منابع مشابه
The Calculus of Variations
The lectures focused on the Calculus of Variations. As part of optimization theory, the Calculus of Variations originated in 1696 when Johann Bernoulli posed the brachistochrone problem. This problem related to the curve between two points along which a ball would require minimal time of travel to reach the bottom. This problem was solved by many different mathematicians of the time, some of wh...
متن کاملAn analytic study on the Euler-Lagrange equation arising in calculus of variations
The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...
متن کاملNON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...
متن کاملdenoising medical images using calculus of variations
we propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows. this method reduces any additive noise and preserves small patterns and edges of images. a pyramid structure-texture decomposition of images is used to separate noise and texture components based on local variance measures. the experimental results show that the proposed...
متن کاملCalculus of Variations
We consider the following obstacle problem for Monge-Ampere equation detDu = fχ{u>0} and discuss the regularity of the free boundary ∂{u = 0}. We prove that ∂{u = 0} is C if f is bounded away from 0 and ∞, and it is C if f ≡ 1.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1925
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1925-04002-1