C64S tape image fileNUMERICAL METHOD  `ROOTS#DIFF 1 =DIFF 2  uDIFF 3  =DIFF 2 7HMOTORCYCLE JUMPI UHORSE RACE^MISSLE LAUNCH rCRACK THE SAFE9yHANGMAN LUNAR LANDERE BREAK AWAY ܕPRACTICE PING POiAUTO RACEN aBOMB SQUAD RUN AWAYʰADDITION AND SUB MORTGAGE LOANuDICE THROW!MULTIPLICATION A= PERPETUAL CALENDq CLOCK ]SAVINGS ACCOUNT vDAYS BETWEEN DAY 9RAILROAD "1"THIS PROGRAMME WILL DETERMINE THE]"ROOTS OF A FUNCTION OF X BY SEARCHING"FOR ZERO VALUES WITHIN A GIVEN RANGE." "WHAT FUNCTION DO YOU WISH SOLVED?Y="; Y$:"170 DEFFNA(X)=";Y$ "GO TO 80"% "PRESS RETURN KEY TWICE":2P"":N0=ZB(10)Rd"RANGE START";Agn"RANGE END ";Bo"THIS RANGE BETWEEN";A;"AND";Bp"MUST NOW BE DIVIDED INTO A NUMBER"q"OF REGIONS SUCH THAT NOT MORE"r"THAN ONE ROOT WILL OCCUR WITHIN"!s"THE SPAN OF ONE REGION."8x"NO.OF REGIONS";CI}TI$"000000"WI(BA)Ck"SEARCHING":tX1AX2X1IX1B0330A(X)XY1A(X1):Y10N0X1X1I2:150Y2A(X2):Y20300X2X1.000001I300Y1Y20280X3(X1X2)2&Y3A(X3)7Y1Y30270AX2X3J180TX1X3]180gX1X2p"150,B(N)X2:PX22"ROOT";N1;"= "(P)((P)100000.5)1000004NN1:Y30:X305"CONTINUING SEARCH":6280 J"NO ";:T010:HHB(T):T#LH0"FURTHER ";?N"ROOTS IN GIVEN RANGE"f"THE SEARCH TOOK ";TI60;" SECS.""IF YOU WANT TO SEARCH ANOTHER""RANGE FOR THE SAME FUNCTION""TYPE A IF NOT PRESS ANY OTHER KEY"59468,12LL$:LL$""456 LL$"A"80 "":900; "ENTER STARTING VALUES FOR X,Y,DY/DX"b "D2Y/DX2,STEP,& FINAL VALUE OF X"}"";X0,Y0,Z10,Z20,H,F""AX0:BY0:CZ10:DZ20NN05)"X"20)"Y"5)(1000A.5)100020)(1000B.5)1000 NNNN1"NN2040-$"PRESS ANY KEY TO CONTINUE LIST"6%""H&T$:T$""38Q'NN0g(XA:YB:Z1C:ZZDp2500y<A1EF600PB1GZ700dC1JnXAH2xYBHA12Z1CHB12ZZDHC12500A2E600B2G700C2JYBHA22-Z1CHB22=ZZDHC22F500OA3EX600aB3Gj700s"C3J},XAH6YBHA3@Z1CHB3JZZDHC3T500^A4Eh600rB4G|700C4JAAHBBH(A12A22A3A4)6"CCH(B12B22B3B4)6@DDH(C12C22C3C4)6[FX0AF.00000130vFX0FA.00000130800EZ1:XGZZ:JXY3Z12ZZ "IF YOU WANT TO USE THE SAME EQUATION" *"WITH DIFFERENT PARAMETERS THEN TYPE A"%/"IF FINISHED TYPE F"84T$:T$""820H>T$"A"10XH59468,12:^"THIS PGM. SOLVES 3RD ORDER EQUNS. OF""THE FORM :-""A*D3Y/DX3+B*D2Y/DX2+C*DY/DX+D*Y+E=0" "WHERE A,B,C,D,E MAY BE CONSTANTS OR FUNCTIONSOFX". "RE-ARRANGE YOUR EQN. IN THE FORM"N "D3Y/DX3 = F(X,Y,Z1,ZZ)"t "WHERE Z1 REPLACES DY/DX & ZZ " "REPLACES D2Y/DX2" "WHAT IS YOUR EQUATION?" "D3Y/DX3= ";L$ "700 J=";L$ "GOTO10 "PRESS RETURN KEY TWICE":& "700J=F(X,Y,DY/DX,D2Y/DX2)"O "YOU NEED INITIAL STARTING VALUES"k "OF X,Y,DY/DX,D2Y/DX2" "PRESS ANY KEY TO CONTINUE" P$:P$""1014 $ ""1 "THIS PROGRAMME USES RUNGE KUTTA"Z"TO SOLVE FIRST ORDER DIFFERENTIAL"{"EQUATIONS OF THE TYPE :-"5)"DY/DX= (FUNCTION OF X & Y)""WHAT IS YOUR EQUATION IN THIS FORM"#"DY/DX= ";K$("390 C=";K$-"GOTO100""2"PRESS RETURN KEY TWICE":Md"ENTER INITIAL VALUES X0,Y0,STEP H"en"& FINAL X VALUE"ux X0,Y0,H,E}8)"X"23)"Y"TI$"000000"AX0BY0NN05)(1000(A).5)100020)(1000B.5)1000NNNN1:NN20180"PRESS ANY KEY TO CONTINUE"2F$:F$""174;NN0CXAKYBT390]K1CiXAH2xYBK1H2390K2CYBK2H2390K3C"XAH,YBK3H6390@K4CJBBH(K12K22K3K4)6TAAHhEX0AE.0000011704rEX0EA.000001170=|410GCXYMv"PROCESSING TIME = ";TI60;"SECS.""IF YOU WANT THE SAME FUNCTION WITH""DIFFERENT PARAMETERS TYPE IN A""IF FINISHED TYPE F"LL$:LL$""424 LL$"A"10059468,12$ ""1 "THIS PROGRAMME SOLVES 2ND ORDER"] "DIFFERENTIAL EQUATIONS OF THE FORM:-"""3)"A*(D2Y/DX2)+B*(DY/DX)+Y=C""A NEW VARIABLE Z IS INTRODUCED SUCH""THAT:-Z=DY/DX""WHICH THEREFORE MEANS :-" 5)"DZ/DX =FUNCTION(X,Y,Z)"4"THIS GIVES TWO FIRST ORDER EQUNS"^"WHICH MAY BE SOLVED SIMULTANEOUSLY""PRESS ANY KEY TO CONTINUE"Z$:Z$""28"RE-ARRANGE YOUR EQUATION IN THE FORM" 3)"D2Y/DX2 =FUNCTION(X,Y,DY/DX)"""OR,WITH THE NEW VARIABLE Z THIS IS:-"6$5)"DZ/DX=FUNCTION(X,Y,Z)"V'"WHAT IS YOUR FUNCTION ?"h("DZ/DX= ";F$z*"530 E= ";F$,"GOTO100."PRESS RETURN KEY TWICE":d"ENTER INITIAL VALUES X0,Y0,DY/DX AT X0,"n"STEP,& FINAL X" X0,Y0,Z0,H,F8)"X"23)"Y"/AX0:BY0:CZ08NN0g5)(1000A.5)100020)(1000B.5)1000~NNNN1:NN20190"PRESS ANY KEY TO CONTINUE"M$:M$""187NN0XA:YB:ZC510A1D530B1EXAH2 YBHA12ZCHB12""510+,A2D46530=@B2ELJYBHA22[TZCHB22d^510mhA3Dvr530|B3EXAHYBHA3ZCHB3510A4D530B4EAAHBBH(A12A22A3A4)6 CCH(B12B22B3B4)6) FX0AF.000001180E FX0FA.000001180N 550V DZ\ i E XYZo  &"IF YOU WANT TO USE THE SAME EQUATION" 0"WITH DIFFERENT BOUNDARY VALUES" :"THEN TYPE A IF FINISHED TYPE F" DR$:R$""580 NR$"A"100 X