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IN0N18 HCSC(U(I,J)HS),VCSC(V(I,J)VS)B IL)HS),VCSC(V(I,1)VS)H*** TRY TO INSERT TEST FOR X AND Y EQUAL 0TJ2NP~HCSC(U(I,J)HS),VCSC(V(I,J)VS)JIJ1NP22:F$:A2$"CURVE FOR Y="ITYPE6A2$"CURVE FOR THETA="ZBLY(J1)DY22:F$:H'RA1$"CURVE FOR X=":\ZALX(I1)DXufITYPE6ZAZI(I1)(ZOZI)(DZ1):A1$"CURVE FOR Z="pIPE3ZAZI(I1)(ZOZI)(DZ1):A1$"CURVE FOR Z=":IDZZAZI(IDZ1)(ZOZI)(DZ1):ZA02230z21:A1$;ZAHCSC(U(I,1HTLHLHHTVTUVUVVT0VTLVLVVTHU(I,J)HT:V(I,J)VTSYYDYZJhXXDX:I~HRUHLH:VRUVLVMRHR:VRMRMRVR SC158MRHS(UHLH)2:VS(UVLV)2 HC140:VC80*:(7):"READY?";F$::34I1N1 >XLX:UH999999:LHUH*UVUH:LVLH6&I1NP?0YLYK:J1NPWDZA(X)nNSLXA1YA2ZA3ybTL2SlT2L2TLvX0T2A1TXY0T2A2TYZ0T2A3TZHT(X0B1Y0B2)VT(X0C1Y0C2Z0C3)HTUHUHHTAT LINE 2":*rB"INSERT IT IN THE FORM:"H|B:" 2 DEF FNA(X)=..."pB:"AFTER YOU DO THIS, TYPE 'RUN'."vBBX)>XV,XATPXV,XABO>4>YVAYD2(UYYV)K>YALE,YVYART,YVQ>ZH?DD1lR?CRDDD.5{\?CRDDD2f?I11000p?DDDDDz?(CRDD)(D1)I1000?(CRDD)(D1)I1000?I?SFDD4? hB:"INSERT YOUR FUNCTION OBYBO0XVAXD1(XVL#4MX(UXLX)2:UXMXC2:LXMXC2F5MY(UYLY)2:UYMYC2:LYMYC2L 5X6LIDO1k6XP(XF),YP(YF)w6NP1ı6XJXF:YJYF6KK2NP6XJXJXI:YJYJYI6DOēXP(XJ),YP(YJ)7LIēXP(XJ),YP(YJ)7KK7 YOUR OWN FUNCTION."5Nu:TXu"<1> X^3 + 3*X^2 - 3*X"ru:"SELECT YOUR OPTION:";u16384,0:NUM$:VV(NUM$)48uVV0VV130000uVV0ġ:20010uSW0:31000uyA(X)XXX3XX3XyB(X)3XX6)4N" WILL NEED TO INSERT A FUNCTION AT"/9N\>N" LINE 100 AND ITS DERIVATIVE AT LINE "bCN|HN" 110. FOR EXAMPLE:"MNRN" 100 DEF FNA(X) = SIN(X)"WN\N" 110 DEF FNB(X) = COS(X)"aNfN" THEN TYPE 'RUN'."pN0uSW1: :u"ERNA(X)(X)WNLX2:UX2:+R INTRO1RDR" SECANT"k&R"-----------------------------":0R"DRAWS SECANT LINES AT SELECTED POINT"::R" OF A GRAPH.":lRAN$vR8:KZ0KZ519120*JKZ0ġ:SW1:17000PKKZ20010,20020,20030,20040,20050VdKl*NA(X)2(.5XX)}/NLX2:UX2:4NA(X)XXX3XX2X9NLX.5:UX2.5:>NA(X)XXXX2XX1CNLX1.5:UX1.5:HNA(X)(X)XMNLX0:UX6:SJ)VJ"<1> F(X) = 2/( 0.5 + X^2 )"/[JU`J"<2> F(X) = X^3 - 2*X^2 + 2*X"[eJjJ"<3> F(X) = X^4 - 2*X^2 + 1"oJtJ"<4> F(X) = SIN(X) + X"yJ~J"<5> F(X) = EXP(X)"J:J"MAKE YOUR SELECTION :";JKZ$:KZ(KZ$)4TP=C>(YVLY)(YVUY)YVAYD2(UYYV):YALE,YVYART,YVI&>QhB:yrB"INPUT YOUR FUNCTION AT LINE 2.":|B" 2 DEF FNA(X)=....."B:"THEN TYPE 'RUN'."B8JSW0:LJ"THE FUNCTIONS ARE :":QJ"<0> YOUR OWN FUNCTION."~@@  B!$ !@@@@ ~`!@"@#x P @ aB #:TH0, B pIBE,4#! ")+J@~@U>P  @Y 9pHz @$ p!`@ @@>`P @H @4m xnyB1@x 0$&*(F ~ 8@A$ D0 ' ! )BLu"1@QH `EM ` pgL  @@@j|@R3 )@? @`@  x@!  @@hZ p(|q@J@!p `LT@P>( |08 @ !@# 'r*"&? @@ 25BA: A}W|@4x  @E$&Lu@SA ~x* @  `~` xq @@`0 ! rE0 x  p @ qD@p pat2&$Xu"1mJAB#Bc6AHIS PROGRAM YOU MUST"? :"INPUT YOUR FUNCTION AT LINE 250."] :"GIVE IT IN THE FORM:" :" 250 DEF FNA(X)=....." :"AND THEN TYPE RUN." :"NOTICE! FNA IS Z AS A FUNCTION OF BOTH" :"X AND Y." ITYPE7Ā  IPE3DZN12320V J?` 22:1:"OBJECT AS SEEN FROM ";L;dj 23:1:"POLAR ANGLE OF ";PHAC;t 24:1:"AZIMUTH OF ";THAC;~ " MORE?";F$:(F$,1)"Y"ė::62450: ITYPE7ĉ::62450: 62450::: :: "IN ORDER TO USE T6:X1313.1'Y(DXF)E7Y18010YMY10Y11791760^10X140,Y1dj HORIZONTAL LINES7C01880X1515.4:P(AX2DXFE2(4C))C23:P&Y1E(2C)(P):Y2E(2C)(P) 0Z0TA0H11690E^7:Y1515.4:P(CY2EYFD2(4A))AmhX1D(2A)(P):X2D(2A)(P)rZ110X1140:Z210X2140:U809Y|Z10Z1279Z20Z2279U0U1791680Z1,U:Z2,U:7:X140(FD)X,0X,159:(AC)):G3D(2A)$X2525.3JY1G1G2(XG3):Y2G1G2(XG3)oZ10X140:U1809Y1:U2809Y2Z0Z279U1179U10U20U21791580Z,U1:Z,U2"22:28:"-ASYMPTOTES-",:6 VERTICAL LINES@H11780JXT317115(WAX2CDXCFCE2(4C2)9W0W(W)GW01490iY1E(2C)W:Y2E(2C)WZ10X140:U1809Y1:U2809Y2Z0Z279U10U1179U20U21791490Z,U1:Z,U2: ASYMPTOTES1:G1E(2C):G2(:" AFTER YOU DO THIS TYPE 'RUN'."+4&I:SFSF40::CD"DEMONSTRATION OF CONVERGENCE":lN"OF UPPER AND LOWER APPROXIMATIONS"X:"TO THE DEFINITE INTEGRAL."b:l"INSERT YOUR FUNCTION AT LINE 20":v"INSERT IT IN THE FORM:":" 20 DEF FNA(X)=..."%0:RX(1)6:IX(1)0:IY(1)10?aLX(2)0:RX(2)6:IX(2)0:IY(2)7caLX(3)0:RX(3)6:IX(3)0:IY(3)6aLX(4)0:RX(4)6:IX(4)0:IY(4)2ob YLX(3)0:RX(3)20:IX(3)0:IY(3)2:IZ(3)01ZC]B(Y)ZXYa]DE$" Y'' = -( Y'/X + Y)"j]CM1]LX(1)1:RX(1)10:IX(1).001:IY(1)1:IZ(1)0]LX(2)2:RX(2)4:IX(2)0:IY(2)2^aA(Y)(Y)aDE$" Y' = SIN(Y)"aCM4aLX(1):IY(1).5:IZ(1)0?VLX(2)0:RX(2)10:IX(2)0:IY(2).5:IZ(2)1gVLX(3).5:RX(3)3:IX(3)0:IY(3).25mV~YB(Y)(Y)YDE$" Y'' = -SIN(Y)"YCM3YLX(1)0:RX(1)20:IX(1)0:IY(1)3.2:IZ(1)0YLX(2)0:RX(2)20:IX(2)0:IY(2)3.1:IZ(2)0+Y" !RCM30&RLX(1)0:RX(1)10:IX(1)0:IY(1)1<'RIZ(1)0i(RLX(2)0:RX(2)10:IX(2)0:IY(2)0:IZ(2)1*RLX(3)0:RX(3)10:IX(3)0:IY(3)1:IZ(3)1RUB(Y)Z4Y(5X)UDE$" Y'' = -Y' -4*Y + SIN(5*X)" VCM2VLX(1)0:RX(1)10:IX(1)0 THE ABOVE NUMBERS:";CH NCN0/NCH09000UNCH21000,22000,23000,24000,25000[BOfLO18000VO"PICK ONE OF THE ABOVE NUMBERS:"[OCNeOCN0ıjOX1LX(CN):X2RX(CN):XIIX(CN):YIIY(CN)oOZIIZ(CN)QRB(Y)YRDE$" Y'' = -AY CHOOSE ONE OF THESE D.E.'S"@N"OR YOU MAY ENTER YOUR OWN."HN:bN" (0) YOUR OWN D.E."{N" (1) Y'' = -Y"N" (2) Y'' = -Y' -4*Y + SIN(5*X)"N" (3) Y'' = -SIN(Y)"N" (4) Y'' = -( Y'/X + Y)"N:N"PICK ONE OFI"Y1hBqM8DS@01:8 (DL%)p `*B@#DFH6m  ( p}p@p@@@@&@@@@~~@@7=$ 01)"Y"1204 A62)(P14)Y5159Y6$X4,Y5/X5,Y5;X4X41GX5X51SX6X61cX4279770qX50770X6R1770X6R1675"PRESS 'T' FOR TEXT... ";:E$: E$"T"800 : *" ANOTHER PROBLEM (Y/N)? ";:E$::(E$," TO RETURN TO TEXT..."7:13)"'PLEASE WAIT'"HJ14000:JQ&:1\0X1140i:X2X1R1vDX3X1R1NX2,159X3,159XY3159(P14)bY4159P1l140,159140,Y3v136,Y4144,Y43X4140X5140X60 Y6(X1|"WOULD YOU LIKE A GRAPHIC DISPLAY? ";:D$:F(D$,1)"Y"500Lh START GRAPHIC DISPLAY:" FOCAL POINT OF PARABOLIC: ";P1" RADIUS OF PARABOLIC: ";R1"*NOTE: RESOLUTION OF X-AXIS MUST = 1" :" AFTER DISPLAY TYPE 'T' "A(K)A(K)940%A(K)0890/"+";?A(K)1960NA(K);"*";X"X";eK2990s"^";K1;{Z0KA(1)01070A(1)01050"+";A(K);$."-";8A(1)A(1)B1040LNA(J)A(J)XA(J1)XX1%J6A(K)A(K)C=KNA(M)A(M)CV ,p  , PRINT POLYNOMIAL:x , Z1*M110404KM21>A(K)01000HZ0920RA(K)1870\"-";f(A(K))1960p940z"-"; MKK& ,30 , SCALE COEFFICIENTS:;: ,DDC1TNKM111_XCCKpbA(K)CA(K)wlKv ,  , COMPUTE COEFFICIENTS OF EXPANDED POLYNOMIAL: ,ULM1K1M1UU1XUJM1K10) ,L0RADSTP" 6XAXA(L)1 @YAYB(L)Q J(X1X279Y1Y159)350[ TX,Yb ^Lh hp r23 |"DO YOU WANT TO DO THIS AGAIN? ";S$ (S$,1)"Y"10 :A ";A$ (A$,1)"Y"100" :4 10:18:"OK"D Q1500:QL : XX79Y79)ĪSSQUARESS1, LSQUARELS1K A(((SSLS)100)100)100x 22:"POINTS PLOTTED: ";LS;" AREA: ";A X,Y K(16384) K127990 130 23 "POINTS INSIDE SMALL SQUARE: ";SS 24:"DO YOU WANT TO DO THIS AGAIN?N IN THIS AREA." 4D 7"THE CALCULATED AREA SHOULD APPROACH 25"g <"AS MANY POINTS ARE PLOTTED."o A: F:"PRESS SPACE BAR TO BEGIN.":K$ d:::3 n0,0159,0159,1590,1590,0 x0,7979,7979,159 X160(1) Y160(1) (N  ::"14)"MONTE CARLO"(L8)"H.EDELSTEIN DEC 26,1979"T:"CALCULATES AN AREA BY A RANDOM PROCESS."#("POINTS ARE RANDOMLY PLOTTED IN AN AREA"-"OF 100 SQ.INCHES. A SMALLER SQUARE " 2"OF 25 SQ.INCHES IS DRAW   "BUT I'VE ONLY GRAPHED A FEW"$**U180Y19:U280Y29CZ0Z279U10U1179U20U21791970SZ,U1:Z,U2[:k EMPTY SET22:22:"NO SOLUTION" WEIRD722:"ANY ORDERED PAIR WILL WORK"X1100:P(279(3)):Q(159(3)):P,Q: 10X140:U1809Y1:U2809Y2L:Z0Z279U10U1179U20U21791870\DZ,U1:Z,U2dN:X7:YFE:0,809Y279,809Ybl INTERSECTING LINESv7X1515.1Y1XD(2A)E(C2):Y2XD(2A)E(2C)Z10X140::AòMAGAZINE.&òENTERED AND MODIFIED?òBY HARRY OWEN JONESOòMEMBER #62aòJAN. 9 1982.ES":"250 AND 1000."8Zú"THIS IS THE OLD LINE : ":250>dÀgnâ23:"TYPE A KEY TO EXIT ...";:A$:oxÉ:|ü50080,0ù33,11::33,40:10ÀòFROM AN ARTICLEòBY MICHAEL A. WYATTòIN THE MARCH 24 ,1981òISSUE OF ELECTRONICS S. PLEASE BE PATIENT."|'K(1)112:K(2)32.08333333:K(3)1279.000076:K(4)15623.66689:K(5)84244.16946:K(6)236957.5129'K(7)375911.6923:K(8)340071.6923:K(9)164062.5128:K(10)32812.50256:K(11)(2)'Pú:"ENTER EQUATION IN S BETWEEN LINOTHER CURVE"0t'" 'S' : END PROGRAM."8~':e'"HAS EQUATION BEEN ENTERED ? Y/N ";:A$k'}'A$"N"50000'"INPUT TIME INCREMENT : ";T':'7:"INVERSION COMPUTING"'':"THIS WILL TAKE ABOUT TWO AND A HALF":"MINUTEAY"& .'7)"------------------------", 8'g B'"ENTER EQUATION IN 'S' BETWEEN LINES":"250 AND 1000" L'"USE F(N) AS VALUE OF EQUATION" V' `'" RIGHT ARROW : MOVE CURSOR RIGHT" j'" LEFT ARROW : MOVE CURSOR LEFT" o'" RETURN : RUN ANY(I1)17000, I1,Y(I1)1I1,Y(I1)13 7C I1,Y(I1)Z I,Y(I)1I,Y(I)1d X:22 b" F(";IT;")=";(V(I)100.5)100 l4020 ': 'K(11),V(281),F(11),Y(281) $'" LAPLACE INVERSION FOR":" TIME - DOMAIN DISPL---DECREMENT CURSOR----! II10 I150408 I1? 4^ I1,Y(I1)1I1,Y(I1)1e 7v Y(I)07000 I1,Y(I1) I,Y(I)1I,Y(I)1 7000 p -----INCREMENT CURSOR---- zII1 I2796040 I279 4 Y(I)1΀V(SUMM10)10= "EQUIPROBABLE DISTRIB. OF NOS. 1 TO ";M] "AVERAGE FREQUENCY IS ";AV "WITH A HIGH OF ";HI;" AND A LOW OF ";LO "DO YOU WANT TO DO THIS AGAIN? ";A$ (A$,1)"Y"ī10 : 10:18)"THE END" P11000:P :0279,150 R1T& S(M(1)1)? "SSX,150SYB(S)SYO ,B(S)B(S)1V 6Rf @0,YMSX,Yo BHI0z DL1M FB(L)HIHIB(L) HL JLO1000 LL1M NB(L)LOLOB(L) PL T ^22 hL1M rSUMSUMB(L) |L Ax:14)"WHERE THE SET OF INTEGERS"; :14)"IS 1 TO M"C :h "WHAT IS YOUR NUMBER (M) ? ";Ms T1000 F(101000M)10 SX(279M) G100 M50G50 SY(GF) Y150(1000M)SY B(100) :3 0,00,15  16384:=(10)"THE EQUIPROBABLE DISTRIBUTION"h2::8)"H. EDELSTEIN SEPT 30,1979"P::"PLOTS 1000 RANDOM INTEGERS RANGING"Z:"BETWEEN 1 AND 100."d:10)"THE EXPECTED FREQUENCY OF"n:14)"EACH INTEGER IS 1000/M"$     X) 15XXNTER EITHER 1 OR 2";N&N0N2510,2N&Y10:Y20:X1B:X2E:20l0X10:X20:Y1YS:Y2YL:20|:Y1H1:Y2H2DX1M1M2M3NX2X1:20XX1bX1H3:X2H4lY1M4M5M6vY2Y1:20Y121:1:F$XBESYA(A(X)C1X(C2X(C3X(C4XC8)))EB(X)C2X(C5X(C6XC7))sF$"(X^4 - 2X^3 - 21X^2 + 22X - 122) / 5"yC117:C215:C32:C41:C53A(X)C2X(C1X(C4X))B(X)C1X(C3XC5)F$"X^3 - X^2 - 17X - 15""E:Y2F1:20)@X1XO:Y1F1:X2XN:Y20:20@J(16384)127360JTXOXNS^270ah16368,0jr255|"PRESS ";::" SPACE BAR ";::" TO CONTINUE.";I$:I$" "390230C124.4:C24.4:C34.2:C4.4:C58.4:C61.2:C7.8:C8.2$#M450:M550:M610:H3.1:H4.1;510:PC.0000000001JN410,460S540a:21:F$"GUESS (>90 EXITS TO MENU)";XOXO901001022:868:XOF1A(XO)"XNXOF1B(XO),(XNXO)(XN)PC370 6X1XO:Y10:X2XO3(2)68& GP3(2),Q3(2)P3(1),Q3(1):E I"PLOT SUBROUTINE ERROR":[ d SCALE CONSTANTSb n3 xXS5:XL5:YS50:YL50:10 BXS(XLXS).3 EXL(XLXS).3 S(EB)280 X-AXIS MARKS M18:M28:M31:H11:H21 Y-AXIS MARKS(G9),Q3(G9):- 7P2N0P2N2Q2N0Q2N166; 8P1P260_ 9G912:P3(G9)P1P3(G9)P264e : <G912:P3(G9)P1P3(G9)P264 = ?73 @P3(G9),Q3(G9)P2,Q2: BP1P270 CP3(1)P3(2)71 DP3(1),Q3(1)P3(2),Q3(2): FP3(1)P )G9G045* *PP1:G70P(N1G8)G7< +PN0PN245\ ,G9G9G0:P3(G9)P:Q3(G9)N1h -G90ı .P1N0P1N2Q1N0Q1N155 /P1P250 0G912:P3(G9)P1P3(G9)P253 1 2G912:P3(G9)P1P3(G9)P253 3 473 5P1,Q1P3G7(Q2Q1)(P2P1):G8Q2G7P2:G906 G80G8N134W G9G9G0:P3(G9)N0:Q3(G9)G8e !G9G045t "QG7N2G8 #QN0QN138 $G9G9G0:P3(G9)N2:Q3(G9)Q %G9G045 &PP1:G70PG8G7 'PN0PN242 (G9G9G0:P3(G9)P:Q3(G9)N0 G5,G6:B P1G1X1G2:P2G1X2G2:Q1G3Y1G4:Q2G3Y2G4Q P1P228d P1N0P1N2ıu Q1N1Q1N1 Q2N0Q2N0 Q2N1Q2N1 Q1N0Q1N0 29 P1N0P1N2Q1N0Q1N1P2N0P2N2Q2N0Q2N130 P1,Q1P2,Q2:#  100)"OPEN HIRES EXEC":33,33D"WRITE HIRES EXEC":_"CLOSE HIRES EXEC":r G1175(XLXS) G252G1XS G3159(YSYL) G4G3YLN00:N1159:N2279:G01:G5G1XG2:G6G3YG4G5N0G5N2ı G6N0G6N1     370 G(16384)128360T16368,0(^370/hIjr24:6:"PRESS ";::" SPACE BAR ";::" TO CONTINUE";|SP$:SP$" "380100I0:S.031R(NI)XR(I)YR(I)15IIS(16384)12842016368,0X(N2)2N3%OLDCLR3121:11P"R = COS (";N;" * THETA)"y:8);"PRESS ANY KEY TO STOP PLOT";(N)N400L6.28X3.14PN:X0PN2SL(50P)I0LS"R(NI),XR(I)6YR(I)@15J(TK$"Y"TK$"YES")ī150+16304,0916301,0G16300,0U16297,0lOLDCLR3OLDCLR4OLDCLROLDCLR1OLDCLR210:1XS1:XL1:YS1:YL1:10X11.6:X21.6:Y10:Y20:20X10:Y11:X20:Y21:20:"R = COS (N * THETA) "O n23:1:"ENTER NEGATIVE OR ZERO N TO EXIT PROGRAM"i x12:15:"ENTER N ";N }22:" " N0500 22:10:"DO YOU WANT TO PRINT OVER":23:12:"THE PREVIOUS PICTURE"; TK$(G9)P264 :4 <G912:P3(G9)P1P3(G9)P264: =B ?73] @P3(G9),Q3(G9)P2,Q2:k BP1P270 CP3(1)P3(2)71 DP3(1),Q3(1)P3(2),Q3(2): FP3(1)P3(2)68 GP3(2),Q3(2)P3(1),Q3(1): I"PLOT SUBROUTINE ERROR": d::10:10(G9)N1 -G90ı3 .P1N0P1N2Q1N0Q1N155A /P1P250e 0G912:P3(G9)P1P3(G9)P253k 1 2G912:P3(G9)P1P3(G9)P253 3 473 5P1,Q1P3(G9),Q3(G9): 7P2N0P2N2Q2N0Q2N166 8P1P260 9G912:P3(G9)P1P3G8 !G9G045 "QG7N2G81 #QN0QN138Q $G9G9G0:P3(G9)N2:Q3(G9)Q_ %G9G045x &PP1:G70PG8G7 'PN0PN242 (G9G9G0:P3(G9)P:Q3(G9)N0 )G9G045 *PP1:G70P(N1G8)G7 +PN0PN245 ,G9G9G0:P3(G9)P:Q3P1N0P1N2ı Q1N1Q1N11 Q2N0Q2N0B Q2N1Q2N1S Q1N0Q1N0[ 29 P1N0P1N2Q1N0Q1N1P2N0P2N2Q2N0Q2N130 P1,Q1P2,Q2: G7(Q2Q1)(P2P1):G8Q2G7P2:G90 G80G8N134 G9G9G0:P3(G9)N0:Q3(G9) 100 G1181(XLXS)- G249G1XS@ G3159(YSYL)N G4G3YLlN00:N1159:N2279:G01:G5G1XG2:G6G3YG4G5N0G5N2ıG6N0G6N1ıG5,G6:P1G1X1G2:P2G1X2G2:Q1G3Y1G4:Q2G3Y2G4P1P228      CONTINUE";!|SP$:SP$" "380*1000?I0:S.031LR(NI)YXR(I)fYR(I)n15xIIS(16384)12842016368,0370SS ANY KEY TO STOP PLOT";*(N)N400<L6.28X3.14OPN:X0PN2^SL(50P)kI0LSx"R(NI),XR(I)6YR(I)@15J(16384)128360T16368,0^370hI r24:6:"PRESS ";::" SPACE BAR ";::" TO TK$"Y"TK$"YES"Ĺ16304,0:16301,0:16300,0:16297,0:150J:Q1oXS1:XL1:YS1:YL1:10X11.6:X21.6:Y10:Y20:20X10:Y11:X20:Y21:20X(N2)2N321:11"R = COS (";N;" * THETA)":8);"PRE:"R = COS (N * THETA) "O n23:1:"ENTER NEGATIVE OR ZERO N TO EXIT PROGRAM"i x12:15:"ENTER N ";N }22:" " N0500 22:10:"DO YOU WANT TO PRINT OVER":23:12:"THE PREVIOUS PICTURE"; TK$B(G9)P264 :4 <G912:P3(G9)P1P3(G9)P264: =B ?73] @P3(G9),Q3(G9)P2,Q2:k BP1P270 CP3(1)P3(2)71 DP3(1),Q3(1)P3(2),Q3(2): FP3(1)P3(2)68 GP3(2),Q3(2)P3(1),Q3(1): I"PLOT SUBROUTINE ERROR": d::10:10(G9)N1 -G90ı3 .P1N0P1N2Q1N0Q1N155A /P1P250e 0G912:P3(G9)P1P3(G9)P253k 1 2G912:P3(G9)P1P3(G9)P253 3 473 5P1,Q1P3(G9),Q3(G9): 7P2N0P2N2Q2N0Q2N166 8P1P260 9G912:P3(G9)P1P3G8 !G9G045 "QG7N2G81 #QN0QN138Q $G9G9G0:P3(G9)N2:Q3(G9)Q_ %G9G045x &PP1:G70PG8G7 'PN0PN242 (G9G9G0:P3(G9)P:Q3(G9)N0 )G9G045 *PP1:G70P(N1G8)G7 +PN0PN245 ,G9G9G0:P3(G9)P:Q3P1N0P1N2ı Q1N1Q1N11 Q2N0Q2N0B Q2N1Q2N1S Q1N0Q1N0[ 29 P1N0P1N2Q1N0Q1N1P2N0P2N2Q2N0Q2N130 P1,Q1P2,Q2: G7(Q2Q1)(P2P1):G8Q2G7P2:G90 G80G8N134 G9G9G0:P3(G9)N0:Q3(G9)г 100 G1181(XLXS)- G249G1XS@ G3159(YSYL)N G4G3YLlN00:N1159:N2279:G01:G5G1XG2:G6G3YG4G5N0G5N2ıG6N0G6N1ıG5,G6:P1G1X1G2:P2G1X2G2:Q1G3Y1G4:Q2G3Y2G4P1P228      gW'  `^ :F Y %^LǏLZ^[_\Z][`1'':"TO BELIEVE"::"THE GRAPH"::"WOULD BE . . . "Y 22:T$(I):X11000:b*255424:A;"X^2 + ";C;"Y^2 + ";D;"X + ";E;"Y + ";F;" = 0">:2H0,80279,80:140,0140,160Q***** 850-870 PRINT DOTS ON THE GRAPH ********R AC7303(Q0).01C$T$(5):W5:760: A=CIQ0C$T$(9):W9_Q0C$T$(1):W1h760(Q0).01C$T$(5):W5:760Q0C$T$(2):W2Q0C$T$(9):W9:125 4:"SO...":::"YOUR"::"CONCLUSIONS"::"LED"::D0E0C$T$(6):W6:XT3%D760LNF0C$" ALL ORDERED PAIRS ":W10cXF0C$T$(9):W9lb760xl A*C<0vFD2(4A)E2(4C)0C$T$(7):W7:760C$T$(3):W3760QFD2(4A)E2(4C): A*C>0Q E N C$=T$(6):W=6:H=1AD24RC0C$T$(8):W8:H1_D24FC0C$T$(9):W9yF0C$T$(6):W6:H1FC0C$T$(8):W8:H1FC0C$T$(9):W9760D0E0590&D0C$T$(6):W6:H10E0C$T$(6):W6:V1:T$(6):W6:V1, rD24FA0C$T$(9):W95 |760O F0C$T$(6):W6:V1g AF0C$T$(9):W9 AF0C$T$(8):W8:V1 760  A=0,C<>0 D0E0C$T$(4):W4:760 D0E0500 E0C$T$(4):W4 D=0:IF D^2-4*C*F=0 THERED PAIRS " I" AC02801 AC0620C 660: A*C>0O  A*C=0` "A0C0540m ,A0430| 6 A<>0,C=0 @D0E0390 JD0E0C$T$(4):W4:760 TD0C$T$(4):W4 ^D24AF0C$T$(8):W8:V1: E=0 hD24AF0C$(6)" A LINE "V :6:"7. TWO INTERSECTING LINES":T$(7)" TWO INTERSECTING LINES " :6:"8. TWO PARALLEL LINES":T$(8)" TWO PARALLEL LINES " :6:"9. THE EMPTY SET":T$(9)" THE EMPTY SET " :6:"10. ALL ORDERED PAIRS":T$(10)" ALL ORD:6:"1. A CIRCLE ":T$(1)" A CIRCLE "[ :6:"2. AN ELLIPSE":T$(2)" AN ELLIPSE " :6:"3. A HYPERBOLA":T$(3)" A HYPERBOLA " :6:"4. A PARABOLA":T$(4)" A PARABOLA " :6:"5. A POINT":T$(5)" A POINT" :6:"6. A LINE":T$ YOU'LL TYPE IN VALUES FOR A,C,D,E,F"3 Z"A = ";AA \"C = ";CO ^"D = ";D] `"E = ";Ek b"F = ";Ft d100 n:3:"NOW FOR YOUR PREDICTION OF THE GRAPH OF " x::6:A;"X^2 + ";C;"Y^2 + ";D;"X + ";E;"Y + ";F;" = 0" :"WILL IT BE..."+ +  **** MATH ANALYSIS ****B *** QUADRATIC FUNCTIONS ***X *** LEMKE ***n( *** 1979 ***2A0:C0:D0:E0:F0:I0:P0:Q0:H0:V0:XT0<::3:"I'LL GRAPH THE EQUATION"F::6:"A*X^2 + C*Y^2 + D*X + E*Y + F = 0"% P:"IF           TTE APPLE CONNECTION, Inc. L(OAD R(UN D(ELETE C(ATLG T(DRIV K(LOK U(NLOK X(ALL E(XIT SP(PAGE ----------------------------------------VOL PG OF SECT-USED LEFT ---------------------------------------- $% 0nmooة$eeVLԒؠ 58nnooؠ o 0n)JJJJ 0șn) 0șVJJJJ 0``Y% $ BU ڑV V Hi&eh L`$V  ɍ ` X0 ` WILLAME)N*m+Jn)m)eeU`8VUU ڑ` :` ^6789 Q@ q . @^`6798 Q`H h``noVVi@iA)moo g p g) pmn/5 qs r ; qa ` `$$(ɠ$C q$W ``H$%  h\  `CATALOG\Y/N\LOAD\LOCK\UNLOCK\RUN\SAVE\DELETE\NOMONC\START\ LENGTH\,D\I/O ERROR\@  UmU+&*Y Y P ,X B АX I8Mt_=gH?J QVQT_ɕ%[^ZZ\[]^Z_[ 0W Г J1  @)ȹ@)ȹ@) q P^ɠ 0   qL MW'WП < XX QLiLLs4      THE SAME POLYNOMIAL, BUT FOR A DIFFERENT NUMBER OF TRIANGLES"}"3 INDICATES YOU WISH TO WORK WITH A DIFFERENT POLYNOMIAL""ENTER 0,1,2, OR 3"HH700,310,220,110570 AZXZ0700bZ1310*lZ22207vZ3110k"0 INDICATES YOU WISH TO PROGRAM TO TERMINATE""1 INDICATER YOU WISH TO CONTINUE WITH THE SAME POLYNOMIAL""-----OVER THE SAME INTERVAL,BUT FOR A DIFFERENT INTERVAL"="2 INDICATES IS ";N;"."# "THE FUNCTION IS "J A;"X^3+ ";B;"X^2+ ";C;"X+ ";D;"."P  "THE APPROXIMATION TO THE AREA IS *****";T;"*****" & 0 :"SELECT ONE OF THE OPTIONS (0,1,2, OR 3); IF YOU DO NOT KNOW WHAT" D"THE OPTIONS ARE TYPE A 4"N400 NP4309 "N MUST BA A POSITIVE WHOLE NUMBER"Z "LESS THAN 500. TRY AGAIN"c 320l T0{ W(SR)N XR(SW)W TT(AX3BX2CXD)  TTW "THE INTERVAL IS (";R;",";S;")." "THE NUMBER OF RECTANGLESD S, REMEMBER R "O.K., ASSIGN NUMERICAL VALUES TO A,B,C, AND D."I "A=";P A[ "B=";b Bm "C=";t C "D="; D SELECTING AN INTERVAL ON THE X-AXIS "SELECT AN INTERVAL (R,S) ON THE X-AXIS" "BY ASSIGNING VALUES TO R AN RECTANGLES WHOSE SUM WILL BE AN APPROXIMATION"Y <"TO THE AREA WE ARE TRYING TO FIND." F"THE POLYNOMIAL FUNCTION IS OF THE FORM" P Z"A*X^3+B*X^2+C*X+D" d n INDICATE THE POLYNOMIAL x"YOU CAN GIVE ANY VALUES (INCLUDING 0) TO A,B,C,9 "THIS PROGRAM COMPUTES APPROXIMATIONS TO THE AREA"v"BOUNDED BY THE X-AXIS AND THE GRAPH OF ANY POLYNOMIAL""FUNCTION OF DEGREE THREE OF LESS OVER AN INTERVAL OF"("THE X-AXIS. THE METHOD USED TO APPROXIMATE THE AREA"/ 2"IS TO BUILD   "TO THE PROGRAM AUTHORS":11)"AND CONTRIBUTORS."b (::6)"";:A$: 2"ANY OF OUR PUBLIC DOMAIN PROGRAM DISKS FROM OUR LARGE LIBRARY CAN BE COPIED ONTO YOUR BLANK DISKS SENT TO US FOR A"Y <"COPY FEE OF ONLY 75 CENTS2000: D$(4)1 X(16384):X1272000B X1552050P 16368,0t D$;"RUN MENU": D$=(CTRL-D) :255:::CPH140H ZK20(80K)* d"INPUT A";A3 iAA; jN0H nX1279Z xYA(XH)2Ke YY20x Y0Y159160 N1 X,Y 165 N1170 X C :24:"HIT ANY KEY TO CONTINUE OR HIT TO RETURN TO MAIN PROGRAM."  :: 3)0,80279,80<(140,0140,159)100:24:"THIS PROGRAM WILL PLOT SEVEN ":"PARABOLAS WHERE F(X)=A*(X-H)^2+K "*"WITH (H,K) THE VERTEX.":2552C177C4Ē6:70<CF"INPUT COORDINATES FOR VERTEX ";H,K   M))E:1 A(Z)E(ZP):1 A.65:V3.65:Z0:C12:X0:D.7:L0k G1.5:A0:F900:U30:M16:I900.01:J.9:K2:H100:N18:P10:Q.5:R1 A9,10,11,12,13,14 A(Z)E(ZZH):1 A(Z)(IZZ)JK:1 A(Z)E((ZM))K:1 A(Z)EE(ZN):1 A(Z)E((Z"4VXUEG:LA:WB((FXX)B):YWUV:Z(CA((XXYY))DY):ZL3gLZ:Z)"*";s::::::7:9)"***** FUNCTION *****":18:"WHICH FUNCTION NUMBER:":"(1,2,3,4,5,6)? ";A::A1A6A(A)4! E30:Y0:W0:B3 YR(I)15IIS5(16384)128420C16368,0L370RX0P)I0LS"R(NI)+,XR(I)86YR(I)@@15WJ(16384)128360eT16368,0n^370uhIr24:6:"PRESS ";::" SPACE BAR ";::" TO CONTINUE";|SP$:SP$" "380100I0:S.031R(NI)XR(I)1:XL1:YS1:YL1:106X11.6:X21.6:Y10:Y20:20SX10:Y11:X20:Y21:20dX(N2)2Nk3w21:11"R = COS (";N;" * THETA)":8);"PRESS ANY KEY TO STOP PLOT";(N)N400L6.28X3.14PN:X0PN2SL(5)P3(2),Q3(2):# FP3(1)P3(2)68B GP3(2),Q3(2)P3(1),Q3(1):a I"PLOT SUBROUTINE ERROR": d::10:10:"R = COS (N * THETA) " n23:1:"ENTER NEGATIVE OR ZERO N TO EXIT PROGRAM" x12:15:"ENTER N ";N N0500 : 1XS 3 473) 5P1,Q1P3(G9),Q3(G9):I 7P2N0P2N2Q2N0Q2N166W 8P1P260{ 9G912:P3(G9)P1P3(G9)P264 : <G912:P3(G9)P1P3(G9)P264 = ?73 @P3(G9),Q3(G9)P2,Q2: BP1P270 CP3(1)P3(2)71 DP3(1),Q3(1G9G9G0:P3(G9)P:Q3(G9)N0) )G9G045F *PP1:G70P(N1G8)G7X +PN0PN245x ,G9G9G0:P3(G9)P:Q3(G9)N1 -G90ı .P1N0P1N2Q1N0Q1N155 /P1P250 0G912:P3(G9)P1P3(G9)P253 1 2G912:P3(G9)P1P3(G9)P253130 P1,Q1P2,Q2:? G7(Q2Q1)(P2P1):G8Q2G7P2:G90R G80G8N134s G9G9G0:P3(G9)N0:Q3(G9)G8 !G9G045 "QG7N2G8 #QN0QN138 $G9G9G0:P3(G9)N2:Q3(G9)Q %G9G045 &PP1:G70PG8G7 'PN0PN242 (N0G5N2ı G6N0G6N1ı* G5,G6:^ P1G1X1G2:P2G1X2G2:Q1G3Y1G4:Q2G3Y2G4m P1P228 P1N0P1N2ı Q1N1Q1N1 Q2N0Q2N0 Q2N1Q2N1 Q1N0Q1N0 29 P1N0P1N2Q1N0Q1N1P2N0P2N2Q2N0Q2NY 100{ BY CHANGING COS IN STATEMENTS 100, 220, 290, AND 420 TO SIN, YOU MAY OBTAIN THE GRAPHS OF R = SIN (N*I). G1181(XLXS) G249G1XS G3159(YSYL) G4G3YLN00:N1159:N2279:G01:G5G1XG2:G6G3YG4 G5     ." Z1000:" THE PROGRAM WAS WRITTEN BY MICHAEL A. WYATT AND WAS MODIFIED BY HARRY OWEN JONES, APPLE-CAN, TORONTO."::: d"MODIFIED BY:"::"HARRY OWEN JONES":"APPLE-CAN, TORONTO":"JAN 10 1982.":23:"TYPE A KEY TO CONTINUE ...";:A$:: OF THE SCREEN. TWO":"OTHER KEYS WILL EITHER RUN THE CURVE" P"AGAIN OR END THE PROGRAM GRACEFULLY. ":"('RETURN' AND 'S' RESPECTIVELY.)"::"THIS PROGRAM CAN BE COMPILED SUCCESS-":"FULLY BY THE MICROSOFT COMPILER FOR A":"SPEED INCREASE OF ABOUT 100%RES OF THIS PROGRAM":"IS THE ON CURVE CURSOR. ALTHOUGH IT MAY":"BE A BIT HARD TO SEE, IT CAN BE MOVED":"LEFT AND RIGHT WITH THE EDITING ARROW"< F"KEYS. SIMULTANEOUSLY, THE VALUE OF THE":"CURVE AT THE CURSOR'S LOCATION IS DIS-":"PLAYED AT THE BOTTOMOD VALUE":"TO TRY IS '.1'.":" AS IS USUAL IN THIS TYPE OF PROGRAM":"THERE IS NO CONVENIENT WAY TO ENTER A" 2"FORMULA 'ON THE RUN'. THUS THE NEED TO":"STOP THE PROGRAM AND CHANGE ONE OF THE":"LINES BEFORE RUNNING.":1000 <" ONE OF THE FEATUF THE" "RESPONSE OF THE TRANSFER FUNCTION AS A":"FUNCTION OF TIME. THE PROGRAM WILL ASK":"FOR A TIME INCREMENT TO BE ENTERED AND":"ALSO WHETHER THE CURVE IS RESIDENT IN"o ("THE PROGRAM. A SAMPLE FUNCTION IS AL-":"READY RESIDENT @ LINE 250. A GOi :(2):9)"LAPLACE INVERSION":8)"-------------------"::" THIS IS A PROGRAM THAT CONVERTS AN" "EQUATION IN THE S-DOMAIN TO PLOTTED":"POINTS IN THE TIME DOMAIN. IT HAS APPL-":"ICATION IN CONTROL THEORY.":" A HI-RES GRAPH IS DISPLAYED OXPH)D1XuYLY(PVBY)D2%bu500<luZHD1X1:ZVD2Y1LvuZH030150\uPP(ZVZH)ruKH(PP):KV(PP)uPHKHR,PVKVRPHKHR,PVKVRu30200uPH,PVRPH,PVRuPVvPH v DERIVATIVE OF X"6RN:"600 Y1= THE DERIVATIVE OF Y"P\N:"THEN TYPE 'RUN'."VNa"SHALL THE TANGENT FIELD BE DRAWN";aA$a(A$,1)"Y"ī302200uQHBX:QVBY5uQQ156uLH20:LVLH7uR7:uPHLHQHQQDuPVLVQVQQNuXLX(AD2(LYYV):XATH,YVXATH,YV$ f?I* p?K N::13);"PROGRAM CAUCHY":k !N:12);"SOLVES SYSTEMS OF"q %N *N5);"ORDINARY DIFFERENTIAL EQUATIONS" /N: 4N"GIVE YOUR SYSTEM BEGINNING AT" 9N >N"LINE 500 IN THE FORM:"HN:"500 X1= THEI))(CRDS(I1))SFDS(I):I19. >I:SFSF44 >N >B0LXSF1:T0UXSF1[ >IB0T0g >XVISF >(XVLX)(XVUX)XVAXD1(LXXV):XV,YATHXV,YATH ?I ? H?B0LYSF1:T0UYSF1 M?IB0T0 R?YVISF \?(YVLY)(YVUY)YVAY0 B(Y0BY)(Y0AY)ī1130; L(X1BX)(X1AX)ī1130X V(Y1BY)(Y1AY)ī1130i `X0,Y0X1,Y1w jXXN:YYN~ tI ~:21:"CONTINUE?";V$ (V$,1)"N"1030 "END?";V$ (V$,1)"Y"1010 ::62450: >I119 >(CRDS( 20000  20000H "TIME INCREMENT FOR THE INTEGRATION?";DT` "INITIAL X,Y?";X,Yk NS100w I1NS 500 XNXX1DT:YNYY1DT $X0AXD1(LXX):Y0BYD2(LYY) .X1AXD1(LXXN):Y1BYD2(LYYN) 8(X0BX)(X0AX)ī113AXXAAX kXABXXABX+ lYAAYYAAY< mYABYYABYL r:3:21:5j |XA,AYXA,BY:AX,YABX,YA~ CRUXLX:16000 16100:"HORIZONTAL DIVISIONS = ";SF CRUYLY:16000 5 16200:"VERTICAL DIVISIONS = ";SF 25000 1000   ODE'S X1.207722:YX&/5008dTH4^nDS(20):I120:DS(I)2(I10):I{:" LIMITS ON X?";LX,UX" LIMITS ON Y?";LY,UY,AX5:BX274:AY5:BY154^D1(BXAX)(UXLX):D2(BYAY)(UYLY)hXAAXD1LX:YABYD2LY jXA     z #??Xı  !Š̠Ӡ ̠ӠԠŠ ŠԠΠǠŠحŠĠԠ   ͠ԠҠŠĠנԠ ӯΠΠ "ΠǠӠŠàԠԠӠԠŠ̠Π   à̠ԠҠàΠԠ Ԡ٧ª٧êٽ ԠҽӨΪ ҠӠԠ àӠԠàӠԠ ŠΠؠŠԠί٠Ƞ ٠̠ ҠӠԠàӠ  ՠ ΠǠ ŠΠΠĠ̠Ԡ ȠΧӠĠȠΧӠĠ ŠΠ A(L) "YAYB(L)5 ,(X1X279Y1Y159)320? 6X,YF @LL JT T23~ ^"DO YOU WANT TO DO THIS AGAIN? ";S$ h(S$,1)"Y"10 r: |10:18)"THE END" P11000:P A0,300"  : "ENTER VALUES: ";A1,A2,A3,B1,B2,B3E AX140O AY80m A(X)A1(X)A2(A3X) B(Y)B1(Y)B2(B3Y) PI3.14159265 R1.01 RADR2PI STPPI128 :3 AXA(0),AY L0RADSTP XAXIN(Y)+B2*SIN(B3*X)"9 Z:"SUGGESTED PARAMETRIC VALUES:"[ d15)"A1, A2, A3, B1, B2, B3"~ n14)"--- --- --- --- --- ---" x15)"25, 25, 10, 25, 25, 10" 15)"25, 50, 10, 25, 50, 10" 15)"50, 25, 10, 20, 10, 5" 15)"25, 50,300, 25, 5  ::15)"CYCLOIDS"F:7)"H.EDELSTEIN NOV 4,1979"r(:"TRACES A POINT ON A CIRCLE THAT IS"2"ROLLING AROUND ANOTHER CIRCLE. "<" THE PARAMETRIC COORDINATES ARE:"F:" X=A1*COS(X)+A2*COS(A3*X)" P:" Y=B1*S    Z ::3:16)"75 CENT":6)"PUBLIC DOMAIN PROGRAM DISKS":::12)"DISTRIBUTED BY:"::12)"ASPEN SOFTWARE"::6)"729--1/4 E. PORTLAND STREET":8)"PHOENIX, ARIZONA 85006":7)"TELEPHONE: (602) 253-0651"1 ::10)"WITH SPECIAL THANKS":8)   BO4+(XZ),(YZ)T+XZXZXW:YZYZYWZ+`+w2D1(BXAX)(UXLX)2D2(BYAY)(UYLY)2XJXF:YJYF2II1NP2XP(XJ)AXD1(X(XJ)LX)2YP(YJ)AYD2(UYY(YJ))3XJXJXI:YJYJYI3ILZI8'TZZ(II)"B'TZUZUZTZ3L'TZLZLZTZ;V'IIA`'W* LINE ALGORITHM:l+X8AXD1(X1LX) +Y8AYD2(UYY1)+X9AXD1(X2LX) +Y9AYD2(UYY2)\+LL(X9X8)f+LM(Y9Y8)p+LMLLLLLMu+LLLL3z+XW(X9X8)LL:YW(YB")HCHC1:HH:HS(HC)H:700$H5YTLYYTLYFYTUYYTUYTXTD(YT)ZeJ11vV$"B"HHHH2HCHC1 HC20HC1HS(HC)H700$J.'UZZ(ZF):LZUZ'KKZFZI$'LLZF(NP1)ZI.'IIKKLX0)A(X0)&D(T)(TA(X0))MX0:XTLX:YTC(XT)T(YTLY)(YTUY)İ900dX1XT:Y1YTxXTUX:YTC(XT) (YTLY)(YTUY)İ900X2XT:Y2YT111000:8304AXD1(X1LX),AYD2(UYY1)AXD1(X2LX),AYD2(UYY2)>(H0)(V$"MS$"DELTA X SLOPE OF SECANT LINE"0]MS$X_"--------------------------------"dbI1HCulHS(I),MS(I){vI"PRESS RETURN WHEN YOU ARE READY.";W$16304,0451MS(HC)(A(X0H)A(X0))HMMS(HC) C(S)M(S475W$"Y"HCHC1:330):21:1N" DO YOU WANT A CLEAN GRAPH ?";kW$:W$"Y"W$"N"505W$"Y"Ģ23:1:200:21:1:"SHALL WE CHANGE THE INTERVAL ?";W$:W$"Y"W$"N"517W$"Y"ė:20:62450::X:'[ "SUMMARY OF THE DELTA X"8 "AND SLOPE VALUES ?";U W$:W$"Y"W$"N"446f W$"Y"ī600s :21:1 "WANT TO DO MORE STEPS ?"; W$:W$"Y"W$"N"455 W$"Y"420 :21:1 "CHANGE DELTA X ?";W$:W$"Y"W$"N" NON-ZERO IN ORDER FOR ME TO DRAW SECANT LINES FOR YOU. TRY AGAIN.":330f r(V$"R")(V$"B")H(H)z |V$"L"H(H) HS(HC)H 700  21:1 21:1:"ANOTHER ITERATION ?"; W$:W$"Y"W$"N"415 W$"Y"İ1000 23:1LX)ĺ"X0 IS OUT OF RANGE. TRY AGAIN.":2609 :21:1a ""RIGHT OR LEFT SECANTS OR BOTH ?"; ,V$:(V$"L"V$"R")(V$"B")300 6(V$)0V$"R" @HC1 J23:1 OHC20HC1 T"WHAT SHOULD DELTA X BE ?";HH hH0ĺ"DELTA X MUST BE13500 10:1 V$"L", V$(V$,1)I ((V$)0)(V$"L")DO0Z V$"D"DO1 UXUX0.01:UYUY0.01:LXLX0.01:LYLY0.01 : :3 AC1:15000 13000 15500 14000 :21:1 "WHAT IS X0?";X0, (X0UX)(X0. TRY AGAIN.":25R #UXLXĺ"SORRY, LIMITS CAN NOT BE EQUAL.":"TRY AGAIN.":25[ %SW1q (IN(UXLX)(NP1)} <I1NP FX(I)LX(I1)INCX PY(I)A(X(I)):Z(I)A(X(I)) ZI dZF1:ZI1 n10000 xUYUZ:LYLZ XF1:XI1:YF1:YI1 16390:SW1:21000#190003AX0:BX279CAY0:BY159I b NP((BXAX)4.25)1xIN(UXLX)(NP1)X(NP),XP(NP),Y(NP),YP(NP),Z(NP),MS(20),HS(20)(21)SWĄ"LIMITS ON X ? ";LX,UX LXUXĺ"YOU REVERSED THE LIMITS       LLR?(XZ),(YZ))\?XZXZXW:YZYZYW/p?5?? N::t#N" NEWTON":"-------------------------":%N"GRAPHICAL AND NUMERICAL STUDY":'N" OF NEWTON'S METHOD.":(NAN$:30000*N+N" IN ORDER TO RUN THIS PROGRAM YOU"/NX)>Y8AYD2(UYY2),>X9AXD1(X3LX)A>Y9AYD2(UYY3)h>(PC1)(AX1)(X1B)ēX5,Y5X8,Y8x>X5X9:Y5Y9>LL(X9X8):LM(Y9Y8)>LMLLLLLM>LLLL2>LL1ı?XW(X9X8)LL:YW(Y9Y8)LL ?XZX80.5:YZY80.5H?IZ1MYCR25LYMYCR2 5-6LINESDOTS1J6XP(XFIRSTI),YP(YFIRSTI)V6NP1ıp6XJXFIRSTI:YJYFIRSTI}6KK2NP6XJXJXINCI:YJYJYINCI6DOTSēXP(XJ),YP(YJ)7LINESēXP(XJ),YP(YJ)7KK7> LINE ALG.:>X8AXD1(X2LJXFIRSTI:YJYFIRSTI!2II1NP=2XP(XJ)AXD1(X(XJ)LX)Y2YP(YJ)AYD2(UYY(YJ))u3XJXJXINCI:YJYJYINCI}3II34RXUXLX4RYUYLY4CRRX4RYCRCRRY4MX(UXLX)24UXMXCR24LXMXCR25MY(UYLY)2 5UY+TXUXUXTX\+TXLXLXTX/f+TYUYUYTY@p+TYLYLYTYHz+IIN+e.D1(BZAZ)(UZLZ).ZLASTIZFIRSTI(NP1)ZINCI.IIZFIRSTIZLASTIZINCI.ZP(II)AZD1(Z(II)LZ)/II/2D1(BXAX)(UXLX)2D2(BYAY)(UYLY)2XIIKKLLZINCI8'TZZ(II),B'TZUZUZTZ=L'TZLZLZTZEV'IIK`'^*UXX(XFIRSTI)q+LXX(XFIRSTI) +UYY(YFIRSTI)+LYY(YFIRSTI) +NP1ı*+XJXFIRSTI:YJYFIRSTI4+II2NP>+XJXJXINCI:YJYJYINCIH+TXX(XJ):TYY(YJ) RTABLE: 1" XN F(XN)"X"-------------------------------"gI01IT1mXV(I0),YV(I0)(AN$216304,0P'UZZ(ZFIRSTI)'LZZ(ZFIRSTI)'KKZFIRSTIZINCI$'LLZFIRSTI(NP1)ZINCI.'XT:Y3YT:16000 PCPC18 XV(IT)X0:YV(IT)A(X0)MITIT1:ITNIıSd$YTUYYTUYu)YTLYYTLY.XTD(YT)8LQ1000`24:20:"WANT A TABLE?(Y/N)";:G$e(G$"Y")(G$"N")1100fG$"Y"İ5000j310 0DX3X0:X2X1$(X3A)X3A3X3BX3BD(X2A)X2ASX2BX2BkY2C(X2):Y3C(X3)(Y2UY)(Y3UY)1035(Y2LY)(Y3LY)1035XTX2:YTY2:(YTUY)(YTLY)İ1060X2XT:Y2YT:XTX3:YTY3:(YTUY)(YTLY)İ1060 X3TERVAL";:16384,0:W$0 b(W$,1)"Y"ė::120A h:62450::V XVAXD1(XVLX)m XV,XASTXV,XASSs  DB(X0) D0ė:"DERIVATIVE NEARLY ZERO AT ";X0: Y0A(X0) X1X0 C(S)D(SX1)Y0 D(S)(SY0)DX1X0X0Y"Y"3108 P24:1:"WANT A TABLE?(Y/N)";:16384,0:G$U Q(G$"Y")(G$"N")336g RG$"Y"İ5000p S310 T23:1:"CLEAR AND RESTART ON SAME INTERVAL?(Y/N)?":16384,0:W$ Y(W$"N")(W$"Y")340 ^W$"Y"260 `:21:1:"CHANGE THE INLX)(0UX)XV0:4005 (1LX)(1UX)XV1:400W (1LX)(1UX)XV1:400 ":16384,0:21:"ESTIMATE OF ROOT ? ";X0 $PC1:IT1 ,1000 6:23:1:"ANOTHER ITERATION? (Y/N)";:16384,0:W$ @W$"N"340 JW$"Y"İ1000 OW$I)) I" XF1:XI1:YF1:YI1- 11000< LY0LY0K UY0UY0^ V$"Y"İ13500i 13000r :3} DOTS0 14000 XAXISAY(BYAY)UY(UYLY) AX,XAXISBX,XAXIS SS4:STSS:XAXISBYSSSS0 XAXISAYSTST0 (0:BAA (AB)(F$"Y")ī360K ABĺ"EQUAL VALUES??? TRY AGAIN!":130T SW1^ 5:1 "EQUAL SCALES? (Y/N)";:16384,0:V$ (V$"Y")(V$"N")135 DX(BA)(NP1) X(1)A:Y(1)A(X(1)) I2NP X(I)X(I1)DX Y(I)A(X( 16390SW1NP80> X(NP),Y(NP),YP(NP),XP(NP)HNI20[XV(NI),YV(NI)wZAX0:BX279:AY0:BY158d20000x16384,0:SWĄ"LIMITS ON X ?";A,B ABĺ"YOU REVERSED THEM. SHALL I CORRECT?";:F$:F$(F$,1):F$"Y"AAA:AB        15)"50, 10, 7, 25, 8, 9"" J "ENTER VALUES: ";A1,A2,A3,B1,B2,B3U AX140_ AY80 A(X)A1(A2X)A1(A3X) B(Y)B1(B2Y)B1(B3Y) PI3.14159265 R1.01 RADR2PI STPPI128  :3 "AXA(0),AYB(N(B3*X)". Z:"SUGGESTED PARAMETRIC VALUES:"P d15)"A1, A2, A3, B1, B2, B3"s n14)"--- --- --- --- --- ---" x15)"25, 2, 1, 25, 2, 1" 15)"25, 5, 7, 25, 5, 7" 15)"50, 7, 5, 25, 6, 4 15)"50, 7, 8, 25, 9, 10"   ::15)"ROSETTE"E:7)"H.EDELSTEIN NOV 4,1979"n(:"TRACES 'ROSE PETALS' AROUND THE"2"POINT OF ORIGIN."<" THE PARAMETRIC COORDINATES ARE:"F:" X=A1*SIN(A2*X) + A1*COS(A3*X)" P:" Y=B1*COS(B2*Y) + B1*SIV(I1)X0XSI,V(I)DL12,J1DL:J6$3000=80LB1X1,Y(I)SLIY Y0XS(I1),Y(I1)X0XSI,Y(I)((DL1272J1DL:JA<3000HP0WZ1X1,Y(I)^dIdzp VELOCITY GRAPH:zYC(YUYD)2X0,YC279,YC21:25:"T"23:17:"VELOCITY GRAPH"I1NP31X1,Y(I)X0XS(I1),W1X)(W2X)Z LV5:UV5Md V(X)W1(W1X)(W2X)W2(W1X)(W2X)Sx d KB(16384)r 16368,0 KB127ı AN$ X0,YUX0,YD279,YD21:25:"T"23:17:"POSITION GRAPH"I1NP31X1,Y(I)X AL0.2:OM2(~ A(X)(ALX)(OMX)7 LV3:UV3d V(X)(ALX)(AL(OMX)OM(OMX))j s XF5 YI1:YF1 A(X)(XX) LV10:UV10 V(X)2X(XX) ( XF132 YI1.6:YF1.6< W10.5F W24 P A(X)(pV(X)(M(X)1)%XF16YI0:YF1.05AXS1.4VA(X)X(1X)4eLV5:UV5zV(X)(12X)4XF13 YI1:YF1 OM2 A(X)(OMX). LV3:UV38 V(X)OM(OMX)L ` XF15j YI0.9:YF1 tY OSCILLATOR" ." (6) BEATS"P L:"ENTER THE NUMBER OF THE ONE YOU WANT:";f `CH$:CH(CH$)48z tCH1CH61120 CH2100,2200,2300,2400,2500,2600  4XF5 >YI0:YF1 CB2 HM(X)XB(XB) RA(X)(M(X)1)fLV3:UV3W:200 ::62450: E "PLEASE SELECT ONE OF THESE TYPES"X "OF MOTION :"^ } " (1) CONSTANT VELOCITY" " (2) CONSTANT ACCELERATION" " (3) HARMONIC OSCILLATOR" " (4) DAMPED OSCILLATOR" $" (5) INCREASING FREQUENCTURN' TO STOP OR RESTART.";- ,SW5000,60003 H 23:"REPEAT ?";e *F$:F$"Y"F$"N"810 4F$"Y"ĉ:62450:200 ;:23 >SW1ĺ"VELOCITY GRAPH ?"; CSW2ĺ"POSITION GRAPH ?"; EF$:F$"Y"F$"N"837 HF$"Y"ĉ:62450:SW3S)YU)% V(I)YDYS(V(INPXF)LV), IQ D$(4):D$;"BLOAD SQUARE,A7676"f 232,252:233,29o SW1w : "PRESS RETURN TO BEGIN";F$ :3 X130 X130,YD1X130,YD1 X130,YHX130,YH X070 :24 "PRESS 'REPH OF POSITION , OR"6 :" 2. GRAPH OF VELOCITY."A AN$:K (1000l <B(X)(A(XXF)YI)(YFYI) P23:"REPEAT ?"; nC120:C25 x:0:1 NP100:T(NP1),Y(NP1),V(NP1) I0NP YS(YDYU)(UVLV) Y(I)YM((YDYU)B(INP[ (4);"BLOAD SQUARE,A7676"5115,252:116,29NYD150:YU15:YHYU3YXS2.1dYM165:" MOTION AND VELOCITY":"--------------------------------": "SIMULATES MOTIONS AND SIMULTANEOUSLY": "SHOWS EITHER" :" 1. GRA     )"Y"1000 :B11,158278,158278,11,1$ FAX,AY5 PL0RADSTPA xXC(L)M YS(L)[ ZZZ(L)f YZYZt X1ĪX1 X278ĪX278 YZ1ĪYZ1 YZ158ĪYZ158 X,YZ L  23 "DO YOU WANT TO DO THIS AGAIN? ";S$ (S$,1 4' `"ENTER VALUES:";BX,BY,ZC,CX,CY; PI3.1415926536C R7T RADR(2PI)b STPPI32j Z0 C(L)AXBX(L(R2))(CXL) S(L)AYBY(L(R2))(CYL) Z(L)ZC(L(R2)) AX140 AY8050(ZC) ( 2:3 <1,E)" .:" Z=K3*SIN(ANGLE)K 8:"SUGGESTED VALUES OF THE PARAMETERS:"i B15)"K1, K2, K3, A, B" L14)"--- --- --- --- ---" V14)"100, 30, .2, 2, 2" X14)"100, 30, .2, 2, 3" Y14)"100, 50, .3,200,100" Z14)"120, 10, .4, 1, ::,10)"SPHERICAL COORDINATES"T:7)"H.EDELSTEIN NOV 4,1979"::"TRACES A SPIRAL CURVE IN THE FORM OF""A SPHERE. USES SPHERICAL COORDINATES:":" X=K1*SIN(ANGLE)*COS(A*ANGLE)" $:" Y=K2*SIN(ANGLE)*SIN(B*ANGL    $-6?XL)) hY(AYBY(CYL))& rX,Y- |L5 22d " DO YOU WANT TO DO THIS AGAIN ? ";B$z (B$,1)"Y"ī110 ::ATRY THESE OR ENTER YOUR OWN."B :" ENTER VALUE FOR A: ";CXg :" ENTER VALUE FOR B: ";CYm ~ PI3.1415927 AX140 BX100 AY80 BY70 ,ANG2.1PI 6STPPI128 @:3 JAXBX,AY TL0ANGSTP ^X(AXBX(CF A AND B,". "YOU WILL CHANGE THE CURVES."\ "HERE ARE SOME SUGGESTED VALUES TO TRY:"b z " A B" " --- ---" " 1 1" " 1 3" " 3 4" " 3 7" :"NOW ONE CYCLE OF 360 DEGREES.Q d::" PRESS THE SPACE BAR TO GO ON...":ANS$Y n: x"THE X,Y COORDINATES HAVE THE FORM:" :" X = COS( ";::"A";::" * ANGLE) :" Y = SIN( ";::"B";::" * ANGLE) :"BY CHANGING THE VALUES O 5-" LISSAJOUX CURVES"X(::" H.EDELSTEIN OCT 19, 1979"d2:::<"A FAMILY OF CURVES GENERATED BY CHANGING"F"ANGLES IN THE POLAR COORDINATES THAT"P:"SPECIFY THE POINTS AS THEY ARE PLOTTED" Z:"THROUGH0ġ:700VV1200,1210 5R(T)3(11T);MR(T)1(T)S0ATES, WITH OR WITHOUT"08"THE RADIUS VECTOR."9BAN$?LYV"SELECT A FUNCTION:"_`}j"<0> YOUR OWN FUNCTION."t:"<1> R = 3 + SIN (11*T)"~:"<2> R = 1 + COS(T)"16384,0:NUM$VV(NUM$)48VV0VV21160VV"THEN TYPE 'RUN' . "**::"EXAMPLE :"K4:"100 DEF FNR(T)=COS(3*T)"o>:"THIS PLOTS R=COS(3*T) ."uH{2:5"POLAR PLOTTER"I139:"-";:I:$" PROGRAM PLOTS AN ARBITRARY FUNTION"."IN POLAR COORDIN"N")672 A$"Y"ī150+ :62450::1 ^ :"THIS PROGRAM PLOTS POLAR EQUATIONS." :"ENTER R AS A FUNCTION OF THETA" :"AS FOLLOWS : "   "100 DEF FNR(T)=...."  :"(NOTE THAT T = THETA HERE.)"  Y4Y0! X(Y50)(Y5279)Y5Y04 ]XU,Y4XU,Y5:X bYU(Y21)YSYC:X4X0W:X5X0Wo l(YU0)(YU159)ı v(X40)(X4279)X4X0 (X50)(X5279)X5X0 X4,YUX5,YU: "NEW THETA INTERVAL? (Y/N)"; 16384,0:A$ (A$"Y")(A$(B$"Y")ēX0,Y0XP,YP" XP,YP( 1 670B X0X1XSXCR Y0Y2YSYCZ !W4 &(Y00)(Y0159)ē0,Y0XA,Y0:580 +(X00)(X0279)ēX0,YAX0,0:610 0 DXU(1X1)XSXC:Y4Y0W:Y5Y0W N(XU0)(XU279)ı S(Y40)(Y4279) XSXAXR:YSYAYR2 X1(X1X2)2:Y2(Y1Y2)2C XSYSYSXST YSXSXSYSa YSYS.9o :3:530z I0N XP(X(I)X1)XSXC YP(Y2Y(I))YSYC XP0XP279510 YP0YP159510 X00X0279500 Y00Y0159500 50N150 N50N501 X1R(T1)(T1):X2X1K Y1R(T1)(T1):Y2Y1V I0Nf TT1TRINx "XPR(T)(T) ,YPR(T)(T) 6XPX1X1XP @XPX2X2XP JYPY1Y1YP TYPY2Y2YP ^X(I)XP:Y(I)YP h |XRX2X1:YRY2Y1T d1000n(24)xN150.X(N),Y(N)MXA274:XC139:YA155:YC80W:21"WANT RADIUS VECTOR DRAWN ?";:16384,0:B$(B$"Y")(B$"N")150:21:"ENTER LIMITS FOR THETA :";T1,T2NB30TRT2T1N(TRNB) N1     7,3,15,6,10,3,15,46,15,30,45,32,48,54,10,32,48,15,18,11,18,33,57,11,18,45,18f ` DAVE WINZLER, 1978g TRIANGLE ILLUSION9 CONFIGURED FOR ROM CARDS X(X)(3.5X.5)20Y lY(Y)1803YrHB044:HC13:HBHC:X,Y:X(X),Y(Y)(N117:X,Y:X(X),Y(Y):N2HC,HB:22cL d 6,10,54,10,57,15,33,57,27,5rB"INSERT IT IN THE FORM:";|B:" 20 DEF FNA(X)=..."cB:"AFTER YOU DO THIS, TYPE 'RUN'."iBBUTPXV,XABO>'>YVAYD2(UYYV)>>YALE,YVYART,YVD>MH?DD1^R?CRDDD.5m\?CRDDD2{f?I11000p?DDDDDz?(CRDD)(D1)I1000?(CRDD)(D1)I1000?I?SFDD8?hB:"INSERT YOUR FUNCTION AT LINE 20":PAYTP0#XVAXD1(XVLX) >XV,XANE)AY)(Y2(NE)BY)ēX2(KK),Y2(KK)X2(NE),Y2(NE):7KK@ 7:UYLY0XAAYUY(BYAY)(UYLY):(XAAY)(XABY)ēAX,XABX,XA:UXLX0YABXUX(BXAX)(UXLX):(YAAX)(YABX)ēYA,AYYA,BY:B^L" SELECT YOUR FUNCTION:"dV`"<0> YOUR OWN EXAMPLE."jt"<1> X = SIN(T)/2"~" Y = COS(T)/4":"<2> X = EXP(T)"" Y = T^3"."" " 100 DEF FNY(T)=....."( C "THEN TYPE 'RUN' . "X ::"EXAMPLE :"x :"90 DEF FNX(T)=COS(3*T)" :"100 DEF FNY(T)=SIN(2*T) "    2:5 "PARAMETRIC PLOTTER" I139:"-";:I $" PLOTS 2-DIME(Y50)(Y5159)Y5Y0* NXU,Y4XU,Y5:R X:21:"NEW INTERVAL FOR T? (Y/N)";d ]16384,0:A$ `(A$"Y")(A$"N")605 bA$"Y"160 l:62450:: v  "ENTER YOUR EQUATIONS AS FOLLOWS:"   " 90 DEF FNX(T)=.....)(X0279)ēX0,YAX0,0:540" F YU(Y21)YSYC:X4X0W:X5X0W] &(YU0)(YU159)ıx ((X40)(X4279)X4X0 *(X50)(X5279)X5X0 0X4,YUX5,YU: DXU(1X1)XSXC:Y4Y0W:Y5Y0W F(XU0)(XU279)ı H(Y40)(Y4159)Y4Y0 J I0N XP(X(I)X1)XSXC7 YP(Y2Y(I))YSYCL XP0XP279460a YP0YP159460l XP,YPr { 600 X0X1XSXC Y0Y2YSYC W4 (Y00)(Y0159)ē0,Y0XA,Y0:580 (X00)(X0279)ēX0,YAX0,0:540 (X00 XPX(T) YPY(T)* XPX1X1XP; "XPX2X2XPL ,YPY1Y1YP] 6YPY2Y2YPq @X(I)XP:Y(I)YPw J TXRX2X1:YRY2Y1 ^XSXAXR:YSYAYR hYSXSXSYS rXSYSYSXS wYSYS.9 |X1(X1X2)2:Y2(Y2Y1)2 :3:480  Z1000n(24)N200.X(N),Y(N)MXA270:XC139:YA155:YC80v:21:"ENTER LIMITS FOR T : ";T1,T2NB50TRT2T1N(TRNB)N200N200N50N50X1X(T1):X2X1Y1Y(T1):Y2Y1I0NTT1TRIN     1NP!2XP(XJ)AXD1(X(XJ)LX)=2YP(YJ)AYD2(UYY(YJ))S3XJXJXI:YJYJYI[3IIa3y3(AC1)(UY0)UY03(AC1)(LY0)LY03(AC1)(UX0)UX03(AC1)(LX0)LX034RXUXLX:RYUYLY:CRRX4RYCRCRRY4C2CR2 +UYY(YF):LYUY +NP1ı/*+XJXF:YJYF<4+II2NPR>+XJXJXI:YJYJYIhH+TXX(XJ):TYY(YJ)yR+TXUXUXTX\+TXLXLXTXf+TYUYUYTYp+TYLYLYTYz+II+2D1(BXAX)(UXLX)2D2(BYAY)(UYLY)2XJXF:YJYF2III "NO. OF RECT.","VOLUME"&I"PRESS RETURN WHEN READY.";F$W16304,0]c{'UMM(MFIRSTI):LMUM'KKMFIRSTIMINCI$'LLMF4MI.'JJKKLLMI8'TMM(JJ)B'TMUMUMTML'TMLMLMTMV'JJ`'*UXX(XF):LXUX:21:1!"VOLUME= ";VOL(L)4NR(L)NS:LL1BL50L1H"V0:14000j3:AX,XABX,XAtX2AXJ1NSNXX2HIHPAYD2(UYH(J))X2,HPNX,HPX2X2HIJp:uI1L1zNR(I),VOL(I)D2((RJ))RJ0İ2500,RJ0İ2000<RJ0İ2000MRJ0İ2500ZIIIIHIjRJ0İ2500{RJ0İ2000RJ0İ2000RJ0İ2500HPAYD2(UYH(J))II,HPIIHI,HPVOL(L)VOL(L)RJ2JVOL(L)VOL(L)PIDX   :21:1J "DO YOU WANT TO SEE THE CYLINDRICAL CROSS SECTIONS?";Y$a (Y$,1)"Y"İ4000l 22:1 "DO YOU WANT A SUMMARY OF THE CYLINDRICAL VOLUMES?";V$ (V$,1)"Y"İ6000 VOL(L)0J1NSIIAX(J1)HI RJH(J):R1LM9D (Q$"I")(UMLM0)H(I)UM:(LM)(UM)H(I)LMiN (Q$"I")(UMLM0)H(I)UM:UM0H(I)LMX HPAYD2(UYH(I))b NXX2HIl X2,HPNX,HPv X2NX:X3X3DX I :21:1 "ERASE THE ORIGINAL CURVE?";E$ (E$,1)"Y"İ5000- MATIONS?";Q$. HI(BXAX)NS:DX(UXLX)NS> X2AX:X3LXJ I1NSZ FOURTHDX4e J04~ M(J)A(X3JFOURTH) J& MFIRSTI0:MINCI10 100005 Q$(Q$,1): (Q$"I")(UMLM0)H(I)0? (Q$"I")(UMLM)0H(I)UM:UM0H(I)II,SCR1IN1N22IIR1W(I),SCR1Z(I)9I?L IN2NPg IIR1W(I),SCR1Z(I)n It  23:1:"HOW MANY SUBINTERVALS DO YOU WANT?";NS M1NS1:DD(BXAX)(NS1) :22:1 "DO YOU WANT THE INNER OR OUTER APPROXI.";P$ ,::62450:E "HOW MANY CROSS SECTIONS DO YOU WANT?";NS_ M1NS1:DD(BXAX)M1k 8J0M1z BIIAXJDD GIX1J(NP1)M1 LRJY(IX)D2 VR1(RJ) `RJ0İ2500 jRJ0İ2000 tRJ0İ2000 ~RJ0İ2500 J  ::62450:224 :21:1] "DO YOU WANT TO SEE THE STEP-FUNCTION APPROXIMATION?";S$t (S$,1)"Y"İ3000 24:1 "DO YOU WANT A CLEAN GRAPH?";G$ (G$,1)"Y"ī224 :22:1 ""PRESS RETURN WHEN YOU WANT THE SCREEN TO BE ERASED13200:13000 :3' XAAYD2UY8 AX,XABX,XAX AX,XAAX,AY:AX,XA0,XA15b SCXAm 14000z :21:1 "DO YOU WANT TO SEE CROSS SECTIONS?";C$ (C$,1)"Y"İ1000 23:1 "DO Y0U WANT A CLEAN GRAPH?";G$ (G$,1)"Y"āI1NP FX(I)X3:X3X3IN. PY(I)A(X(I))5 ZIM dXF1:XI1:YF1:YI1X n11000e pUY(UY)| r(LY)UYUY(LY) tLYUY x: 10:1 "DO YOU WANT DOTS OR LINES?";V$ V$(V$,1) ((V$)0)(V$"L")DO0 V$"D"DO1 AGAIN.":25J #LXUXĺ"SORRY, LIMITS CAN'NT BE EQUAL"::"TRY AGAIN":25 )X(NP),XP(NP),Y(NP),YP(NP),Z(NP),W(NP),M(5),H(NP),NR(50),VOL(50) *I1NP +Z(I)(ITWOPINP) ,W(I)E(ITWOPINP) -I 2IN(UXLX)(NP1) 3AC0 7X3LX <x 1639017000/E0.13:TWOPI8(1)OAX(80E1):BX(27880E)\AXAX20lAY2:BY156L1:PITWOPI2 NP((BXAX)4)1N11:N2NP2"WHAT ARE YOUR LIMITS ON X?";LX,UX LXUXĺ"YOU REVERSED THE LIMITS. TRY      DS(I))(CRDS(I1))SFDS(I):I192p?I:SFSF48z?bhB:"INSERT YOUR FUNCTION AT LINE 2":rB"INSERT IT IN THE FORM:"|B:" 2 DEF FNA(X)=..."B:" AFTER YOU DO THIS TYPE 'RUN'."BXVAXD1(XVLX)>XV,XATPXV,XABO>>YVAYD2(UYYV)>YALE,YVYART,YV>H?I119#f?(CR0XAAYUY(BYAY)(UYLY):AX,XABX,XA@:(AC1)(UX0)UX0X:(AC1)(LX0)LX0:UXLX0YABXUX(BXAX)(UXLX):YA,AYYA,BY;+XJXJXI:YJYJYIH+TXX(XJ):TYY(YJ)R+TXUXUXTX\+TXLXLXTXf+TYUYUYTYp+TYLYLYTYz+II+J1X4P0:Y4Y0%J2X4P1:Y4Y1:J3X4P2:Y4Y2`X4AXD1(X4LX):Y4AYD2(UYY4)((X4AX)(X4BX))((Y4AY)(Y4BY))690X3X4XS:Y3Y4XSX5X4XS:Y5Y4XSX3,Y3X5,Y5:X3,Y5X5,Y3JR0UXLX:UXUXR02:LX3216,0:3003&Y0A(P0):Y1A(P1):Y2A(P2)I0D4Y2Y1:D3Y1Y0:A9((P1P0)D4(P2P1)D3)((P22P12)(P1P0)(P12P02)(P2P1))DB9(D4A9(P22P12))(P2P1)NC9Y0A9P02B9P0XP(X)A9XXB9XC9bXS3lJ13vBY)))ēX4,Y4X5,Y5X9D"WANT TO TRY ANOTHER PARABOLA?";V$V$(V$,1):V$"Y"Ą"DO YOU WANT A CLEAN GRAPH?";W$:(W$,1)"Y"224V$"Y"250"PRESS RETURN WHEN DONE.";A$:::62450:P2(2UXLX)3:P1(LXUX)2:P0(UXLX2)DS1 TX9LXUXININ4 hY4P(X9):Y5P(X9IN)Z rY4AYD2(UYY4):X4AXD1(X9LX) wY5AYD2(UYY5):X5AXD1(X9INLX) |(DS1)((Y4AY)(Y4BY))ēX4,Y4 (DS1)((Y5AY)(Y5BY))ēX5,Y5(DS0)(((Y4AY)(Y4BY))((Y5AY)(Y5 24:19 "GIVE THE THREE POINTS THROUGH WHICH THE"f "PARABOLA SHALL PASS. IF YOU JUST TYPE" "RETURN THE COMPUTER WILL CHOOSE THEM." 530 "P0,P1,P2 ,550 6:24:1 @"DO YOU WANT DOTS OR LINES?";V$ EDS0 J(V$,1)"D"((V$)0)(V$"L")DO0* V$"D"DO15 13000> :3I 15000] CRUXLX:16200 15500::22:5:"ONE HORIZONTAL DIVISION= ";SF CRUYLY:16200 15570:5:"ONE VERTICAL DIVISION= ";SF 14000 "PRESS RETURN WHEN READY.";A$P(NP),MS(50),HS(50) <I1NP4 FX(I)X3:X3X3INF PY(I)A(X(I))M ZIe dXF1:XI1:YF1:YI1p n11000x x: 10:5 "FULL OR HALF SCALE?";W$ (W$,1)"H"İ750 10:1 "DO YOU WANT DOTS OR LINES?";V$ V$(V$,1) :I 1 "WHAT ARE YOUR LIMITS ON X?";LX,UXh LXUXĺ"YOU REVERSED THE LIMITS. TRY AGAIN.":25 #LXUXĺ"SORRY, LIMITS CAN'NT BE EQUAL"::"TRY AGAIN":25 (NP((BXAX)4)1 -X3LX 2IN(UXLX)(NP1) 3AC0 7X(NP),XP(NP),Y(NP),Y 1639017000'AX5:BX2747AY5:BY154V FOR INFORMATION CONTACTs SCHOOL OF MATHEMATICS GEORGIA INSTITUTE  OF TECHNOLOGY ATLANTA, GEORGIA 30332 ATTN: M.J. CHRISTENSEN DS(20):I120:DS(I)2(I10)     000.5)10006BB(A15))@XR345TJ"PRESS 'C' TO CONTINUE DATA. ";:B$:dTB$"C"185Y"TOTAL LENGTH OF SURFACE =";(L12000.5)1000^"NEW SET OF SPEC'S ('Y' OR 'N'). ";:C$:h(C$,1)"Y"120r8)"***END OF CALCULATIONS***"$ APPROX. LENGTH BETWEEN POINTS: L((A2)(Y22))G X0L0S L1L1Ln  SET UP TABLE RESULTS "X =";X;:12:"Y =";(Y1E5.5)1E5;:26:"L =";(L1E5.5)1E5 XXA XB300 "XR190 ,:"APPROX. LENGTH SO FAR =";(L11PUT VARIABLE FOR TABLEL :"FOCAL PT=";P1;:15:"RAD=";R1;:24:"RES=";A1{ "---------------------------------------" CALCULATE Y AXIS POINTS Y(X2)(P4) START TABLE CALC X0Y10 X0230 Y1((XA)2)(P4) Y2YY1 VARIABLE FOR GRAPHICS% P1PD "RADIUS OF PARABOLIC: ";R` VARIABLE FOR GRAPHICSi R1R "RESOLUTION OF X-AXIS: ";A VARIALBE FOR GRAPHICS A1A X0 SET RESULTS TABLE LENGTH TO 15 BA15 L10 PROVIDE IN"0 P"TWO POINTS AND TOTAL. A GRAPHIC DISPLAY"V Z"CAN BE GENERATED UPON REQUEST." d23:"PRESS 'C' TO CONTINUE. ";:A$: nA$"C"120 s x:9)"PARABOLIC CALCULATIONS" DATA INPUT FROM 130 TO 150 :"FOCAL POINT OF PARABOLIC: ";P:"THIS PROGRAM WILL CALCULATE THE CURVA-"X "TURE OF A PARABOLIC. INPUTS REQUIRED" ("ARE THE FOCAL POINT, THE RADIUS OF" 2"CURVE AND THE RESOLUTION OF X-AXIS." <"OUTPUTS WILL BE X-AXIS INCREMENTS," F"Y-AXIS, APPROXIMATE LENGTH BETWEEN  ==================== : **** WRITTEN BY ****V ** FRANK W CLAUDE **r **** JUNE 1982 **** ==================== INFORMATION LINES 10 TO 100 :5:9)"PARABOLIC CALCULATIONS":7)"WRITTEN BY FRANK W CLAUDE", UR FUNCTION AT LINE 100."7Nu:"GIVE IT IN THE FORM:"WXu:" 100 DEF FNA(X)=..."sbu:"AND THEN TYPE RUN."lu:"NOTICE! FNA IS Z AS A FUNCTION OF BOTH"vu:"X AND Y."u ,J)HS),VCSC(V(I,J)VS)# VI:JI TV22:1:"OBJECT AS SEEN FROM ";L;n ^V23:1:"POLAR ANGLE OF ";PHAC; hV24:1:"AZIMUTH OF ";THAC; YF$:F$"YES"19000 ]62450::: 0u:: :u"IN ORDER TO USE THIS PROGRAM YOU MUST"Du:"INPUT YOX(I1)DX;4 RHCSC(U(I,1)HS),VCSC(V(I,1)VS)@ &RJ2NPj 0RHCSC(U(I,J)HS),VCSC(V(I,J)VS)t :RJ:I UJ1NP U22:F$: U U21:"CURVE FOR Y= ";LY(J1)DY; UHCSC(U(1,J)HS),VCSC(V(1,J)VS) VI2NP VHCSC(U(IOVTLVLVVT& OU(I,J)HT:V(I,J)VT1 OYYDY8 OJF OXXDX:I\ PHRUHLH:VRUVLVs PMRHR:VRMRMRVR PSC158MR PHS(UHLH)2:VS(UVLV)2 (PHC140:VC80 R:(7):F$::3 RI1NP R22:F$: R R21:"CURVE FOR X= ";L .OI1NP 8OYLY! BOJ1NP- LOZA(X)D VOSLXA1YA2ZA3R `OS0ī460] jOTL2Sk tOT2L2TL| ~OX0T2A1TX OY0T2A2TY OZ0T2A3TZ OHTX0B1Y0B2 OVTX0C1Y0C2Z0C3 OHTUHUHHT OHTLHLHHT OVTUVUVVT HAL VIEWING ANGLE?";TH% RNAC(1)45; \NPHPHAC:THTHACf NA1(PH)(TH):A2(PH)(TH):A3(PH)} NB1(TH):B2(TH) NC1(PH)(TH):C2(PH)(TH):C3(PH) NDX(UXLX)(NP1) ODY(UYLY)(NP1) OXLX:UH999999:LHUH $OUVUH:LVLHd30000,n"LIMITS ON X?";LX,UXGxUXLXTLX:LXUX:UXTa"LIMITS OF Y?";LY,UY|UYLYTLY:LYUY:UYT6JNP127JU(NP,NP),V(NP,NP)8J:21 N"VIEWING DISTANCE?";L*NFR.2:L2FRL>N"POLAR VIEWING ANGLE?";PH HN"AZIMUT     ING ANGLE?";PH1"AZIMUTHAL VIEWING ANGLE?";TH@AC(1)45VPHPHAC:THTHACA1(PH)(TH):A2(PH)(TH):A3(PH)B1(TH):B2(TH)C1(PH)(TH):C2(PH)(TH):C3(PH)ITYPE6ıDX(UXLX)(NP1)DY(UYLY)(NP1)D ON Z. ";ZO,ZI0:C1(6DT17:DZ7?@U(DZ,DT),V(DZ,DT)_JUH9E25:LHUH:UVUH:LVLHiT1670r^740xhrNP12:N112|U(NP,NP),V(NP,NP):21ITYPE3ITYPE4IPE3"VIEWING DISTANCE?";LFR.2:L21"POLAR VIEWER THE POSITIVE BOUND ON Z. ";ZO-ZI0:C1<DT17:DZ3WU(DZ2,DT),V(DZ2,DT)yUH999999:LHUH:UVUH:LVLH1670740*** PLOT GRAPH OF AN ELLIPTIC PARAOLOIDA(X)XX(AA)YY(BB) ""PLEASE ENTER THE UPPER BOUN2,DT)(2UH999999:LHUH:UVUH:LVLH2<1670;F740APMZI1DZYdJ1DTnnU(DZI,J)U(I,J)xV(DZI,J)V(I,J)JITEU(I,J):TMV(I,J)*** PLOT GRAPH OF A CONEA(X)(XX(AA)YY(BB)) "PLEASE ENT PLOT GRAPH OF A HYPERBOLOID OF TWO SHEETSUA(X)(1XX(AA)YY(BB))CSIGNdZIC:ZT12 "PLEASE ENTER THE POSITIVE UPPER LIMIT ON Z. ";ZOZOCĺ"THE UPPER LIMIT ON Z MUST BE GREATER THAN C.":1290DT17:DZ3(U(DZ2,DT),V(DZ ERBOLOID OF ONE SHEET?Q(X)XX(AA)YY(BB).9999ZA(X)(Q(X))CSIGN"PLEASE ENTER THE POSITIVE BOUND ON Z. ";ZOZIZODT17:DZ9U(DZ,DT),V(DZ,DT)UH999999:LHUH:UVUH:LVLH1670740****TLVLVVTR*** IF YOU DON'T WANT TO SCALE JUMP HERE TO A DIFFERENT SUBROUTINEZJ1bI1r$NPDT:N1DZ.IPE3Z0İ1370:ZTZ:7408IPE3Z0N12DZB2040LITYPE2ıV`jt~ *** PLOT GRAPH OF A HYP zIPE3ZT0ZZ,SLXA1YA2ZA37TL2SET2L2TLVX0T2A1TXgY0T2A2TYxZ0T2A3TZHT(X0B1Y0B2)VT(X0C1Y0C2Z0C3)U(I1,J1)HT:V(I1,J1)VTHTUHUHHTHTLHLHHTVTUVUVVT VHI(CC)!RX(HJ)(HJ)(AA): RY(HJ)(HJ)(BB)X*ITYPE2RN1HIHI(CC)z4ITYPE3RNHIHI(CC).9999>ITYPE4RNHIHI(CC)HITYPE5RNHIRRO(RN(RXRY))\XRO(HJ):YRO(HJ)fSIGN1:HI0SIGNSIGNpZA(X)(1.001(XX(AA)YY(BB)))CSIGN; ZOC:ZO0ZOZOJ DT17:DZ7U ZIZOl U(DZ,DT),V(DZ,DT) UH999999:LHUH:UVUH:LVLH 1670 I11DZ HI(I11)(ZOZI)(DZ1)ZI J11DT HJ(J11)(1)8(DT1) RN1.0001HIICAN7590 D7:18:"2", N8:2:"A?";A> X8:8:"B?";BN bICAN7630a l8:14:"C?";C vITYPE6ĸA(X)XX(AA)YY(BB) ITYPE660,1150,1260,1450,1550,260   FOR AN ELLIPSOID DETERMINE THE DOMAIN IN THE X-Y PLANE% A(X)ITYPE2Ģ6:14:"-":4807 ICAN7Ģ6:14:"=":480H 6:14:"+";[ 6:10:"---";x ITYPE3Ģ6:8:"-":520 6:8:"+"; ICAN7Ģ6:16:"Z":550 6:16:"---"; 6:20:"="; 6:22:"1" &7:6:"2"; 07:12:"2"; : 6 @. JITYPE4ITYPE5ITYPE6ICAN7> T4:6:"2";O ^4:12:"2";_ hICAN7380o r4:18:"2" |5:5:"X"; 5:11:"Y"; ITYPE4Ģ5:17:"2" ICAN7430 5:17:"Z" ITYPE3ITYPE6Ģ6:2:"-"; 6:4:"---";  :"7) OTHER"- :"PLOT NUMBER?";ITYPE_ ITYPE7ITYPE0ĺ"ILLEGAL PLOT NUMBER":200q ITYPE7ī240z 320 2460 "LIMITS ON X?";LX,UX UXLXTLX:LXUX:UXT "LIMITS OF Y?";LY,UY "UYLYTLY:LYUY:UYT ,1650 d16390n:Kx"SELECT THE NUMBER OF THE GRAPH YOU WISH TO PLOT"a:"1) ELLIPSOID":"2) HYPERBOLOID OF ONE SHEET":"3) HYPERBOLOID OF TWO SHEETS":"4) CONE":"5) ELLIPTIC PARABOLOID":"6) HYPERBOLIC PARABOLOID"      TR*xhp  @IH$0j &%|AA|> `D@ @ @ x @@`  @ @Hq @ 8p p8`@  @@ @ PK3MqDKo@N$`j @DAQ5@F! i@A@(%U`? 0 @0A4r$@];@ (*xA@xx$@    @??`    "@@@  `"TH 1 `p0$@@ A@"E2D04 I]0 ( ~yA"I,"0R uU@ `D I4I$vPJp!p@ @@@8 @ :o|@`"  AA@@@B ^xT!J b @` @2 N  @P(@@D)!L@I~@@@Iv L2 BxA, !@ @ I%( U` @p`@|@,x>x  H @@ < @QAk@44L@?@@AAT@ `P            X;:8:(Y1E5.5)1E5;:20:(E1E5.5)1E5;:31:(F1E5.5)1E5s INCREMENT X AXIS BY AMOUNT OF RESOLUTION} XXA XR310 XD190 DD(A15)  ""PRESS 'C' TO CONTINUE... ":A$ ,A$"C"180 6 L"OPT FP=";:20:"+ FPERR=";:31:"- FPERR="X CALCULATE OPTIMUM FOCAL POINT RESULTSj Y(X2)(P4) CALCULATE MAXIMUM POSITIVE FP ERROR Y1(X2)(P14) CALCULATE MAXIMUM NEGATIVE FP ERROR Y2(X2)(P24) EY1Y FY2YD x"ENTER MAX (+) FOCAL POINT: ";P1I "ENTER MAX (-) FOCAL POINT: ";P2n "ENTER RADIUS OF PARABOLIC: ";R "ENTER RESOLUTION OF X-AXIS: ";A X0 SET UP RESULTS TABLE LENGTH TO 15 LINE DA15 SET UP TABLE HEADING, :"X=";:8: ==================6 *** WRITTEN BY ***P **FRANK W CLAUDE**j *** JUNE 1982 *** ==================d:"PARABOLIC FOCAL POINT ERROR CALCULATIONS"m INPUT DATA LINES 110 TO 150n"ENTER OPTIMUM FOCAL POINT: ";P#      ):"PRESS RETURN WHEN READY."5F$::U((4)"BLOAD SPIDER.X,A8192"2:22:"PRESS RETURN WHEN DONE.":F$:62450<:3