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...Bindel fall matrix computations cs notes for calculus numerical linear algebra is not just about but also analysis the branch of mathematics that deals with real functions and operations such as dierentiation integration their generalizations this particularly relevant when we deal error will soon warmup derivative a dot product consider valued expression ytx function vector variables n t x y r how would compute gradient respect to these usual method taught in rst class be write terms each components then partial derivatives i e xxy j xj notation ne dealing which are summing over only one variable more complicated expressions it quickly becomes painful coordinates neat trick work along coordinate directions an arbitrary direction d s ds wedenote directional by giving tidy yt variational reasoning gateaux deriva tives often used mechanics pde theory functional where spaces involved innite dimensional have always felt deserves widely some facts wewill make frequent use humble rule ab b c...