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Written in the Socratic/Moore method, this book presents a sequence of problems which develop aspects in the field of semigroups of operators. The reader can discover important developments of the subject and quickly arrive at the point of independent research.
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients.
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