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Exemplu subiect Geometrie Diferentiala

 
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Adriana Nistor
Thales


Joined: 07 Aug 2008
Posts: 116
Location: Bucuresti

PostPosted: Sat Feb 01, 2014 6:12 pm    Post subject: Exemplu subiect Geometrie Diferentiala Reply with quote

EXAMEN CURBE SI SUPRAFETE, grupa 201, 1.02.2014


1 Determinati punctele de maxim si de minim ale curburii curbei:
\gamma(t)=(a cos(t),b sin(t)) a,b\in\mathbb{R}, t\in [0,2\pi]
2 Parametrizati prin lungime de arc curba:
\gamma(t)=(e^t, e^{-t},\sqrt{2}) , t\in \mathbb{R}
3 Ce puteti spune despre o curba spatiala cu proprietatea ca toate tangentele ei trec printr-un punct fix?
4 Determinati planul tangent in punctul (1,1,1) la suprafata parametrizata prin:
h(u^1,u^2)=(u^1,u^2, u^1u^2) , (u^1,u^2)\in\mathbb{R}^2
5 Fie suprafata data implicit: y(1+x^2+z^2)=1
Determinati punctele in care se anuleaza curbura ei gaussiana.
6 Aratati ca daca a doua forma fundamentala a unei suprafete se anuleaza identic, atunci suprafata face parte dintr-un plan.
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