Calculus of variations establishes a framework to determine the extrema of functionals—mappings from functions to real numbers—which has been pivotal in elucidating natural principles such as the ...
Calculus to the level of ODEs, partial derivative and multiple integrals, some knowledge of PDEs helpful but not essential. Students should have a certain comfort level with dealing with advanced ...
Variational problems in phase transition systems centre on energy functionals that balance interfacial costs and bulk or nonlocal interactions to determine collective patterns of coexisting phases.
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Machines are getting better at maths – artificial intelligence has learned to solve university-level calculus problems in seconds. François Charton and Guillaume Lample at Facebook AI Research trained ...