mast20009-2-D

Orthogonal Curvilinear Coordinates 2-D cases 1. Cartesian coordinates, Polar coordinates 2. 关于Polar coordinates 的θ, r的确定。 ☆3-D cases 1. 关于cylindrical, Spherical 的basis 个factors 的确定CPU E ducatio n 0,11 11011 1170 teid O Ii Otto T ti Spherical 3D polar Cylindrical f 0,21 xy S f 01 Polat Coordinates Z I 2 a feto 4 d ETO 2T 1 ZEE 2,2 L t o g xecosocl 2 r z y esmo f Z those f 01 f tsino Change of basis(coordinates). CPU E ducatio n f Terminal condition Jacobian 0,4 Phi lyarphi Spherical Sff fax y z dxdydz J fit b 01 Hinodidodo Cylindrical Sff toxin dxdydz J ftp0 tfdedodz 1. 对于scalar function的path integral 2. 对于Vector fields的path integral 3. Surface parametrisation 1. 地位同等于 parametrasption (相当于 种 具,有了他我们可以研究更多的问题) CPU E ducatio n fetds I di workdone fffds I ids flux Path integral scalar function vector fields Definition Path integral (Vector fields ) CPU E ducatio n 7 parametrize Parametrised Surfaces 原理: 两个vector来表示3D中的物体,surface Identity few surfaces: CPU E ducatio n I I x y Z n lower hemisphere 4 2 2 2 7 Spherical 4 E To 4 Otto ZT UEFI TJ Cylindrica K 44 L t LET014 ZE to e Otto 2T t t 2 Lf 0,21 t 0,0 MI ZETo e’d 更近 步,我们怎么样通过已知信息(φ(u ,v))去求其他的信息 “partial derivative” CPU E ducatio n FOXFu p outward inward surface版本的scalar path integral. CPU E ducatio n al Hector surface integral E CI Fa Fa II d5 J FI Elaine Fuxtul dude dotproduct I scalar function f 2 2 Vector function F 12,2 Meta dot product éosstridice Txt Te 112 D LET Fz vector 4 7.7 41 44dz I 17 7 d5 fix i Ads tds I di IM Ids S tic Integral theorem. CPU E ducatio n S Green Than Divergence Than Stokes Thr Gauss Divergence Thu Green Thn Pdxtody I 14 Ty dxdy F dxidyl F P.M Area 218 Sent Clio Divergence F Dharma f boundary DStokes Thn Jax 15 1 ids ground excluded Hate My U S S use J 7 71 d5 J I xx s ds t xx s d5 Is d5 f Xx s 10,0 i as ADT If X F du JI F d5 ground included on F d5 J d5 11 idsSi I 7 du I F con 11 Is