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18.024ESG Problem Set 12 Pramod N. Achar
 

Summary: 18.024­ESG Problem Set 12
Pramod N. Achar
Spring 2000
In this problem set you will prove an analogue of the Fundamental Theorem
of Calculus, Stokes' Theorem, etc. To set up the context of the problem, let us
define an operator div
on vector fields on R2
by
div
(P(x, y)i + Q(x, y)j) =
Q
x
-
P
y
.
Let C denote a curve in Rn
with endpoints a and b. Let S denote a surface
whose boundary is the closed curve Bd S. Let V denote a solid region in R3
with

  

Source: Achar, Pramod - Department of Mathematics, Louisiana State University

 

Collections: Mathematics