Conventions
-----------
-> represents the key that stores data into a variable.
This is the key
straight above the "DEL" key.
^ represents an expontent. This
is the key straight above the "AC" key.
(e.g. 2^4 = 16)
e represents scientific notation. This
is the "EXP" key on the bottom row,
exactly in the middle (e.g.
1.2e-8 = 1.2 X 10^-8)
=> represents the then conditional statement.
Push: "shift", "Range",
F1, F1.
# represents the display symbol.
Push: "shift", "Range", F5.
theta represents the symbol theta. Push: "ALPHA", "Range".
PI represents the symbol for pi. Push shift
"EXP". (i.e. 3.14159...)
/ represents the division symbol.
(i.e. 6/3 = 2)
* represents the multiplication symbol.
(i.e. 6*3 = 18)
f_1 represents function 1 on the function menu. Push:
"shift", "0", F3, 1.
All programs assume that any function
on the function menu is stored in
with X as its independent variable.
<= represents less than or equal to. Push:
"shift", "Range", F2, F6.
$ represents the integral sign. Push:
shift "X,theta,T". "X,theta,T" is
the key on the far left,
third from the top.
Abs represents absolute value. Push: "shift", "Graph",
F3, F1.
For simplicity I will represent
the square root as a quantity to the
one-half power. So, the
square root of x is (x)^.5. Also notice the
difference between the letter
"O" and the number 0.
"MAIN MENU" will
'CIRCLE' will graph
'ELLIPSE' will graph
access any program
a circle given the
an ellipse given the
by entering the
radius and coordinates
corresponding
number on the menu.
of the center.
coefficients.
Prog 0
Prog 1
Prog 2
"MAIN MENU"
'CIRCLE'
'ELLIPSE'
"1. COMPUTATION"
" "
"(X-H)^2 + (Y-K)^2 = 1"
"2. GRAPHING"?->theta
"(X-H)^2 + (Y-K)^2 = R^2"
" A^2 B^2"
theta=1=>Goto 1
"H="?->H
" "
theta=2=>Goto 2
"K="?->K
"(X-H)^2 + (Y-K)^2 = 1"
Lbl 1
"R="?->R
" B^2 A^2"
"1. QUADRATIC"
Range H-4.7, H+4.7, 1,
"1 OR 2"?->Z
"2. SUMMATION"
K-3.1, K+3.1, 1, 0, 2PI,
Z=1=>Goto 1
"3. TRAPEZOIDAL"
PI/36
Z=2=>Goto 2
"4. SLOPE"
Graph Y=(R^2-(X-H)^2)^.5
Lbl 1
"5. SIMPSON'S"
+ K
"A="?->A:"B="?->B
"6. NEWTON'S"
Graph Y=-(R^2-(X-H)^2)^.5
"H="?->H:"K="?->K
"7. CONSTANTS"?->r
+ K#
Range H-4.7, H+4.7, 1,
r=1=>Prog 5
K-3.1, K+3.1, 1, 0, 2PI,
r=2=>Prog 7
'PARABOLA' will graph a
PI/36
r=3=>Prog 8
parabola given the
Graph Y=
r=4=>Prog A
coefficients.
((1-(X-H)^2/A^2)B^2)^.5
r=5=>Prog E
+ K
r=6=>Prog F
Prog 3
Graph Y=-
r=7=>Prog G
'PARABOLA'
((1-(X-H)^2/A^2)B^2)^.5
Goto 3
"(X-H)^2 = 4P(Y-K)"
+ K#
Lbl 2
"(Y-K)^2 = 4P(X-H)"
Lbl 2
"1. CONICS"
"1 OR 2"?->Z
"A="?->A:"B="?->B
"2. TANGENT"
Z=1=>Goto 1
"H="?->H:"K="?->K
"3. CONNECT"
Z=2=>Goto 2
Range H-4.7, H+4.7, 1,
"4. CENTROID"
Lbl 1:"H="?->H
K-3.1, K+3.1, 1, 0, 2PI,
"5. TANGENT-PARAM"
"K="?->K
PI/36
"6. CONICS 2"?->Z
Graph Y=
Graph Y=
Z=1=>Prog 6
((X-H)^2 / (4P)) + K#
((1-(X-H)^2/B^2)A^2)^.5
Z=2=>Prog 9
Lbl 2:"H="?->H
+ K
Z=3=>Prog B
"K="?->K:"P="?->P
Graph Y=-
Z=4=>Prog C
Graph Y=(4P(X-H))^.5 + K
((1-(X-H)^2/B^2)A^2)^.5
Z=5=>Prog D
Graph Y=-(4P(X-H))^.5 + K#
+ K#
Z=6=>Prog H
Lbl 3
'QUADRATIC' will find the
'CONICS' is a menu
roots of a quadratic given
for the conics programs.
'HYPERBOLA' will
the coefficients.
graph a hyperbola
Prog 6
given the
Prog 5
"CONICS"
coefficients.
'QUADRATIC'
"1. CIRCLE"
" ":" "
"2. ELLIPSE"
Prog 4
"(-B+-(B^2-4AC)^.5)"
"3. PARABOLA"
'HYPERBOLA'
" 2A"
"4. HYPERBOLA"?->A
"(X-H)^2 - (Y-K)^2 = 1"
"A="?->A
A=1=>Prog 1
" A^2 B^2"
"B="?->B:"C="?->C
A=2=>Prog 2
" "
((-B+(B^2-4AC)^.5 / 2A)#
A=3=>Prog 3
"(Y-K)^2 - (X-H)^2 = 1"
((-B-(B^2-4AC)^.5 / 2A)#
A=4=>Prog 4
" A^2 B^2"
"1 OR 2"?->Z
'SUMMATION' will find the
"TRAPEZOIDAL" will
Z=1=>Goto 1
sum from I to N if the
approximate the area
Z=2=>Goto 2
function is stored in f_1
under a curve if the
Lbl 1
and I and N are entered.
function is stored in
"A="?->A:"B="?->B
f_1 and the upper and
"H="?->H:"K="?->K
Prog 7
lower limits are given.
Graph Y=
'SUMMATION'
((1-(X-H)^2/A^2)*-B^2)
" ":" ":" ":" "
Prog 8
^.5+ K
" STORE EQ. IN f_1"#
"TRAPEZOIDAL"
Graph Y=-
"I="?->I:"N="?->N
"STORE FUNCTION"
((1-(X-H)^2/A^2)*-B^2)
0 -> A
"IN f_1"#
^.5 + K#
Lbl 1
"UPPER LIMIT"?->B
Lbl 2
I->X
"LOWER LIMIT"?->A
"A="?->A:"B="?->B
A + f_1 -> A
"NUMBER OF DIVISIONS"
"H="?->H:"K="?->K
Isz I
?->N
Graph Y=
I <= N => Goto 1
0 -> E
((1-(X-H)^2/-B^2)A^2)
A#
(B - A) / N -> F
^.5 + K
'SLOPE' will give
A -> X
Graph Y=-
the equation that
.5f_1 -> C
((1-(X-H)^2/-B^2)A^2)
connects 2 points.
Lbl 1
^.5 + K#
Isz E
Prog A
E = N => Goto 2
'TANGENT' will give
"SLOPE"
A + EF -> X
the equation for the
"(X,Y)"?->A:?->B
C + f_1 -> C
tangent line at the
"(X,Y)"?->C:?->D
Goto 1
entered point.
((B-D)/(A_C))->M
Lbl 2
"Y=MX + B"
B -> X
Prog 9
"M="
C + .5f_1 -> C
'TANGENT'
M#
CF#
"STORE EQ. IN f_1"#
"B="
" ":" ":" ":" "
((-MA) + B)
"WHAT IS THE"
"X COORDINATE OF"
"CENTROID" will find
"THE POINT OF"
"CONNECT" will connect
the center of a region
"TANGENCY"?->Z
a variable number of
bounded by two curves
"Y=MX + B"
points in the order
stored in f_1 and f_2.
1e-8 -> D
they are entered.
NOTE: f_1 > f_2
Z + D -> X
f_1 -> P
Prog B
Prog C
Z - D -> X
"CONNECT"
"CENTROID"
f_1 -> Q
"NUMBER OF POINTS"?->Z "STORE
EQUATIONS"
((P-Q) / 2D) -> M
"ENTER POINTS"
"IN f_1 AND f_2"#
"M ="
"IN (X,Y) FORM"
"UPPER LIMIT"?->A
M#
0 -> theta
"LOWER LIMIT"?->B
Z -> X
Lbl 1
"2^N DIVISIONS"?->C
f_1 -> R
"X"?->A[theta]
$(X(f_1-f_2),B,A,C->U
(-MZ + R) -> B
"Y"?->A[theta + 1]
$(.5(f_1^2-f_2^2,B,A,C
"B= "
theta + 2 -> theta
->V
B#
theta < 2Z => Goto 1
$(f_1-f_2,B,A,C->W
"SET RANGE"
0 -> theta
"X="
"1. YES"
Lbl 2
U/W#
"2. NO"?->T
Plot A[theta],A[theta+1]
"Y="
T=2=>Goto 1
theta + 2 -> theta
V/W#
Range Z-4.7,Z+4.7,1,
Plot A[theta],A[theta+1]
Range (U/W)-4.7,(U/W)+
R-3.1,R+3.1,1,0,
Line
4.7,1,(V/W)-3.1,(V/W)+
360,3.6
theta=2Z-2=>Goto 3
3.1,1,0,360,3.6
Lbl 1
Goto 2
Graph Y=f_1,[B,A]
Graph Y=f_1
Lbl 3
Graph Y=f_2,[B,A]
Graph Y=MX +B#
Plot A[0],A[1]
A -> X
Plot A[2Z-2],A[2Z-1]
Plot A, f_1
"TANGENT-PARAM" will
Line#
Plot A, f_2
find the cartesian
Line
formula for a tangent
"SIMPSON'S" approximates
B -> X
line at the entered
the area under a curve
Plot B, f_1
point.
by using simpson's rule.
Plot B, f_2
Line#
Prog D
Prog E
"NEWTON'S METHOD"
"TANGENT-PARAM"
"SIMPSON'S RULE"
approximates the zero
"STORE X IN f_1"
"STORE EQUATION"
of a function stored
"STORE Y IN f_2"
"IN f_1"#
in f_1 and the
"POINT OF"
"UPPER LIMIT"?->B
derivative stored in
"TANGENCY"?->A
"LOWER LIMIT"?->A
f_2.
"Y=MX+B"
"2^N DIVISIONS"?->N
1e-8 -> D
((B-A)/2^N)->D
Prog F
A + D -> T
0->K
"NEWTON'S METHOD"
f_1 -> T
A -> X
"STORE FUNCTION
f_2 -> Q
f_1 -> C
IN f_1 AND DERIVATIVE
A - D -> T
Lbl 1
IN f_2"
f_1 -> R
Isz K
"INITIAL GUESS"?->G
f_2 -> S
A + KD -> X
"DECIMAL"
((Q-S)/(P-R))->M
4f_1 + C -> C
"ACCURACY"?->T
"M="
Isz K
Lbl 1
M#
A + KD = B=>Goto 2
G -> X
A -> T
A + KD -> X
(X - f_1/f_2) -> O
"B="
2f_1 + C -> C
Abs(G-O) < T => Goto 2
((-Mf_1) + f_2)#
Goto 1
O -> G
Lbl 2
Goto 1
B -> X
Lbl 2
"CONSTANTS" will
f_1 + C -> C
O#
store certain
((B-A)/(3*2^N))*C#
fundamental
constants in certain
"CONICS 2" will
letters and then will
tell what type of
display which letters
conic an expression
contain which values.
is and then will
graph it.
Prog G
"CONSTANTS"
Prog H
"ELECTRONIC"
"CONICS 2"
"CHARGE = Q"
"AX^2 + BXY + CY^2 +"
1.60217733e-19 -> Q
"DX + EY + F"
Q#
"A(X^2)"?->A
"PLANK'S = H"
"B(XY)"?->B
6.6260755e-34 -> H
"C(Y^2)"?->C
H#
"D(X)"?->D
"AVAGADRO'S = N"
"E(Y)"?->E
6.0221367e23 -> N
"F"?->F
N#
B^2-4AC<0=>"ELLIPSE, A
"BOLTZMANN'S = K"
POINT, OR NOTHING."#
1.380658e-23 -> K
B^2-4AC>0=>"HYPERBOLA,
K#
A PAIR OF INTERSECTING
"RYDBERG = R"
LINES, OR NOTHING."#
1.0973731534e7 -> R
B^2-4AC=0=>"PARABOLA,
R#
LINE, OR A PAIR OF
"GRAVITATIONAL"
PARALLEL LINES."#
"CONSTANT = G"
Graph Y=((-BX+E)+
6.67259e-11 -> G
((BX+E)^2-4C(AX^2+DX+
"MOLAR GAS"
F))^.5)/2C
"CONSTANT = r"
Graph Y=((-BX+E)-
8.314510 -> r
((BX+E)^2-4C(AX^2+DX+
r#
F))^.5)/2C#
"PERMITIVITY"
"OF A VACUUM = E"
8.854187817e-12->E
E#
"SPEED OF"
"LIGHT = C"
299792458->C
C#