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Practice Prelim 2 - Multivariable Calculus Engineering | MATH 1920, Study notes of Calculus
Practice Prelim 2 Material Type: Notes; Class: Multivariable Calculus Engrs; Subject: Mathematics; University: Cornell University; Term: Fall 2011;
Typology: Study notes
2010/2011
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- Consider the vector field F(x, y) =
y r^3
i −
x r^3
j,
where r =
x^2 + y^2.
(a) (5 pts) Calculate the divergence of F, div F. (b) (10 pts) For a closed curve C that does not go around the origin, evaluate the outward flux
C F^ ·^ n^ ds.^ Can Green’s Theorem be used here?^ Explain your answer. (c) (10 pts) For the unit circle C around the origin, find the outward flux
C F^ ·^ n^ ds. Can Green’s Theorem be used here? Explain your answer.