Other valuable treatises and memoirs have been written by Strauch (1849), Jellett (1850), Otto Hesse (1857), Alfred Clebsch (1858), and Carll (1885), but perhaps the most important work of the century is that of Weierstrass.
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Lagrange contributed extensively to the theory, and Legendre (1786) laid down a method, not entirely satisfactory, for the discrimination of maxima and minima.
Calculus of variations, a field of mathematical analysis that deals with maximizing or minimizing functionals
Calculus of variations tells us that this is equivalent to finding such that
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He has made significant seminal contributions in the specific areas of finite element method, plate theory, solid mechanics, variational methods, mechanics of composites, functionally graded materials, fracture mechanics, plasticity, biomechanics, classical and non-Newtonian fluid mechanics, and applied functional analysis.
The first efforts were based on optimal control approaches which grew out of the calculus of variations developed at the University of Chicago in the first half of the 20th century most notably by Gilbert Ames Bliss.