This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y = x 2 + z 2 and in the halfspace { ( x, y, z )  y 1 } . We assume that the surface is oriented in the positive direction of the yaxis. 17.8b. Suppose S is a surface with boundary C . Show that if v is a xed vector and F ( x, y, z ) = x, y, z , then 2 S v d S = C ( v F ) d r . 17.8c. Suppose F is a vector eld. Consider two surfaces S and S which possess the same boundary C . Use sketches (note plural) to describe how S and S must be oriented so that S curl( F ) d S = S curl( F ) d S . 17.8d. Suppose F is a vector eld. Expanding upon the above problem: Suppose that S is a closed surface (that is, S is a boundary for a region of space). Show that S curl( F ) d S = 0 ....
View
Full
Document
 Winter '08
 Fish
 Multivariable Calculus

Click to edit the document details