21. Menger On The Calculus Of Variations Karl Menger wrote an article What Is Calculus of Variations and What Are Its Applications? This interesting article, written by an outstanding mathematician http://www-history.mcs.st-and.ac.uk/Extras/Calculus_of_Variations.html

Menger on the Calculus of Variations Karl Menger wrote an article What Is Calculus of Variations and What Are Its Applications? This interesting article, written by an outstanding mathematician and expert in the field, gives insights into both the history of the topic and also into understanding Menger's views on mathematics:- The calculus of variations belongs to those parts of mathematics whose details it is difficult to explain to a non-mathematician. It is possible, however, to explain its main problems and to sketch its principal methods for everybody. The first human being to solve a problem of calculus of variations seems to have been Queen Dido of Carthage. When she was promised as much land as might lie within the boundaries of a bull's hide, she cut the hide into many thin strips, put them together into one long strip, the ends of which she united, and then she tried to secure as extensive a territory as possible within this boundary. History does not describe the form of the territory she chose, but if she was a good mathematician she covered the territory in the form of a circle, for today we know: Of all surfaces bounded by curves of a given length, the circle is the one of largest area. The branch of mathematics which establishes a rigorous proof of this statement is the calculus of variations. Newton was the first mathematician to publish a result in this field. If a body moves in the air, it meets with a certain resistance, which depends on the shape of the body. The problem Newton studied was, what shape of body would guarantee the least possible resistance? Applications of this problem are obvious. The rifle bullet is designed in such shape as to meet with a minimum resistance in the air. Newton published a correct answer to a special case of this problem, namely, that the surface of the solid considered is obtained by revolving a curve around an axis. But he did not give the proof or the calculations that had led him to the answer. So Newton's solution had no great effect on the development of mathematics.

22. Calculus Of Variations Calculus Math Calculus of Variations English Science Math Calculus Calculus of Variations and Geometric Measure Theory at Pisa http://www.ltn.net/T/Idioma/English/Science/Math/Calculus/Calculus_of_Variations

LTN Calculus of Variations: English: Science: Math Calculus Calculus of Variations : Calculus of variations is the study of finding minima and maxima of functions. Math Calculus Calculus of Variations: Enter your search terms Submit search form English Science Physics Classical Mechanics: Lagrangian and Hamiltonian Mechanics Calculus of Variations and Geometric Measure Theory at Pisa Science: Calculus, Calculus Calculus of Variations Preprints on various topics on the calculus of variations of Variations and Geometric Measure Theory at Pisa . Brachistochrone Problem Science: Brachistochrone, Calculus Calculus of Variations Gives details on how to arrive at the general solutions Problem Includes definition of terms. Brachistochrone Construction - Calculus of Variations Science: Brachistochrone, Calculus Calculus of Variations Here one can see a graph of the brachistochrone for the given endpoint Construction Calculus of Variations Java applet. Calculus of Variations and Optimal Control - Calculus of Variations Science: Calculus, Calculus Calculus of Variations Calculus of variations and optimal control of Variations and Optimal Control Calculus of Variations Optimization.

23. Gate30, Gate 30 - Your Source For Everything Useful On The Web Jan 2, 2007 Calculus of Variations and Geometric Measure Theory at Pisa Preprints on various topics on the calculus of variations. http://www.gate30.com/findsubmit/map.asp?type=cat&path=/Science/Math/Calculu

24. Introduction To The Calculus Of Variations File Format PDF/Adobe Acrobat Quick View http://www.cse.yorku.ca/~kosta/CompVis_Notes/calculus_of_variations.pdf

25. Brainflux: Calculus Of Variations Calculus of Variations Euler s Equation Fourier Analysis Calculus of Variations is really great. It has things like Euler s Equation http://brainflux.org/Math/Calculus_of_Variations/index.html

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26. Calculus Of Variations - Conservapedia Dec 5, 2008 The calculus of variations is the optimization of functionals. An important related concept is the EulerLagrange equation. http://cptransitive.com/Calculus_of_variations

Calculus of variations From Conservapedia Jump to: navigation search The calculus of variations is the optimization of functionals . An important related concept is the Euler-Lagrange equation Retrieved from " http://cptransitive.com/Calculus_of_variations Category Calculus Views Page talk page View source History Personal tools Log in Search Popular Links Main Page Educational Index Debate Topics Recent changes ... Random page Help Help Index Statistics Conservapedia Commandments World History World History Lectures World History Homework Edit Console What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 5 December 2008, at 19:18. This page has been accessed 447 times. About Conservapedia

27. Calculus Of Variations 2008/9 Schools Wikipedia Selection. Related subjects Mathematics. Calculus of variations is a field of mathematics that deals with functionals, as opposed to ordinary calculus http://schools-wikipedia.org/wp/c/Calculus_of_variations.htm

Calculus of variations 2008/9 Schools Wikipedia Selection . Related subjects: Mathematics 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. 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 mechanics is the principle of least action. The theory of optimal control concerns a specific kind of problem in the calculus of variations. Many important problems involve functions of several variables. Solutions of boundary value problems for the Laplace equation satisfy the Dirichlet principle.

28. Calculus Of Variations | Ask.com Encyclopedia Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. http://www.ask.com/wiki/Calculus_of_variations?qsrc=3044

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32. Kifb Browser WordNet senses for the word calculus_of_variations. nouns. calculus of variations the calculus of maxima and minima of definite integrals http://godel.iis.sinica.edu.tw/cgi-bin/kifb/kifb_cgi?english=calculus_of_variati

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34. Answers.com - Is The Distance Covered By A Straight Line Connecting Two Points This problem can be solved with the Calculus of Variations. See http//en. wikipedia.org/wiki/calculus_of_variations The_Euler.E2.80.93Lagrange_equation http://wiki.answers.com/Q/Is_the_distance_covered_by_a_straight_line_connecting_

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38. Printable Version - Wikimedia Foundation commons.wikimedia.org/w/index.php? calculus_of_variations Which Topic In Maths Do You Hate? � Non Aviation Forum 24 posts 21 authors - Last post Nov 6, 2006Calculus of Variations http//en.wikipedia.org/wiki/calculus_of_variations I don t hate but I don t like it either. http://commons.wikimedia.org/w/index.php?title=Category:Calculus_of_variations&a

39. Calculus Of Variations Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. http://www.nexthomegeneration.com/Calculus_of_variations

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