HP 15c - Manual (Page 79)

Section 3: Calculating in Complex Mode 79
Keystrokes Display
l5 059- 45 5 Recalls c.
- 060- 30 Calculates Im(P(z
k
)) – c.
|n 061- 43 32
Labels used: A, B, 0, 1, 2, 3, and 4.
Registers used: R
0
, R
1
, R
2
(x
0
), R
3
(y
0
), R
4
(h), R
5
(c), R
6
(x
k
), and Index register (k).
Matrix used: A.
One special feature of this program is that if an x
k
value lies beyond the domain of the
streamline (so that there is no root for _ to find), then the step size is decreased so that
x
k
approaches the boundary where the streamline turns back. This feature is useful for
determining the nature of the streamline when y
k
isn't a single-valued function of x
k
. If h is
small enough, the values of z
k
will lie on one branch of the streamline and approach the
boundary. (The second example below illustrates this feature.)
To use this program:
1. Enter your subroutine labeled "B" into program memory. It should place into the real
X-register Im(P(z)) when calculating streamlines or Re(P(z)) when calculating
equipotential lines.
2. Press 6´m% to reserve registers R
0
through R
6
(and the Index register).
(Your subroutine may require additional registers.)
3. Enter the values of n and h into the Z- and Y-registers by pressing
nvhv.
4. Enter the complex value of z
0
= x
0
+ iy
0
into the X-registers by pressing
x
0
vy
0
´V.
5. Press ´A to display the successive values of x
k
and y
k
for k = 1, ... , n and finally
the descriptor of matrix A. The values for k = 0, ... , n are stored in matrix A.
6. If desired, recall values from matrix A.
Example: Calculate the streamline of the potential P(z) = 1/z + z passing through
z = −2 + 0.1i .
First, enter subroutine "B" to compute Im(P(z)).
Keystrokes Display
´bB 062-42,21,12
v 063- 36 Duplicates z.
⁄ 064- 15
+ 065- 40 Calculates 1/z + z.
´} 066- 42 30 Places Im(P(z)) in X-register.