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Accumulation
Authors: Bill Davis, Horacio Porta and Jerry Uhl
©19962007
Publisher: Math Everywhere, Inc.
Version 6.0
2.05 2D Integrals and the GaussGreen Formula
LITERACY
What you should be able to handle away from the machine.
·
L.1)
Here's a plot of a certain surface
z
=
f
@
x, y
D
over the rectangle R in the xyplane consisting of all points
8
x, y, 0
<
with

2
§
x
§
2 and

1
§
y
§
3:
Here's an embellishment of the same plot:
Each of the vertical plotted poles has its base at a point
8
x, y, 0
<
in the rectangle R. What
does the length of each plotted pole measure?
·
L.2)
Given a specific function f
@
x, y
D
, how do you expect the output from the
Mathematica
instructions
Plot3D[f[x,y], {x,0,4}, {y, 3, 5}]
and
ParametricPlot3D[{x, y, f[x,y]}, {x, 0, 4}, {y, 3, 5}]
to be related?
·
L.3)
Here's a plot of a certain surface z
=
f
@
x, y
D
over (or under) the rectangle R in the xyplane
consisting of all points
8
x, y, 0
<
with

1
§
x
§
2 amd

1
§
y
§
3 shown with a plot of R:
Why does the plot signal that
Ÿ Ÿ
R
f
@
x, y
D
„
x
„
y
>
0?
·
L.4)
Here's a plot of a certain surface z
=
f
@
x, y
D
over (or under) the rectangle R in the xyplane
consisting of all points
8
x, y, 0
<
with

1
§
x
§
1 and

1
§
y
§
2
shown with a plot of R:
Why does the plot signal that
Ÿ Ÿ
R
f
@
x, y
D
„
x
„
y
<
0?
·
L.5)
Here's a plot of a certain surface z
=
f
@
x, y
D
over (and under) the rectangle R in the xy
plane consisting of all points
8
x, y, 0
<
with

1
§
x
§
2 and

1
§
y
§
3
shown with a plot of R:
Why does the plot strongly suggest that
Ÿ Ÿ
R
f
@
x, y
D
„
x
„
y
>
0?
How does the sign of f
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This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Integrals

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