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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the calculus of variations, a topic in mathematics, the direct method is a general method for constructing a proof of the existence of a minimizer for a given functional. The method relies on methods of functional analysis and topology.The direct method may often be applied with success when the space V is a subset of a reflexive Banach space W. In this case the Banach Alaoglu theorem implies, that any bounded sequence (un) in V has a subsequence that converges to some u0 in W with respect to the weak topology.