Fluent Essays

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If 6) the Consider s Let C In w class In - this Its what a) b) f Does about , smooth I = s . on , form a constant which chant is function .) smooth . anti and function smooth a IR . . the is , such that derivatives anything change this coordinate ? → IR . da each w , I chant exist e , - in there f Think do , is Remember everywhere ) .) da - either I O = a in = Does ( is w w almost C with chart second w coefficient d O O a chart that , coordinate . other w Also ① introduced we , Note ( do - with circle give or an why w always S ? . - ? df exist . ) argument not - why or 1 Homework 1) Week : In class 2 we that saw f l I I part , an a) internal open : a - . 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IR to singular values points The : x. the are IR : C what value regular a , . vector a defining la ) for Dxf ( I - and as that means - . submanifold n IR E = This smooth a a M n dimension of , IR IR : construct choosing by f , y, the f which f af Cx , y ) = O other is f by applying ? to this zero the . points of IR . → ? f b) Sketch f ( D as which c) Repeat of Ca ) these and f- , l Cb ) D of subsets are - 1 for - f- and , IR to ) , . dimensional flag ) - - manifolds x t y . ? ... Purchase answer to see full attachment