Fun with the HP 15C
Happy Independence Day, United States!
Fractional Derivative: kth Derivative of f(x) = x^n
This program
calculates the kth derivative of x^n. The program allows for partial
derivatives of x^n (where k is not an integer, such as half-integers).
Formula:
d^k/dx^k x^n =
n!/(n-k)! * x^(n-k)
Input:
R0: point (x’)
R1: n
R2: k
Program:
|
Step
|
Key
|
Code
|
|
001
|
LBL A
|
42, 21, 11
|
|
002
|
RCL 0
|
45, 0
|
|
003
|
RCL 1
|
45, 1
|
|
004
|
RCL - 2
|
45, 30, 2
|
|
005
|
y^x
|
14
|
|
006
|
LAST x
|
43, 36
|
|
007
|
x!
|
42, 0
|
|
008
|
1/x
|
15
|
|
009
|
*
|
20
|
|
010
|
RCL 1
|
45, 1
|
|
011
|
x!
|
42, 0
|
|
012
|
*
|
20
|
|
013
|
RTN
|
43, 32
|
Example:
d/dx^4 x^8 at x = 6
R0 = x’ = 6
R1 = n = 8
R2 = k = 4
Result: 2177280
d/dx^1.5 x^3.4 at x = 1
R0 = x’ = 1
R1 = n = 3.4
R2 = k = 1.5
Result: 5.5469
Sight Reduction Table
The program
calculates altitude and azimuth of a given celestial body.
Inputs:
R1: Local Hour Angle
(LHA), west is positive, east is negative
R2: The observer’s
latitude on Earth, north is positive, south is negative (L)
R3: Declination of
the celestial’s body, north is positive, south is negative (δ)
Each entry will need
to be in decimal format. If your angels
are in HMS (hours-minutes-seconds) format, convert the angels to decimals by →H
before storing the values.
Formulas:
Altitude:
H = asin (sin δ sin
L + cos δ cos L cos LHA)
Azimuth:
Z = acos ((sin δ –
sin L sin H) ÷ (cos H cos L))
If sin LHA < 0
then Z = 360° - Z
Outputs:
Altitude (in
decimal), R/S, Azimuth (in decimal)
Program:
|
Step
|
Key
|
Code
|
|
001
|
LBL C
|
42, 21, 13
|
|
002
|
DEG
|
43, 7
|
|
003
|
RCL 3
|
45, 3
|
|
004
|
SIN
|
23
|
|
005
|
RCL 2
|
45, 2
|
|
006
|
SIN
|
23
|
|
007
|
*
|
20
|
|
008
|
RCL 3
|
45, 3
|
|
009
|
COS
|
24
|
|
010
|
RCL 2
|
45, 2
|
|
011
|
COS
|
24
|
|
012
|
*
|
20
|
|
013
|
RCL 1
|
45, 1
|
|
014
|
COS
|
24
|
|
015
|
*
|
20
|
|
016
|
+
|
40
|
|
017
|
ASIN
|
43, 23
|
|
018
|
STO 4
|
44, 4
|
|
019
|
R/S
|
31
|
|
020
|
SIN
|
23
|
|
021
|
RCL 2
|
45, 2
|
|
022
|
SIN
|
23
|
|
023
|
*
|
20
|
|
024
|
CHS
|
16
|
|
025
|
RCL 3
|
45, 3
|
|
026
|
SIN
|
23
|
|
027
|
+
|
40
|
|
028
|
RCL 4
|
45, 4
|
|
029
|
COS
|
24
|
|
030
|
RCL 2
|
45, 2
|
|
031
|
COS
|
24
|
|
032
|
*
|
20
|
|
033
|
÷
|
10
|
|
034
|
ACOS
|
43, 24
|
|
035
|
STO 5
|
44, 5
|
|
036
|
RCL 1
|
45, 1
|
|
037
|
SIN
|
23
|
|
038
|
TEST 2 (x<0)
|
43, 30, 2
|
|
039
|
GTO 1
|
22, 1
|
|
040
|
3
|
3
|
|
041
|
6
|
6
|
|
042
|
0
|
0
|
|
043
|
RCL - 5
|
45, 30, 5
|
|
044
|
STO 5
|
44, 5
|
|
045
|
LBL 1
|
42, 21, 1
|
|
046
|
RCL 5
|
45, 5
|
|
047
|
RTN
|
43, 32
|
Source: “NAV 1-19A Sight Reduction Table” HP 65 Navigation Pac. Hewlett Packard, 1974.
Three Point Lagrangian
Interpolation
This program
calculates a point (x0, y0) given three known points (x1, y1), (x2, y2), and
(x3, y3) where x0 is in between min(x1, x2, x3) and max(x1, x2, x3). Ideally, x1 < x2 < x3.
Input:
R0 = x0 (on the x
stack)
Store before running
the program:
R1 = x1, R4 = y1
R2 = x2, R5 = y2
R3 = x3, R6 = y3
Other registers
used: R7, R8, R9
|
Step
|
Key
|
Code
|
|
001
|
LBL E
|
42, 21, 15
|
|
002
|
STO 0
|
44, 0
|
|
003
|
RCL 4
|
45, 4
|
|
004
|
STO 7
|
44, 7
|
|
005
|
RCL 5
|
45, 5
|
|
006
|
STO 8
|
44, 8
|
|
007
|
RCL 6
|
45, 6
|
|
008
|
STO 9
|
44, 9
|
|
009
|
RCL 0
|
45, 0
|
|
010
|
RCL - 1
|
45, 30, 1
|
|
011
|
STO * 8
|
44, 20, 8
|
|
012
|
STO * 9
|
44, 20, 9
|
|
013
|
RCL 0
|
45, 0
|
|
014
|
RCL – 2
|
45, 30, 2
|
|
015
|
STO * 7
|
44, 20, 7
|
|
016
|
STO * 9
|
44, 20, 9
|
|
017
|
RCL 0
|
45, 0
|
|
018
|
RCL – 3
|
45, 30, 3
|
|
019
|
STO * 7
|
44, 20, 7
|
|
020
|
STO * 8
|
44, 20, 8
|
|
021
|
RCL 1
|
45, 1
|
|
022
|
RCL – 2
|
45, 30, 2
|
|
023
|
STO ÷ 7
|
44, 10, 7
|
|
024
|
CHS
|
16
|
|
025
|
STO ÷ 8
|
44, 10, 8
|
|
026
|
RCL 1
|
45, 1
|
|
027
|
RCL – 3
|
45, 30, 3
|
|
028
|
STO ÷ 7
|
44, 10, 7
|
|
029
|
STO ÷ 9
|
44, 10, 9
|
|
030
|
RCL 2
|
45, 2
|
|
031
|
RCL – 3
|
45, 30, 3
|
|
032
|
STO ÷ 8
|
44, 10, 8
|
|
033
|
STO ÷ 9
|
44, 10, 9
|
|
034
|
RCL 7
|
45, 7
|
|
035
|
RCL + 8
|
45, 40, 8
|
|
036
|
RCL + 9
|
45, 40, 9
|
|
037
|
RTN
|
43, 32
|
Example:
R1 = 5, R4 = 0.4
R2 = 10, R5 = 0.9
R3 = 15, R6 = 1.3
R0 = 12, result:
1.0720
R0 = 8, result:
0.7120
Source: R. Woodhouse.
“Lagrangian Interpolation Routines” Datafile Summer 1984 Vol. 3 No. 3,
Page 14
Quadratic Equation with Complex
Coefficients
This program solves
the equation where B and C are complex numbers:
x^2 + B*x + C = 0
where the roots are:
x = -B/2 ± √(B^2/4
– C)
Store the following
values before running:
R1 = real(B), R2 = imag(B)
R3 = real(C), R4 =
imag(C)
Output:
Root 1 (press [ f ],
hold (i) for the complex part), R/S, Root 2
Program:
|
Step
|
Key
|
Code
|
|
001
|
LBL C
|
42, 21, 13
|
|
002
|
GSB 1
|
32, 1
|
|
003
|
GSB 2
|
32, 2
|
|
004
|
+
|
40
|
|
005
|
R/S
|
31
|
|
006
|
GSB 1
|
32, 1
|
|
007
|
GSB 2
|
32, 2
|
|
008
|
-
|
30
|
|
009
|
RTN
|
43, 32
|
|
010
|
LBL 1
|
42, 21, 1
|
|
011
|
RCL 1
|
45, 1
|
|
012
|
RCL 2
|
45, 2
|
|
013
|
I
|
42, 25
|
|
014
|
2
|
2
|
|
015
|
CHS
|
16
|
|
016
|
÷
|
10
|
|
017
|
RTN
|
43, 32
|
|
018
|
LBL 2
|
42, 21, 2
|
|
019
|
RCL 1
|
45, 1
|
|
020
|
RCL 2
|
45, 2
|
|
021
|
I
|
42, 25
|
|
022
|
x^2
|
43, 11
|
|
023
|
4
|
4
|
|
024
|
÷
|
10
|
|
025
|
RCL 3
|
45, 3
|
|
026
|
RCL 4
|
45, 4
|
|
027
|
I
|
42, 25
|
|
028
|
-
|
30
|
|
029
|
√
|
11
|
|
030
|
RTN
|
43, 32
|
Example:
x^2 + (-1 + i)*x +
(3i) = 0
R1 = -1, R2 = 1
R3 = 0, R4 = 3
Results:
1.8229 – 1.8229i
-0.8229 + 0.8229i
x^2 + 3*x + (-5 +
6i) = 0
R1 = 3, R2 = 0
R3 = -5, R4 = 6
Results:
1.3862 – 1.0394i
-4.3862 + 1.0394i
Eddie
All original
content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
unauthorized distribution for commercial purposes without express and written
permission from the author is strictly prohibited. This blog entry may be distributed for
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