes derived an expression for the frictional force exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a continuous viscous fluid by solving the small fluid-mass limit of the generally unsolvable Navier-Stokes equations:
If the particles are falling in the viscous fluid by their own weight, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the bouyant force exactly balance the gravitational force.
en.wikipedia.org /wiki/Stokes'_law   (139 words)

  
 Navier-Stokes Equations: Stokes' Theorem   (Site not responding. Last check: 2007-11-05)
Here I'll record the standard form of Stokes' theorem.
This theorem is used in nearly every branch of mechanics as well as electromagnetics.
Stokes' Theorem also plays a role in many secondary theorems such as those pertaining to vorticity and circulation.
www.navier-stokes.net /nsms.htm   (82 words)

  
 Stokes theorem   (Site not responding. Last check: 2007-11-05)
[hep-th/0301039] Boundary charges in gauge theories: using Stokes theorem in the...
Calculus III (Math 2415) - Surface Integrals - Stokes' Theorem...
Stokes' Theorem ex- A related operation, called the...
www.scienceoxygen.com /math/712.html   (85 words)

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