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Calculus of variations is a field of mathematics that deals with functionals, as opposed to ordinary calculus which deals with functions. Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions – those making the functional attain a maximum or minimum value – or stationary functions – those where the rate of change of the functional is precisely zero. Perhaps the simplest example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is obviously a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as geodesics. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, where the optical length depends upon the material of the medium. One corresponding concept in mechanics is the principle of least action. Many important problems involve functions of several variables. Solutions of boundary value problems for the Laplace equation satisfy the Dirichlet principle. Plateau's problem requires finding a surface of minimal area that spans a given contour in space: the solution or solutions can often be found by dipping a wire frame in a solution of soap suds. Although such experiments are relatively easy to perform, their mathematical interpretation is far from simple: there may be more than one locally minimizing surface, and they may have non-trivial topology. From Wikipedia under the
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From Yahoo Image Search: "Calculus of Variations" Calculus help with some end of chapter problems!? Q. Ok, I need some calculus help! I appreciate any answers I recieve! thanks! A surveyor needs to determine the distance across a lake. The surveyor selects two points, A and B, on one side of the lake, and one point, C, on the other side of the lake forming a triangle. The distance between points A and B is 50 feet. Angle A measures 70 , and angle B measures 65 . A bridge will be built between points A and C. How long will the bridge be, rounded to the nearest foot? Select one. A. 38 B. 40 C. 48 D. 50 E. 64 What is the exact solution for cos2 x + 4 cos x + 4 = 4 on the interval [0, 2 ]? Select one. A. 0 B. /3 C. /6 D. 2 /3 E. /2 A business owner is comparing the costs of purchasing inventory and the profit from the sale of the… [cont.] Asked by Jennifer W - Fri Apr 17 17:47:23 2009 - - 2 Answers - 0 Comments A. 1st: use the law of sines...50 / sin C = x / sin B...trivial to do 2nd: if you cannot see the answer then let cos x = t and try it...again easy 3rd: all linear are direct!! and these are calculus problems ?? Answered by ted s - Fri Apr 17 17:59:55 2009 Home schooling proponent/writer admits that home schooling in high-school does children a disservice? Q. "After my earlier article, a bunch of people wrote me with variations on the question: 'Well, OK, tough guy, but how in the hell are you going to teach them calculus?' I can promise you that neither Leslie nor I will be teaching them any such thing, and about the only thing to say is that we're well aware that eventually they'll need or want things we cannot provide. There certainly are home-schoolers with an ideological opposition to formal schooling, but that doesn't describe us or most of our peers. On balance it seems unlikely that we'll home-school Nini and Desmond all the way through high school." Thoughts? Asked by Culture Warrior - Mon Oct 19 00:51:40 2009 - - 3 Answers - 0 Comments Is 1/ = 0?
Q. I understand in calculus that the limit of 1/x as x approches infinity is 0. However, can I simply write 1/ = 0 or is this against any rules, just like writing 1/0 is undefined. If it IS possible to write it as 1/ = 0, then shouldn't * 0 = 1? Or 1/0 = ? Shouldn't these variations in what should be the same equation be prove in itself that 1/ does not equal 0 and is, in fact, undefined? Asked by Justin - Fri Jun 30 15:42:21 2006 - - 12 Answers - 0 Comments A. Yep, you've got it. You can't just say 1 / = 0 since it's not true. The limit is 0, sure, but not just straight up like you have it written. The answer is undefined. Answered by Ian M - Fri Jun 30 15:46:35 2006 From Yahoo Answer Search: "Calculus of Variations" |
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