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[AMR] updated first 4.5 sections
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@@ -2,7 +2,7 @@
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\label{sec:ms-lin}
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$\vec{f}(\vec{x}) \approx \vec{f}(\vec{\overline{x}}) + \mat{J}_{\vec{f}} \big|_{x = \overline{x}}(\vec{x} - \vec{\overline{x}})$, $f'$, no vec in 1D; $\vec{\overline{x}}$ lin. p.
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\shortdefinition[Jac.] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$; cols for vars of each eq.
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\shortdefinition[Jacobian] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$; cols for vars of each eq.
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It may also be a single value (if just one var in the state)
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\shortdefinition[Gradient] $\nabla \vec{f}$ is vec, each comp. for par diff of var
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