Casio fx-3650P vs. Casio fx-3650P II: Programs
Here are four programs that are done with both the fx-3650P and fx-3650P II to illustrate some programming similarities and differences.
When we start a new program with the fx-3650P II, we are prompted to the choose the appropriate mode at the beginning:
COMP (main calculation with real numbers)
CMPLX (complex numbers, primarily complex number arithmetic)
SD (single-derivation mode, single-variable statistics)
REG (regression mode, two-variable statistics)
BASE (base conversions and Boolean logic)
Left: Casio fx-3650P (2002), Right: fx-3650P II (2013)
Program 1: Exponential Distribution
This program calculates:
PDF: e^(-X ÷ A)
CDF (lower tail): 1 - e^(-X ÷ A)
where:
A = 1/λ parameter (i.e. average waiting time, time for an event to occur/fail/succeed)
X = time parameter
fx-3650P, 25 bytes:
? → A : ? → X :
e(-X ÷ A) ÷ A ◢
1 – e(-X ÷ A)
fx-3650P II, 25 bytes:
? → A : ? → X :
e^(-X ÷ A) ÷ A ◢
1 – e^(-X ÷ A)
Example 1:
Inputs: A = 100, X = 50
Outputs: 6.065306597E-3 (*10^-3), 0.39346934
Example 2:
Inputs: A = 50, X = 3
Outputs: 0.01883529, 0.058235466
Program 2: Using Newton’s Method to get the real root of the cubic equation that is closest to zero:
x^3 + A * x^2 + B * x + C = 0
Using Newton’s Method:
x1 = x0 – f(x0) / f’(x0) [ let y = f(x0) / f’(x0) ]
x1 = x0 - (x^3 + A * x^2 + B * x + C) / (3 * x^2 + 2 * A * x + B)
fx-3650P, 72 bytes:
? → A : ? → B : ? → C : 0 → X :
Lbl 0 :
(X³ + AX² + BX + C) ÷ (3X² + 2AX + B) → Y :
√(Y²) → D :
X – Y → X :
D ≥ 1E-8 ⇒ Goto 0 : X
√(Y²) returns Abs(Y) in Comp mode.
D is set up to be the control variable, where
D = abs((x^3 + A * x^2 + B * x + C) / (3 * x^2 + 2 * A * x + B))
fx-3650PII, 67 bytes:
? → A : ? → B : ? → C : 0 → X : 1 → Y :
While Abs(Y) ≥ 1E-8 :
(X³ + AX² + BX + C) ÷ (3X² + 2AX + B) → Y :
X – Y → X :
WhileEnd: X
We could have used the derivative function (d/dx) but typing out the derivative took less room.
Example 1: X³ + 2X² – 5X + 4 = 0
Inputs: A = 2, B = -5, C = 4
Output: -3.663076827
Example 2: X³ – 3X² + 9X + 6 = 0
Inputs: A = -3, B = 9, C = 6
Output: -0.5481911635
Program 3: Sum of the polynomial: Σ((AX + B)^C, X = 1 to Y)
fx-3650P, 57 bytes:
0 → M : ? → A : ? → B : ? → C : ? → Y : 1 → X :
Lbl 0 :
(AX + B)^C M+ : X + 1 → X : X > Y ⇒ Goto 1 : Goto 0 :
Lbl 1 : M
fx-3650PII, 41 bytes:
0 → M : ? → A : ? → B : ? → C : ? → Y : 1 → X :
For 1 → X To Y : (AX + B)^(C) M+ : Next : M
Example 1: Σ((5X – 3)^2, X = 1 to 8)
Inputs: A = 5, B = -3, C = 2, Y = 8
Output: 4092
Example 2: Σ((2X + 1)^3, X = 1 to 10)
Inputs: A = 2, B = 1, C = 3, Y = 10
Output: 29160
Program 4: Complex Roots of Unity
x^n = 1
where:
x = cos(2 * m * π / n) + i * sin(2 * m * π / n) = r * e^(2 * m * i / n)
m = 0 to n – 1, i = j = √-1
fx-3650P, 47 bytes:
Switch to complex mode. The CMPLX indicator will be displayed but not shown as a step.
Rad : ? → A : 0 → B :
Lbl 0 :
cos(2 B π ÷ A) + i × sin(2 B π ÷ A) ◢
1 + B → B : A > B ⇒ Goto 0 : 1
We must have an else condition when the jump command is used, that is why the second one is there. Also, that one “indicates” the end.
fx-3650PII, 34 bytes:
Rad : ? → A :
For 0 → B To A :
cos(2 B π ÷ A) + i × sin(2 B π ÷ A) ◢
Next : 1
The second one “indicates” the end and can be omitted.
In complex mode, the real and imaginary parts are displayed on part at a time. A settle R←→I indicator displays at the right hand side of the screen. Switch between seeing the parts by pressing [ SHIFT ] [ EXE ].
Example 1: x^3 = 1
Input: A = 3
Outputs:
1 + 0 i
-0.5 + 0.866025403 i
-0.5 - 0.866025403 i
Example 2: x^5 = 1
Input: A = 5
Outputs:
1 + 0 i
0.309016994 + 0.951056516 i
-0.809016994 + 0.587785252 i
-0.809016994 - 0.587785252 i
0.309016994 - 0.951056516 i
Eddie
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