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linear_approximation [2014/03/21 11:11] 127.0.0.1 external edit |
linear_approximation [2014/04/11 16:42] nikolaj |
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| | @#55CCEE: context | @#55CCEE: $x\in\mathcal O$ | | | @#55CCEE: context | @#55CCEE: $x\in\mathcal O$ | | ||
| | @#55CCEE: context | @#55CCEE: $f:\mathcal O\to Y$ | | | @#55CCEE: context | @#55CCEE: $f:\mathcal O\to Y$ | | ||
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| | @#FFBB00: definiendum | @#FFBB00: $J_x^f$ | | | @#FFBB00: definiendum | @#FFBB00: $J_x^f$ | | ||
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| | @#55EE55: postulate | @#55EE55: $J_x^f$ ... bounded linear operator from $X$ to $Y$ | | | @#55EE55: postulate | @#55EE55: $J_x^f$ ... bounded linear operator from $X$ to $Y$ | | ||
| | @#55EE55: postulate | @#55EE55: $\mathrm{lim}_{h\to 0}\ \Vert f(x+h)-f(x)-J_x^f(h)\Vert / \Vert h\Vert\ =\ 0$ | | | @#55EE55: postulate | @#55EE55: $\mathrm{lim}_{h\to 0}\ \Vert f(x+h)-f(x)-J_x^f(h)\Vert / \Vert h\Vert\ =\ 0$ | | ||
