Complex Potentials - HP -15C Advanced Functions Handbook

SectionS: Calculating in Complex Mode 89
Keystrokes
ff1fscil2
1 I ENTER I
GOGlD(hold)
I * S y |
Behold)
Display
1.00
6
1.00
-3.24
3.82
7.87
1.23
0.0008
Run mode.
Specifies [sell 2 format.
00 Enters first limit of
integration, 1 +0i.
00 Enters second limit of
integration, 1 + 6i.
-01 Calculates/and displays
Re(/)=/
1
(after about
9 minutes).
-01 Displays Im(7) = I
2
.
-04 Displays Re( A/) = A/!.
-03 Displays Im(A7) = A/
2
.
This result /is calculated much more quickly than if/
x
and /
2
were
calculated directly along the real axis.
Complex Potentials
Conformal mapping is useful in applications associated with a
complex potential function. The discussion that follows deals with
the problem of fluid flow, although problems in electrostatics and
heat flow are analagous.
Consider the potential function P(z). The equation Im(P(z)) = c
defines a family of curves that are called streamlines of the flow. That
is, for any value of c, all values of z that satisfy the equation lie on a
streamline corresponding to that value of c. To calculate some points
z/t on the streamline, specify some values for x^ and then use I SOLVE | to
find the corresponding values of y^ using the equation
lm(P(x
k
If the Xk values are not too far apart, you can use y^ _ i as an initial
estimate for y
k
. In this way, you can work along the streamline and
calculate the complex points z
k
= x^ + iy^. Using a similar
procedure, you can define the equipotential lines, which are given
byRe(P(2)) = c.