Integral 3D GThis program allows the user to estimate triple integrals. The programNcan be used for integrals in rectangular, cylindrical or spherical coordinatesGThe user may specify any of the 6 possible orders of integration. The Mestimates start out with 4 intervals in each direction. This number doubles Iwith each approximation. Therefore, the amount of labor for the program Nincreases by a factor of 8. With each new approximation, about 2 more digits Jof accuracy are obtained. Therefore if the last two estimates agree to 3 Oplaces, the last one is probably accurate to 5 places. The run of the program "may be halted by pressing any key.
This program was produced at The United States Naval Academy.
Press any key to continue
Insert
INTEGRALS 3D
F1 &1-Rec. 3D, 2-Cylindrical, 3-Spherical
CTRL-t for
, CTRL-s for
Order d
b
h(
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
.i31>Error in file name, please reenter. Press any key to continue
Data saved in file
. Press any key to continueU
Restore file Name -No file name given, press any key to continue
.i31-Error in file name, press any key to continue
r
p^2 sin
Data restored from file
. Press any key to continueU
r
p^2 sin
Are you sure?
Value of a is incorrect
Value of b is incorrect
b must be greater than a
Error in g()
Error in h()
Error in u(,)
Error in v(,)
)*x*x*sin(z)
Error in function definitionU
?<3u;
n estimate of the integral
Integral found to 5 digitsU
Press any key to continueU
7 < A U Z _ t
! ; T m z
!+!0!C!H!a!f!
"("-"E"S"e"j"w"
#)#.#;#N#S#k#y#
$/$=$O$T$a$t$y$
%;%J%V%[%
&C'K'S'u'z'
***<*A*a*f*s*x*
,7,<,I,N,W,d,
.)...
.F/K/X/k/
0(0-0:0M0u0
1!1.1A1i1|1
2!242\2o2
3&3+3E3J3d3i3
43484Y4^4
5!5/5=5G5W5a5w5
6R6\6s6
7'777N7^7n7
8"858>8G8L8d8w8
9 9!949>9U9e9u9
:%:.:3:K:b:{:
;1;6;P;U;n;s;
=!=4=F=K=
?7?M?c?y?
@#@I@
@,AKAPAYArA
C6CUC^C
C<DJDXD
E3EEEJE
E Implicit GThis program allows the user to graph an implicity defined function andKup to 6 lines tangent to the graph. The user inputs the window boundaries,FXmin, Xmax, Ymin and Ymax. The user next inputs the implicity definedIfunction in the form, f(x,y)=0. Next, the user may enter up to 6 tangent@lines. These may either be entered in the form y=mx+b or x=ny+c!This program was produced at the
U.S. Naval Academy
Press any key to continue
<
U
Insert
Implict
Xmin
Xmax
Ymin
Ymax
f(x,y)=
CTRL-O
for Options menu,
CTRL-F
for Function ListU
Save file Name
.im1-Error in file name, press any key to continue
Data saved in files
and
. Press any key to continueU
Restore file Name -No file name given, press any key to continue
.im1-Error in file name, press any key to continue
Data restored from files
and
. Press any key to continueU
Are you sure?
Value of Xmin is incorrect
Value of Xmax is incorrect
xmax must be larger than xmin
Value of Ymin is incorrect
Value of Ymax is incorrect
Ymax must be larger than Ymin
Error in function definition
Error in line equation
7<Hu
*<Pu
Please waitU
<-----X----->
<-----Y----->U
U
# 5 : ? L ^ c h }
!!"4"N"S"X"e"x"
#2#L#Q#V#c#v#
$0$`$l$q$
%H%T%Y%r%w%|%
'7'Q'V'['u'z'
(((-(2(K(P(U(o(t(y(
) )%)*)C)H)M)e)j)o)
*!*+*;*D*P*U*s*
+'+E+]+h+
,=,M,`,s,
-.-K-x-
.!.;.@.E.^.c.h.
/3/8/=/W/\/a/z/
0'0,090K0P0U0Z0
1=1J1i1u1}1
2+282@2L2[2c2l2
3&3K3W3d3l3t3
5:6|6
6?7~7
8D8e8q8~8
8#9/9<9D9L9]9
:@:L:Y:a:i:z:
;";b;j;
<Q<r<~<
=0=<=I=Q=Y=j=
>Q>r>~>
?0?<?I?Q?Y?j?
@Q@r@~@
A0A<AIAQAYAjA
BQBYB
C4C@CMCUC]CnC
D"DbDjDrD}D
E&E7E
E+F3F;FFFgFsF
H0H<HIHQHYHjH
H)IkIsI
J)JNJZJgJoJwJ
J*K2KrKzK
L&L.L6LGL
MaNiN
O7OHOZOhO
PIPUPbPjPrP
Q8Q=QFQVQ
R5R?RQR^RcRhR
S7SASoS
T0TXTdTlTyT
T(U;UDUuU
< U
Integral 2D GThis program allows the user to estimate double integrals. The programGcan be used for integrals in rectangularor polar coordinates. The userGmay specify either possible order of integration. The estimates start Gout with 4 intervals in each direction. This number doubles with each Iapproximation. Therefore, the amount of labor for the program increasesGby a factor of 4. With each new approximation, about 3 more digits of Gaccuracy are obtained. Therefore if the last two estimates agree to 3 Oplaces, the last one is probably accurate to 6 places. The run of the program "may be halted by pressing any key.
This program was produced at The United States Naval Academy.
Press any key to continue
Insert
Integral 2D
1-Rec. 2D, 2-Polar
CTRL-t for
b
h(
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
.i21>Error in file name, please reenter. Press any key to continue
Data saved in files
and
. Press any key to continueU
Restore file Name -No file name given, press any key to continue
.i21-Error in file name, press any key to continue
Data restored from files
. Press any key to continueU
Are you sure?
Value of a is incorrect
Value of b is incorrect
b must be greater than a
Error in g()
Error in h()
Error in function definitionU
<-----X----->
<-----Y----->
n estimate
Integral 5 digitsU
U
! & 3 E J O \ m r w
!+!4!F!T!n!
!3"@"Q"V"["h"y"~"
#"#+#=#K#e#
$7$H$M$R$p$u$z$
%/%B%\%a%f%s%
&-&@&Y&^&c&p&
' '%'>'C'H'a'f'k'
(!(O(T(u(z(
)#)()5):)B)P)^)c)x)
)#*3*d*n*
+%+.+3+K+^+h+
,3,8,Q,V,[,t,y,~,
-%-*-/-H-M-R-\-a-
.&.7.Z.c.
/ 0,0H0V0l0
1&121Q1^1}1
2$2,282A2Y2b2
3(393J3m3v3
4&4F4W4h4
575D5d5u5
6#6/6G6\6r6|6
7A7J7q7
898w8
9#919G9l9z9
:#:=:J:d:p:x:
;(;@;I;w;
< <1<T<]<
=-=>=O=r={=
>+>K>\>m>
?.?C?Y?c?
@F@v@
@DA\AvA
A&BABIBUB^BvB
C*C=CNC\CxC
D2DCDQDsD|D
E#E4EEEhEqE
F&F9FJFXFtF
GBGcGoG
G8HlH|H
I6I>IRIWI
J(J5JgJyJ
KDKVKgKzK
L"L>LKLkL|L
M9MBM]MnM
N.N7NRNcNvN
O-O6OYObO
P!P)P3PwPGQTQfQkQpQ
R&R7RoR}R
S%SdSrS
S%T3TAT
U1UBU]UoUtUyU
; U
Vector Field ?This program allows the user to plot vector fields in the form:
f1(x,y)i+f2(x,y)j.JThe user may specify the area of the plane to be plotted using Xmin, Xmax,GYmin and Ymax. The user may also choose the number of points where theIvector field will be drawn. Up to 20X20 points may be specified. Ten is
a good starting point.
This program was produced at The United States Naval Academy.
Press key to continue
Insert
Vector Field
Xmin
Xmax
Ymin
Ymax
F3 #Number of points per line (20 max)
f1(x,y)
f2(x,y)
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
.vf1>Error in file name, please reenter. Press any key to continue
Data saved in files
and
. Press any key to continueU
Restore file Name -No file name given, press any key to continue
.vf1-Error in file name, press any key to continue
Data restored from files
. Press any key to continueU
Are you sure?
Value of Xmin is incorrect
Value of Xmax is incorrect
xmax must be larger than xmin
Value of Ymin is incorrect
Value of Ymax is incorrect
Ymax must be larger than Ymin
Number of intervals is wrong
Error in number of intervals
Must have 1<=# of intervals<=20
Error in function definitionU
<-----X----->
<-----Y----->U
U
# ( - : L Q V c u z
# 1 6 K U k
!1!<!Z!r!}!
")"9"K"j"}"
#5#:#?#Y#^#c#}#
$#$<$\$y$
%0%J%R%W%w%
&'&G&L&Z&h&
'+'Q'n'
(((5(T(`(
)#)-)=)G)U)i)n)
*W*c*o*w*
+ +(+9+\+t+}+
,B,a,i,v,
-%-F-
-/.;.G.O.W.h.
<
Contour ?This program allows the user to plot contour lines of the form: f(x,y)=c.KThe user may specify the region of the plane to be plotted by giving valuesIfor Xmin, Xmax, Ymin and Ymax. Up to 15 contour lines may be plotted forEdifferent values of c by specifing a smallest value, c_min, a largest8value, c_max and a number of contour lines to be plotted
This program was produced at The United States Naval Academy.
Press any key to continue
Insert
Contour
Xmin
Xmax
Ymin
Ymax
f(x,y)=
No. of contours (15 max)
Min contour value (c_min)
Max contour value (c_max)
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
.cn1-Error in file name, press any key to continue
Data saved in files
and
. Press any key to continueU
Restore file Name -No file name given, press any key to continue
.cn1-Error in file name, press any key to continue
Data restored from files
. Press any key to continueU
Are you sure?
Value of Xmin is incorrect
Value of Xmax is incorrect
xmax must be larger than xmin
Value of Ymin is incorrect
Value of Ymax is incorrect
Ymax must be larger than Ymin
Error in function definition
Error in number of contours%Number of contours must be an integer
Error in c_min
Error on c_max"For one contour c_max must = c_minU
Please waitU
<-----X----->
<-----Y----->U
CNot enough memory to run contour plotter, press any key to continueU
- 2 7 D V [ ` u
4 9 > X ] b |
!;!@!\!a!
"""'"/"="K"P"e"o"
# #3#K#V#t#
$7$B$]$n$~$
%%%=%H%v%
&"&<&A&F&`&e&j&
' '2'7'<'A'k'p'|'
($(1(P(\(d(w(
)')3)B)J)S)t)
*2*>*K*S*[*l*
,!-c-
-&.e.
.+/L/X/e/m/u/
0#0+030D0i0u0
1'131@1H1P1a1
2 2I2Q2
283Y3e3r3z3
4#40484@4Q4v4
485Y5e5r5z5
6#60686@6Q6v6
687Y7e7r7z7
8#80888@8Q8v8
889@9
:':4:<:D:U:
; ;I;Q;Y;d;
="=-=N=Z=g=o=w=
?#?0?8?@?Q?v?
@R@Z@
A5AAANAVA^AoA
BYBaBiBtB
CoDwD
DHEPE
F:FfFtF
G0GIGNGSG
G!H-H:HBHJH[H~H
J)J.J7JHJSJ
J=
U
Slope LThis program uses the slope of secant lines to approximate the derivative. KThe program draws secant lines from the point, x0, at which the derivative Lis to be approximated to points both to the left and the right of the point.HThe slopes of these lines are computed and shown on the left side. The Ginitial distance is 1 unit. This distance is then cut in half and the Iprocedure is repeated. When the points get close to x0, the program will:rescale the graph. The user can stop the run at any time.
This program was produced at The United States Naval Academy.
Press any key to continue
Insert
Slope
f(x)=
x0=
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
.sl1-Error in file name, press any key to continue
Data saved in files U
Restore file Name -No file name given, press any key to continue
.sl1-Error in file name, press any key to continue
Data restored from file U
Are you sure?
Error in function definition
Error in x0U
Rescaling
<-----X----->
<-----Y----->
Any key stopsU
<-----x----->
<-----y----->
Any key stops
U
4 J _ q v {
9 U b
!Q!^!}!
"."7"p"
#>#R#p#
#-$I$V$u$
%b%o%
&.&7&l&
'5'='k'
(+(D(I(h(
)()-)A)Z){)
<
Integral
Trapezoidal rule
Simpson's rule
Left endpoints
Right endpoints Midpoints
rAndom points
Integral is approx.U
o<Mu5
6<Au2
Integral 5This program computes approximations to the integral,
f(_) d_
aJwhere the independant variable, _, may be x, y, z, or t. The function, f,Kmay be a multiline defined function with up to 3 parts. Approximations may?be computed using Riemann Sums with the function evaluation at
eft endpoints,
ight endpoints,
idpoints, r
ndomly choosen points or
rapozoidal or
impson
s :rule. Up to 3 approximations may be computed at one time.
This program was produced at The United States Naval Academy.
Press any key to continue
Insert
off Integral
Independent variable (x,y,z,t)
Interval of integration, a
Func.(part 1)
Interval a1=a
(For multiline functions only)
Func.(part 2)
Interval a2=b1 b2
Func.(part 3)
Interval a3=b2 b3=b eft pts,
ight pts,
idpoints, r
ndom pts,
rapozoidal rule,
impson
s rule Method 1
Number of intervals (998 max) Method 2 Method 3
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
.in1-Error in file name, press any key to continue
Data saved in files
and
. Press any key to continueU
Restore file Name -No file name given, press any key to continue
.in1-Error in file name, press any key to continue
Data restored from files
. Press any key to continueU
Are you sure?
Variable not allowed
Value of a is incorrect
Value of b is incorrect
b must be larger than a
Error in function definition
Error in value of b1
b1 must be larger than a
b1 must not be larger than b
Error in b2
b2 must be greater than b1"b2 must be less than or equal to b
Check independant variable
Technique incorrect
Error in number of intervals$Number of intervals must be positive"Maximum number of intervals is 998/For Simpson`s rule, # of intervals must be even#Integral is 0, try another functionU
G<Hu
:<Pu
-<Qu
U
2 7 <
* / 4 A S X ] j |
!#!+!=!B!G!O!\!l!q!v!~!
"!"&".">"C"H"P"b"g"l"t"
#$#6#;#@#H#P#]#o#t#y#~#
&'&,&1&F&X&e&j&o&
'0'B'G'L'Y'j'o't'
( (5(G(L(Q(^(p(u(z(
)!)&);)M)R)W)d)v){)
***/*4*A*S*X*]*r*
+,+1+6+C+S+X+]+j+|+
,!,&,3,C,H,M,Z,l,w,
-/-4-9-N-`-e-j-w-
.".3.8.=.J.\.a.f.s.
/1/6/;/@/
0%0/0=0P0^0q0
1&101>1N1X1f1y1
2"2'292G2U2h2v2
3!3/3B3P3_3m3{3
4 4*4/4C4H4c4h4
5'5K5Z5f5k5
7)7;7@7E7O7n7s7
8(828I8N8e8j8
9*9;9@9M9`9e9}9
:%:*:7:J:O:g:u:
;*;/;<;O;T;k;p;};
< <3<8<P<^<p<u<
="=4=9=F=Y=^=v=
>6>;>k>p>z>
???Q?V?[?`?i?n?s?
BkBsB{B
C3C8C=CJC]C
D/DBDjD}D
E6ETEnEzE
F,FJFVF[F
G#G(G5G:GLGXG
I.I3IEIQI
K!K.KGKLKeKjKoK
L"L;L@LEL_LdLiL
M3M8M=MBMjMoM
N-N?NDNINNNVNdNrNwN
O&O>OUO^O
O'P0PWPxP
Q(Q@QIQpQ
R)R_R
RMSiS
T8TsT
U*U=UVUfUrUwU
VAVQVdV}V
W%W=WFWhWxW
X,YHY|Y
ZRZbZyZ
[![:[?[D[^[c[h[
\3\8\=\V\[\`\y\~\
\ <
U
<-----X----->
<-----Y----->U
Rescaling
Any key stopsU
Root .This program will find the root of an equation
by using one of three methods.The methods are: bisection, secant, and Newton
This program was produced at
The U.S. Naval Academy
Press any key to continue
Insert
Root
method (
isection,
ecant,
ewton
function
derivative
Xmin
Xmax
Ymin
Ymax
Ymin and Ymax are optional
F5 Number of digits accuracy (1-6)
CTRL-o
for Options menu,
CTRL-f
for function listU
Save file Name
#-Error in file name, press any key to continue
Data saved in filesU
Restore file Name -No file name given, press any key to continue
.rt1-Error in file name, press any key to continue
Data restored from file U
bisection secant Newton's
Are you sure?
Error in X_max
Error in X_min
X_max must be larger than X_min
Error in deriviative definition
Error in function definition
&Can not find root of constant function
Error in Y_max
Error in Y_min Y_min must be smaller than Y_maxU
Any key stops
Function not defined
Exact root found
Der. not defined
Derivative 0 # iters.
Root found
digitsU
Any key to stop
May not be root between
and
is an exact root
Iteration
Exact root
Root found
digitsU
Any key stops
May not be root between
and
is an exact root
Iteration
Exact root
Root found
digitsU
F1 to return
to menu or
enter guess
Input error
Any key
to continue
Enter lf endpt
Enter rt endptU
U
Q ] k w
, ? D \ j |
! !.!@!E!R!e!j!
"#"H"Z"_"d"m"r"w"
$c$k$s$
&8&=&J&]&
','1'>'Q'y'
( (%(2(E(m(
)()-)?)K)
+!+&+4+<+U+Z+t+y+
,+,0,H,M,R,z,
-=-O-T-Y-a-o-}-
.0.9.m.
/%/8/P/_/
0"090B0v0
1,1F1K1e1j1
3:3I3[3`3j3|3
4%474<4d4z4
5#545F5V5[5h5y5
6<6\6a6j6r6
9@9I9p9{9
:3:I:i:n:
;1;6;?;_;
<+<7<U<^<z<
=+=2=C=U=Z=l=q=
>6>V>
@)@6@U@`@y@
B:BCBfBoB
C8CCCYCoC
D D4D9DJD\DuDzD
E0ESE\E
F,F>FTFYFvF
G3GVGyG~G
I,IQI^I}I
J&J"K,KPKaKsKxK
L$L1LCLZLlLqL
M!M9MBMeMwM|M
N0NCNUNZNlNqN~N
O'O,O=OOOTOYO^OgOlO
Title:
Xmin :
Xmax :
Xtick:
Ymin :
Ymax :
Ytick:
. y = f(x) ==>
y = g(t) ==>
xstep
modify
color
F6 other fns
save
F8 load file
display
quitU
Insert On
Insert OffP
BS DEL HOME END INS(toggle ON or OFF) ^HOME(del line)
(prev/next field) U
***U
y = f(x)
x = g(y)
r = f(t)
datafile
==> U
Mathematics Plotting Program
CTRL-o
for Options menu,
CTRL-f
for function list
Xmin :
Xmax :
color"Only function color can be changed
quit
Are you sure? (Y/N)
modify)Modify key can only be used on a function0Can't modify a function which is already defined other fnsU
Min is not less than Max
Step must be positiveU
Unable to open data file U
Illegal function definition
Illegal constant definition
Min is not less than Max
Xmin :
Xmax :
Xtick:
Ymin :
Ymax :
Ytick:
Title:
<-----X----->
<-----Y----->
Illegal format in data file
Undefined function
when
Mathematics Plotting Program LThis program will plot up to 6 equations. The equations can be in the form Jy=f(x), x=g(y), polar, parametric or from a datafile. To change the type,Hmove the cursor to a function input line and press F4 while the line is Iblank. To blank an input line press ctrl-home. F6 displays the other 3 3function input boxes. This program was written at The United States Naval Academy.
/PageLen 11 def!/LabelSize 10 72 div 3.75 div def /TextSize 12 72 div 3.75 div def!/Numsize 8 72 div Scaleby div def@Transby 1 add inch PageLen 1 sub inch Scaleby inch sub translate