Math 241, Section E1H, Fall 2013, Final Exam Information

6 param e tric surface s surfaces defined by

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Unformatted text preview: and normal version (involving divergence) 16.6: Param e tric Surface s Surfaces defined by parametrization r(u,v) Surfaces defined by the graph of a function z=f(x,y) (or y=g(x,z) or x=h(y,z)) Tangent planes to surfaces given in parametrized form Surface area and surface area element dS (two formulas, one for surfaces that are graphs as above, and the other for surfaces given in parametrized form) Parametrization and surface area element dS for sphere of radius a centered at the origin Summary: Surfaces, Surface Integrals, and Divergence Theorem (from a previous semester) 16.7: Surface inte grals Surface integrals of scalar functions, scalar surface area element (two formulas, one for surfaces z=f(x,y), the other for surfaces given in parametrized form) Applications of scalar surface integrals: area, mass, and center of mass of surfaces Surface integrals of vector fields, vector surface area element dS (two formulas, one as a scalar surfaces integral involving the outward normal component of F, the other involving the parametrization r(u,v)) Application/interpretations of vector surface integrals: flux (rate of flow) of "stuff" of various kinds (e.g., fluid, electricity, heat) 16.8: Stoke s' The ore m Stokes' Theorem 16.9: Div e rge nce The ore m (also calle d Gauss' The ore m ) Divergence Theorem Relevant review questions from the text Chapter 16 (page 1135- 1138) Concept check: 1 - 15. GOOD LUCK! www.math.illinois.edu/~ stefanm/math241- fa13- final.html 3/4 12/22/13 M ath 241, Section E1H, Fall 2013, Final Exam Infor mation Last modif ied: Wednesday 11 December 2013 www.math.illinois.edu/~ stefanm/math241- fa13- final.html 4/4...
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