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picture1_Geometry Pdf 167183 | Lec13 Item Download 2023-01-25 02-28-03


 116x       Filetype PDF       File size 0.87 MB       Source: staff.ustc.edu.cn


File: Geometry Pdf 167183 | Lec13 Item Download 2023-01-25 02-28-03
lecture 13 geometry and dynamics of smooth vector fields 1 geometry of vector fields the integral curves suppose we have a smooth vector eld dened on an euclidian region in ...

icon picture PDF Filetype PDF | Posted on 25 Jan 2023 | 2 years ago
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...Lecture geometry and dynamics of smooth vector fields the integral curves suppose we have a eld dened on an euclidian region in calculus ode learned conception such they are so that given is tangent to everywhere here example elds with many drawn above can be generalized manifolds easily begin one need explain conceptions curve rst m manifold by denition map i where interval r for any at point d dt standard coordinate let x tm called if t note really mean parametrized parametrization part dierent parametrizations same geometric picture represent n consider then straight lines parallel axis as c check this function f rn remark although has e horizontal line passing it not since y must which equivalent system solution acost bsint asint bcost these circles centered origin plane angle counterclockwise orientation general re no longer however hard see ia xa ax study further properties convert equation relating vectors into equations functions do prove lemma local chart p u v denote coordina...

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