THE FOLLOWING ARE FOR YOUR OWN STUDY, NOT TO SUBMIT Thomas’ Calculus, Early Transcendentals, 12th Edition Section Suggested Problems 1.1 4,6,7,8,10,12,17-20,23,27,30,45,46,50,51,52,63,64,70,72 1.2 5,9,11,16,21,23,25,29,33,39,51,55,68,71,79 1.3 1,5,7,8,13,15,43,47,49,55 1.4 None 1.5 1,5,6,9,10,21-24 1.6 1-6,8,10,11-16,18-24,31,32,41,43,47,52,53,65,66,70,71 2.1 ...

 

16.5 and 16.6: Surfaces, Area, and Surface Integrals E. Kim Notation follows Thomas’ Calculus: Early Transcendentals (12th Edition) as closely as possible Parametric form Suppose r(u,v) = f(u,v)i + g(u,v)j + h(u,v)k with bounds a ≤ u ≤ b and c ≤ v ≤ d denes a surface S. • The region R: the region in uv-space: a ≤ u ≤ b and c ≤ v ≤ d. • Surface area dierential: dσ = kr ×r k dudv. u v • Surface area integral: ¨ dσ=¨ kru×rvkdudv=ˆ dˆ bkru×rvkdudv. S ...