HP 15c - Manual (Page 73)

Section 3: Calculating in Complex Mode 73
Since all roots have negative real parts, the system is stable, but the margin of stability (the
smallest in magnitude among the real parts, namely -0.1497) is small enough to cause
concern if the system must withstand much noise.
Contour Integrals
You can use f to evaluate the contour integral

C
dz z f ) (
, where C is a curve in the complex
plane.
First parameterize the curve C by z(t)= x(t) + i y(t) for t
1
≤ t ≤ t
2
. Let G(t)=f(z(t))z’(t). Then
 
 
 

2
1
2
1
2
1
)) ( Im( )) ( Re(
) ( ) (
t
t
t
t
C
t
t
dt t G i dt t G
dt t G dz z f
These integrals are precisely the type that f evaluates in Complex mode. Since G(t) is a
complex function of a real variable t, f will sample G(t) on the interval t
1
≤ t ≤ t
2
and
integrate Re(G(t))—the value that your function returns to the real X-register. For the
imaginary part, integrate a function that evaluates G(t) and uses } to place Im(G(t))
into the real X-register.
The general-purpose program listed below evaluates the complex integral
  b
a
dz z f I ) (
along the straight line from a to b, where a and b are complex numbers. The program
assumes that your complex function subroutine is labeled "B" and evaluates the complex
function f(z), and that the limits a and b are in the complex Y- and X-registers, respectively.
The complex components of the integral I and the uncertainty ΔI are returned in the X- and
Y-registers.
Keystrokes Display
|¥ Program mode.
´CLEARM 000-
´bA 001-42,21,11
® 002- 34
- 003- 30 Calculates b – a.
O4 004 44 4 Stores Re(b – a) in R
4
.
´} 005- 42 30
O5 006- 44 5 Stores Im(b – a) in R
5
.
|K 007- 43 36 Recalls a.
O6 008- 44 6 Stores Re(a) in R
6
.
´} 009- 42 30
O7 010- 44 7 Stores Im(a) in R
7
.
0 011- 0