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OOGgccqpxsssssssppxxx|<<~?>~||xxxxppp```@@@`?~|x|~|||||||p@@p|~><|xp`@>|x|xpx}yyyyyyyAA?~|xpp`ppx|~? ?? 33@``@@glloLL LlOgloloG @`@glolo@@gLLL GaamGGlg`GGlg`G  xL| x@@xMLLxMyyM MyxAxMx|Yq @lllLglllgG LlL`@GLOLo033366m~0>3>33~G<`G}rccb``acccq{{{{8008????~ |lL COoooog CgoooocCFFLLXXPpqa88`}}}}>????~ | ~FCCFL ____|GG|GGccp{{{{ ;1q``qp`aas{{{{8008 0y| |}}}}AAQg((h' $C@0j ed`y < I1@@q q s8EE9EE8> ` `$DC0ANPQN@'h(' WPG((H@stq q8AyEx:NPQ@GhHHG#$p# @ (*Y9AyEy: QQQO~C%%C~_DDD qAAAaq9`ppxxx|xxx|AsGN8088 CcˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^L iõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- ( t Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈m浍浭m䵍䵐`"L ŵ8ŵH ~(` d ֠z# u`z!#XIJ    Ӡ ӠӠȠ͠àΠҠӠ  ԠҠӠΠҠӠ Π ӱ  ӠȠXIJ]!Ϡ ԠӠϠ ŠƠӠ͠ Ӡ ؠӠ ΠOGRAM NOW GIVES YOU A PLOT":I "OF YOUR DATA POINTS AND THE FITTED":t "FUNCTION, RESTRICTED TO THE FIRST": "QUADRANT (X,Y > 0).": " YOU WILL BE ASKED TO SET SCALES": "ON EACH AXIS." 23:"PRESS (RETURN) TO GO ON. ";A$ING FUNCTION' D3221,3223,3225,3227D F(X)V(2)XV(1):3230d F(X)(V(3)XV(2))XV(1)n 3230 F(X)((V(4)XV(3))XV(2))XV(1):3230 F(X)(((V(5)XV(4))XV(3))XV(2))XV(1) 3300 PLOT AXES :5:" THE PRK1 >QA(I,K)A(K,K):A(I,K)0FHJK1N:A(I,J)A(I,J)QA(K,J):lRR(I)R(I)QR(K):INII1:2110r\fV(N)R(N)A(N,N):IN111pQ0:JI1N:QQA(I,J)V(J)zV(I)(R(I)Q)A(I,I):: PLOTTING ROUTINE  DEFINE FITTQ(Q):Q4ĀMQ3110'RQ21501\3000MN1V(1)R(1)A(1,1):ZK1N1dIK1lLK(A(I,K))(A(L,K))LIINII1:2040 LK2100JKN:QA(K,J):A(K,J)A(L,J) A(L,J)Q:*QR(K):R(K)R(L):R(L)Q4IRESS (RETURN) TO GO ON. ";A$'::5M :"-- CONTINUATION OPTIONS --":t*" 1 - GRAPH POINTS AND FUNCTION"z/4" 2 - FIT ANOTHER FUNCTION, SAME DATA"9>" 3 - ENTER NEW DATA":C" 4 - END PROGRAM"E H"WHAT NEXT? ";Q:J111:"-";::2J1N:" ";J1,V(J):::dQ0:J1NP:QQY(J)::MQNP:T0:G0:J1NPQ0:K1N:QQV(K)X(J)(K1)::TT(Y(J)Q)2GG(Y(J)M)2::G0T100:780T100(1TG) "PERCENT GOODNESS OF FIT = ";T23:"PJ)0:K1NP.R(J)R(J)Y(K)X(K)(J1)::TJ1N:K1N:A(J,K)P(JK2)::^2000:"BEST FIT POLYNOMIAL OF DEGREE ";D:"HAS COEFFICIENTS AS FOLLOWS: "::1);"X POWER COEFFICIENT"1);:J17:"-";::17);REE?": ," C. STOP?":9 6"TYPE A, B, OR C: ";A$I @A$"A"110Y JA$"B"150t T:"RUN STOPPED":5000 ^ND1:D22D XJ1D2:P(J)0:K1NP bP(J)P(J)X(K)J:::P(0)NP lR(1)0:J1NP:R(1)R(1)Y(J) v:N1660 J2N:R():D1D4150 DNP350N :5:" THE NUMBER OF DATA POINTS MUST BE":| "GREATER THAN THE DEGREE OF THE POLY-": "NOMIAL YOU ARE FITTING": "DO YOU WANT TO: ": " A. ENTER MORE DATA POINTS?": "" B. CHANGE POLYNOMIAL DEG"PRESS (RETURN) TO GO ON";A$:3340( W :5:" WHAT TYPE OF POLYNOMIAL FIT":t "DO YOU WANT TO TRY?": " 1. LINEAR": " 2. QUADRATIC": " 3. CUBIC": " 4. QUARTIC": " ENTER 1,2,3, OR 4: ";D D(D(NP):NP1NP75110F :" NOW ENTER YOUR DATA POINTS IN THE":\ "FORM X,Y :"::w "POINT","X(I),Y(I)": J1NP "X(";J;"),Y(";J;")", "";X(J),Y(J) J" :"NOW A PLOT OF YOUR DATA IN THE FIRST"::"QUADRANT (X>0,Y>0)"::AIRS AND SELECT THE":0 Z"POLYNOMIAL DEGREE."Z d(23):"PRESS (RETURN) TO GO ON. ";A$ n::5:" THE PROGRAM CAN HANDLE FROM 1": x"TO 75 DATA PAIRS. ": " HOW MANY DATA PAIRS? ";NP X(NP),Y(NP),A(8,8),R(8),V(8),P(14) NP 38400 :B(10):" LEAST SQUARES CURVE FITTING"SI11000:I^(:(5)2" THIS PROGRAM USES THE LEAST SQUARE":<"METHOD TO FIND A POLYNOMIAL FUNCTION":F"FITTING DATA PAIRS (X,Y). YOU WILL": P"ENTER THE DATA P      d< A61A208F A94A204>P A83B71C78A210:QQ2^Z A73B78C84A211:QQ2~d A65B66C83A212:QQ2n A83B81C82A218:QQ2x A76B79C71A220:QQ2 A69B88C80A221:QQ2 A67B79C83A222:QQ2 :(6):(5):"INPUT FUNCTION ? "9 9:5:"F(X) = ";A$V FINI(176)256(175)3d FOLDFINIp L(A$) STR(112)256(111) Q1L A(STRQ1):B(STRQ):C(STRQ1) A42A202 A43A200( A45A2012 A47A203 F(X) F(X+1)-F(X)"7(I):(4):XXSIVKI((AKX))AKl (I):(16):((AK(F(X))))AK(I):(29):((AK(F(X1)F(X))))AK K*(23):"HIT ANY KEY TO GO ON":T$4100>(23):"HIT ANY KEY TO GO ON":T$H720!NIMUM MUST NOT EXCEED MAXIMUM":660B:"INCREMENT VALUE ? ";IVh(23):"HIT ANY KEY TO GO ON":T$r:I3" X F(X) F(X+1)-F(X)"J((XLXS)IV)K0JII2:I21I3:(23):"HIT ANY KEY TO GO ON":T$::" X ))))AKXIb4l"HIT ANY KEY TO GO ON":T$=v520F100Lw(3):"WHAT IS THE MINIMUM VALUE OF X":" FOR YOUR TABLE ? ";XS:"WHAT IS THE MAXIMUM VALUE OF X":" FOR YOUR TABLE ? ";XLXSXL700#:"MIX + ";((AKB))AK I ? "HIT ANY KEY TO GO ON":T$H 260Q 100W  " X F(X) F(X+1)-F(X)" I3212 &(I):(4) 0"";X :X99999640 D(I):(16):((AKF(X)))AKN(I):(30):((AK(F(X1)F(X(3I):(6):((AKY1))AK3 r(3I):(11):"";X2A |Y2F(X2)a (3I):(16):((AKY2))AKq X1X2410 :"VALUES OF X1 AND X2 MUST BE":"FURTHER APART." 470 M(Y2Y1)(X2X1) BY1MX1 (3I):(26) "Y= ";((AKM))AK;""2"520 M$"1"650; :"YOU MUST TYPE 1,2,3,4,OR 5"D 190J ^ (3):(1):"X1"r (3):(6):"Y1" "(3):(11):"X2" ,(3):(16):"Y2" 6(3):(26):"EQUATION" @I2192 J(3I):(1):"";X1 TX199999510 ^Y1F(X1) h VALUES OF X"= :(5):"3 TABLE OF SECANT LINE EQUATIONS"e (8):"FOR GIVEN PAIRS OF X-VALUES" :(5):"4 NEW FUNCTION" :(5):"5 STOP PROGRAM" :" TYPE YOUR CHOICE: ";M$ M$"5"Ā M$"4"90 M$"3"260 M$OR X"+ P(23):"HIT ANY KEY TO GO ON":K$7 Z:2500= dI iAK1000h n(3):"SELECT YOUR TABLE:" x:(5):"1 TABLE OF F(X) AND F(X+1)-F(X)" (8):"OVER A GIVEN INTERVAL" :(5):"2 TABLE OF F(X) AND F(X+1)-F(X)" (8):"FOR SELECTED  8192A$(100)"(A$""X2:(3):"THIS PROGRAM WILL GIVE TABLES OF VALUES"<:" FOR A GIVEN FUNCTION OF X."F::"YOU WILL TYPE IN THE FUNCTION AND"::" CHOOSE THE TABLE YOU WISH TO SEE." K::"TO END A TABLE TYPE 99999 F  A$ 795 'TING THE FITTED FUNCTION."9 " X-AXIS SCALE = ";SXX " Y-AXIS SCALE = ";SY_ 6l I0274w PX5I PYF(ISX10)(10SY) PY155PY PX0PX2793550 PY0PY1593550 PX,PY I~"PRESS (RETURN) TO GO ON. ";S SCALE = ";SX-; " Y-AXIS SCALE = ";SY4< 3@> I1NPjH PX5(X(I)SX)10:PY155(Y(I)SY)10J PX(PX):PY(PY)K PX0PX2793420N PY0PY1593420R PX,PY\ I "PRESS (RETURN) TO GO ON ";A$: :::: 21:"PLOT ::: 3340 3501% :1C 5,05,159:0,155279,155`# I145510:3,I7,I:I& I1526510:I,153I,157:I( :::* 21:"X-AXIS SCALE? ";SX4 "Y-AXIS SCALE? ";SY5 ::::9 21:"PLOTTING YOUR DATA": " X-AXI:"IS LIMITED TO A 5 BY 5. ENTER TEH":"INFORMATION AS PROMPTED."s :"HOW MANY ROWS IN B ";:RB:RB1RB5210 :"HOW MANY COLUMNS IN B ";:CB:CB1CA5220 RRB:CCB SA0:SB1 150 10 ,D2000B .CARBĢ12:"NUMBER OF COLULUMNS IN A ";:CA:CA1CA5120. yRRA:CCA< zSA1:SB0E }150M 10X J1Ca :4w 10);"COLUMN ";J} I1R:5);"ROW ";I;13);:X SA1A(I,J)X SB1B(I,J)X : B " FOR DISPLAY PURPOSES, THE SIZE OF B":10);"WHICH NUMBER ";:X+ #X1X5301 %L (X100,200,300,400,500 d" FOR DISPLAY PURPOSES, THE SIZE OF A":"IS LIMITED TO A 5 BY 5. ENTER THE":"INFORMATION AS PROMPTED." n:"HOW MANY ROWS IN A ";:RA:RA1RA5110 x:"HOW MANY CO A(5,10),C(5,5),B(5,5)? ::4:12);"M A T R I C E S"b8:10);"1. ENTER A MATRIX A"10);"2. ENTER A MATRIX B"10);"3. COMPUTE THE MATRIX PRODUCT":13);"OF A AND B"10);"4. COMPUTE THE INVERSE OF A"10);"5. STOP"       2 TO DO ANOTHER ON THESE AXES,"<" OR 3 TO QUIT.";NKOUNTKOUNT1UR[iR34900KOUNTNĢ21:"YOU ONLY ASKED FOR ";N;" LINES!":R4100,185,4900  180$.3218"GOOD-BYE"B0 HUI5 KVSLOPEI;: H0H279K0K159H1H:K1KBN IQX I12005gb HUI:KVSLOPEIl H0H279K0K159H2H:K2Kq Iv H1,K1H2,K2H21,K2H11,K1{  21 400021"TYPE 1 TO ERASE AND DO ANOTHER,"$"K2H21,K2H11,K1 4000A SUBROUTINE FOR POINT AND SLOPEG O 21c "ENTER X0,Y0";n X0,Y0 BETA(KOUNT) U140X010:V80(Y010) U,VU1,V 22 "ENTER THE SLOPE" SLOPE  PAUSE1500:PAUSE & I02005 U214010X2:V28010Y2- *U2,V2U21,V2C 4S(Y2Y1)(X2X1)R >I12005] HHU1Ij MKV1SI RH0H278K0K158H1H:K1K:2160 pI zI12005 HU1I KV1SI H0H278K0K159H2H:K2K:2200 I H1,K1H2, 2 POINTS  21C "ENTER X1, Y1 "N X1,Y1k U114010X1:V18010Y1| BETA(KOUNT) U1,V1U11,V1  21 "ENTER X2, Y2 " X2,Y2 X2X1ēU1,0U1,159U11,159U11,0:4000 PS"ī3000# "CHECK YOUR TYPING!", 210@  PLOT AXES F M 3^ 0,80279,80q 140,0140,159 141,0141,159 I027910 I,78I,82 I1,78I1,82 $I .I015910 8138,I143,I BI G  SUBROUTINE FOR GIVE ME EITHER TWO POINTS ON THE"J "LINE OR ONE POINT AND THE SLOPE."c PAUSE12500:PAUSEi s 1000y 21 "TYPE '2P' OR 'PS' TO TELL ME WHICH."; PAUSE11000:PAUSE METHOD$ METHOD$"2P"ī2000 METHOD$" BETA(1)1#BETA(2)21BETA(3)5?(BETA(4)6M2BETA(5)3Sd{n"SO YOU WANT TO GRAPH SOME LINES."sx"HOW MANY LINES WOULD YOU LIKE TO GRAPH?"NKOUNT1KOUNTNĺ"COME ON, NOW!":140" "YOU CAN    : A83B73C78A223:QQ2> A84B65C78A224:QQ2^ A65B84C78A225:QQ2v FINI,A:FINIFINI1|  FINI,58:FINI1,177 FINI2,0:FINI3,0:FINI4,0 FOLD10,(FINI3)256 FOLD11,FINI3256(FOLD10) F(X)к1;10);AR;25);AZ/I2N:HH2:M2M[J1M2:XAJH:20:TZTZY:TRTRY:JoARTRH:AZTZHM;10);AR;25);AZI::"** HIT RETURN TO CONTINUE **";:X$:1000h,:5:" WHEN REQUESTED, PLEASE GIVE ME THE":"INTERVAL (A,B) O ";:NF N1N18ĺ:" *** FEWER DOUBLINGS PLEASE !! ***"::214L j XA:20:TZY:XB:20:TRY TZ(TZTR)2:HBA ARTRH:AZTZH M1 :" DIV";10);"RECTANGLES";25);"TRAPEZOIDS"" ---";10);"----------";25);"----------":":"CURRENT FUNCTION FROM A POINT A TO A ":"POINT B. I WILL ASK YOU FOR A AND B," "AND THE MAXIMUM NUMBER OF TIMES YOU":"WANT THE NUMBER OF TRAPEZOIDS DOUBLED.": " WHAT IS A ";:A " WHAT IS B ";:B: " NUMBER OF DOUBLINGNG FORM:":9 n"20 Y=F(X) ":"RUN ": s"WHERE F IS AN APPROPRIATE FUNCTION":"OF X. '' INDICATES FOR YOU TO":"HIT THE RETURN KEY." xS :" I WILL USE RECTANGLES AND TRAPEZOIDS":"TO APPROXIMATE THE INTEGRAL OF THE 61573,.171324493,.295524225,.269266719,.219086363,.149451349 .066671344,.202578242,.198431485,.186161,.166269206,.139570678,.107159221,.070366047,.030753242  Y(XX)  d:" PLEASE ENTER THE DESIRED FUNCTION":"IN THE FOLLOWI87,.932469514,.148874339,.433395394,.679409568,.865063367 .973906529,0,.201194094,.394151347,.570972173,.724417731,.848206583,.937273392,.987992518= 1,.888888889,.555555556,.652145155,.347854845,.568888889,.478628671,.236926885,.467913935,.3607 NP%(7),KE%(8),Z(24),W(24)*1000tI17:NP%(I):I:I18:KE%(I):I:I124:Z(I):I:I124:W(I):I2,3,4,5,6,10,151,2,4,6,9,12,17,259  .577350269,0,.774596669,.339981044,.861136312,0,.53846931,.906179846,.238619186,.6612093     :I1RA:J1RA:" ";(A(I,J)100.5)100;:::_::"HIT RETURN TO CONTINUE ";:X$:1012:18);::"SMILE"::24:X1RA:J1RA:(J1)81);((C(I,J)),7);::::"THE INVERSE OF A":I1RA:J1RA:(J1)81);((A(I,JRA)),7);:::::"HIT RETURN TO SEE THEIR PRODUCT"I1RA:J1RA:S0:T1RA:SSA(I,RAT)C(T,J)::A(I,J)S::X$:34EBB.00001ĺ:"NON-INVERTIBLE MATRIX. HIT RETURN. ";:X$:10yTA(I,I):KI12RA:A(I,K)A(I,K)T::A(I,I)1K1RA:KI450TA(K,I):A(K,I)0:LI12RA:A(K,L)A(K,L)TA(I,L):KK11000::"MATRIX A"2I)81);((A(IX,JX)),7);::::x::"INVERSE OF A":IX1RA:JXRA12RA:(JX1RA)81);((A(IX,JX)),7);:::BB(A(I,I)):IBI:RAI428KI1RA:(A(K,I))BBBB(A(K,I)):IBK:IIBāKI2RA:TA(I,K):A(I,K)A(IB,K):A(IB,K)T:OR A !!":X11000::10"TRA{CATĢ12:"A MUST HAVE THE SAME NUMBER OF ROWS":"AND COLUMNS !":X11000::10I1RA:J1RA:C(I,J)A(I,J)::I1RA:JRA12RA:A(I,J)IJRA:: I1RA::"MATRIX A":IX1RA:JX1RA:(JX1CA:(J1)81);((A(I,J)),7);::::mt"MATRIX B":I1RB:J1CB:(J1)81);((B(I,J)),7);::::v"PRODUCT MATRIX":I1RA:J1CB:(J1)81);((C(I,J)),7);::::x"HIT RETURN TO CONTINUE";:X$:10RA0Ģ12:"INPUT A MATRIX F(JX1)81);((B(IX,JX)),7);::) D:A J:"PRODUCT MATRIX"^ TIX1I:TCB:IIXTJ1k UT0345 VJX1T:(JX1)81);((C(IX,JX)),7);: Y: ^S0:T1CA:SA(I,T)B(T,J)S::C(I,J)S h:T1D:::(r:"MATRIX A":I1RA:J1MNS IN A MUST EQUAL THE":"NUMBER OF ROWS IN B.":X11000::10V 1I1RA:J1CBh 5:"MATRIX A"u 6IX1RA 8IXIĞ :JX1CA:(JX1)81);((A(IX,JX)),7);:JX <::IX =:"MATRIX B" >IX1RB @JX1CB:" ";:JXJĞ! BST GIVE":"ME THE ENDPOINTS OF AN INTERVAL THAT" "CONTAIN A ROOT. YOU ALSO MUST GIVE ME":"THE NUMBER OF DECIMAL PLACES YOU'D" "LIKE IN THE ANSWER." : "WHAT IS THE LEFT HAND ENDPOINT ";:XL: "WHAT IS THE RIGHT HAND ENDPOINT ";:;XN;23);FX" \(XNX0)ACC2200/ fX0XN:I p:" *** FAILED TO CONVERGE ***"::"HIT RETURN TO CONTINUE";:X$:10000 :" *** DESIRED ACCURACY ATTAINED ***"::"HIT RETURN TO CONTINUE ";:X$:100000 :" FOR INTERVAL HALVING, YOU MU ACC(.1)10 SIG10N.51 XX0:20:FXY; I%18H I1MAXT I%I%1 I%19Ģ24:"HIT RETURN TO CONTINUE";:X$::"ITERATION";16);"X";30);"F(X)"::I%1 *XX0.001:20:FDY 4XNX0FX(FDFX).001 >XXN:20:FXY R5);I;11)> "NUMBER OF DECIMAL PLACES YOU WANT IN ":"THE ANWER."::f "GIVE ME AN INITIAL GUESS ";:X0: "GIVE ME A MAXIMUM # OF ITERATIONS ";:MAX: "GIVE ME THE # OF DECIMAL PLACES ";:N:N1N9ĺ:" *** BETWEEN 1 AND 9 PLEASE ! ***"::2050G" =' B" 3. FALSE POSITION"K L::"WHICH ";:X:X1X31060a VX2000,3000,4000 :" NEWTON-RAPHSON REQUIRES THAT YOU":"GIVE ME AN INITIAL GUESS AT THE " "ROOT, A MAXIMUM NUMBER OF TIMES TO":"ITERATE THE ALGORYTHYM, AND THE "=F(X) "d :"WHERE F IS AN APPROPRIATE FUNCTION":"OF X. AFTER ENTERING YOUR FUNCTION," "TYPE:"::" RUN ":: " $:4:"SELECT METHOD TO BE USED:": ) ." 1. NEWTON-RAPHSON" 3 8" 2. INTERVAL HALVIN  1000Y(X)3X N:4:5);"***** ROOT FINDING DEMO *****"8:"CURRENT FUNCTION:"::20:::"DO YOU WANT A DIFFERENT FUNCTION ";:X$(X$,1)"N"1060(X$,1)"Y"1000 :"TYPE YOUR FUNCTION AS IN THIS EX:"::"20 Y     4. SIMPSON'S RULE"'.15);"5. STOP"8:" WHICH NUMBER ";:S:S1S5ĺ:"***** CORRECT NUMBER PLEASE ! ****":1080BS100,200,300,400,500SN TO CONTINUE ";:X$1000(::W::" **** INTEGRATION DEMO ****"::"CURRENT FUNCTION IS :":20:::" OPTIONS:";15);"1. DIFFERENT FUNCTION"15);"2. TRAP-RECT RULE"15);"3. GAUSS-LEGENDRE"$15);" B = ";B7::"# OF PANELS";20);"INTEGRAL":XXA:20:ENY:XB:20:ENENYjM2:W(BA)2uI1N~NE0J1M2:XAJW:20:NEYNE:JAREAW3(EN4NE)ENEN2NE:WW2:MM23);M4;20);AREAI::"HIT RETURA, B AND THE NUMBER"B"OF TIMES YOU WANT THE INTERVAL HALVED."\::"WHAT IS A ";:At:"WHAT IS B ";:B:"HOW MANY HALVING ";:NN1N18ĺ:" *** FEWER DOUBLINGS PLEASE !! ***"::420:" FUNCTION : ":20:"A = ";A;"UFDW(J)JvZ(J)0XZ(J)CD:20:FY:XZ(J)CD:20:SUSUW(J)(FY)[xJ:GACSU:a5:" I WILL USE SIMPSON'S RULE TO APPRO-""THE INTEGRAL OF THE CURRENT FUNCTION":"FROM THE POINT A TO THE POINT B. I WILL";:"ASK YOU TO GIVE ME GABM15:350:8);M;20);GASD:" ** HIT RETURN TO CONTINUE **";:X$:1000l^I17:MNP%(I)360cI:"**** ERROR ****":I12000:I:1000hJFKE%(I):JLKE%(I1)1:C(BA)2:D(AB)2:SU0mXD:20:FDYrJJFJL tZ(J)0SUS= ";BY4::5);"ORDER";20);"INTEGRAL APPROX.":5);"-----";20);"----------------":u6M2:350:8);M;20);GA8M3:350:8);M;20);GA:M4:350:8);M;20);GA<M5:350:8);M;20);GA>M6:350:8);M;20);GA@M10:350:8);M;20);F INTEGRATION. I WILL":"THEN USE GAUSS-LEGENDRE QUADRATURE ":"FORMULAS OF ORDERS 2,3,4,5,6,10 AND 15"."TO APPROXIMATE THE INTEGRAL.":::" WHAT IS A ";:A0:" WHAT IS B ";:B132::"FUNCTION :":20:::" A = ";A;" B UATIONS (1 - 11) ";:NdN1N11ĺ:" *** WRONG NUMBERS ***";::"HOW MANY EQUATIONS ";:N:202sN1N:NN1:"MAXIMUM NUMBER OF ITERATIONS ";:MAX::"ACCURACY REQUIREMENT ";:ACC2000::" GIVE ME AN INITIAL GUESS "::$I,I):A(K,I)0:LI1N1:A(K,L)A(K,L)TA(I,L):L7 K> I :" ******* DONE *******"::"HIT RETURN FOR ANSWERS";:X$ ::I0N:" X(";I1;") = ";A(I,N1):I::"HIT RETURN TO CONTINUE ";:X$ 3000 280:10:"HOW MANY EQRETURN T O CONTINUE";:X$:3000 T$"Y"ĺ" ** ITERATION ";I1;" **":K0N::L0N1:6L1);((A(K,L)),5);:L::K::"** HIT RETURN TO CONTINUE **";:X$ TA(I,I):KI1N1:A(I,K)A(I,K)T:K:A(I,I)1 K0N:KI1500 TA(KLOW ME":"TO CONTINUE THE ALGORYTHYM."J :"HIT RETURN TO START";:X$: I0N:B(A(I,I)):IBI:KI1N:(A(K,I))BB(A(K,I)):IBK :IIBāKIN1:TA(I,K):A(I,K)A(IB,K):A(IB,K)T:K* B.00001ĺ:"**** MATRIX SINGULAR ****"::"HIT "* PLEASE ! GIVE ME PROPER NUMBERS ! *"::102< lN1N1F n2000 s::T$"N":N6ĺ"DO YOU WANT ME TO SHOW YOU THE MATRIX":"DURING THE DIAGONALIZATION";:T$& xT$"Y"ĺ:"I WILL PUT THE MATRIX ON THE SCREEN.":"YOU WILL HAVE TO HIT RETURN TO ALF PRINTING OUT THE MATRIX DURING EACH":"PASS. ROW INTERCHANGE IS USED TO PUT":"THE ENTRY WITH LARGEST MAGNITUDE ON THE":"DIAGONAL & CHECK FOR SINGULARITY."::" ** HIT RETURN **";:X$: f" HOW MANY EQUATIONS (1 - 11) ";:N:NN11 iN0N10ĺ:f Y(11)A(10,11)$ 1000d::5:" GAUSS-JORDAN ELIMINATION WILL BE USED":"TO SOLVE YOUR SYSTEM. WHEN PROMPTED,":"ENTER THE APPROPRIATE INFORMATION.":"IF YOUR SYSTEM HAS LESS THAN SIX UN-":"KNOWNS, YOU WILL BE GIVEN THE OPTION e"O     HIT RETURN TO CONTINUE";:X$:10000-;X0XM4@IJ:" *** DESIRED ACCURACY NOT ATTAINED ***"::"HIT RETURN TO CONTINUE";:X$:10000':10:"DO YOU WANT TO GO AGAIN ";:X$:(X$,1)"Y"1000'(X$,1)"N"10000$':NNTINUE";:X$::"ITERATION";20);"X-LEFT";32);"X-RIGHT"::I%1]XMXLFL(XRXL)(FRFL)oXXM:20:FMYFLFM0FRFM:XRXM"FLFM0FLFM:XLXM,5);I;16);XL;29);XR#6(XMX0)ACCĺ:" *** DESIRED ACCURACY ATTAINED ***"::":100009"WHAT IS THE MAXIMUM # OF ITERATIONS ";:MAX"HOW MANY DECIMAL PLACES IN YOUR ANSWER ";:N:N1N9ĺ:" *** BETWEEN 1 & 9 PLEASE !! ***"::4080I%18ACC.1NX0XLI1MAX@I%I%1:I%19Ģ24:"HIT RETURN TO CO"WHAT IS THE RIGHT HAND ENDPOINT ";:XRXLXR0ĺ:"*** ENDPOINTS IN THE WRONG ORDER !! ***"::"HIT RETURN TO CONTINUE";:X$:10000XXL:20:FLY:XXR:20:FRYFLFR0ĺ:" *** NO ROOT IN INTERVAL ***"::"HIT RETURN TO CONTINUE";:X$SITION METHOD, YOU":"MUST GIVE ME THE ENDPOINTS OF AN":"INTERVAL CONTAINING A ROOT, THE MAXIMUM":"# OF TIMES THE ALGORYTHYM IS ITERATED &""THE NUMBER OF DECIMAL PLACES YOU WANT":"IN THE ANSWER.":::"WHAT IS THE LEFT HAND ENDPOINT ";:XL*ES HALVED";18);"X-LEFT";28);"X-RIGHT"::I%1M XM(XRXL)2:XXM:20:FMYm! FLFM0XRXM:FRFM:3120" FLFM0XLXM:FLFM0 5);J;16);XL;28);XR: J::"*** DONE ***"::"HIT RETURN TO CONTINUE ";:X$:10000:" FOR THE FALSE POFRFL0ĺ:"THERE'S NOT AN ODD NUMBER OF ROOTS IN":"THE INTERVAL YOU GAVE ME.":"":"HIT RETURN TO CONTINUE ";:X$:10000 J1:I150:JJ2:BJSIG3090 I I50 I%18. J1I:I%I%1:I%19Ģ24:"HIT RETURN TO CONTINUE";:X$::"TIMXR:i "HOW MANY DECIMAL PLACES IN ANSWER ";:N:N1N9ĺ:"*** BETWEEN 1 AND 9 PLEASE ***"::3060v SIG.1N BXRXL:B0ĺ:"YOU GAVE ME THE ENDPOINTS WRONG !!":"HIT RETURN TO CONTINUE ";:X$:10000 XXL:20:FLY:XXR:20:FRY} TRIX ADDITION,SUBTRACTION ***"F 5:"*** SCALAR MULTIPLICATION ***"N :a "1. ADDITION"w "2. SUBTRACTION" "3. SCALAR MULTIPLICATION" :"WHICH"; D:D0D33070  D33120 "VALUE OF SCALAR";& S0 "DIMENSIONA(J,K) K I1R' IJ23805$ YA(I,J)B. K1R1]8 A(I,K)A(I,K)YA(J,K)dB KkL IrV Jz` :j I1Rt "X";I;"=";A(I,R1)~ I : "MORE DATA"; RE$:RE$"Y"RE$"YES"2000 40 7000 " *** MANSTANT "; \A(J,I) fI# pJ. zJ1R9 IJRM A(I,J)02230T I (7);(7);(7);"SORRY--;"::"NO UNIQUE SOLUTION": 2440 K1R1 XA(J,K) A(J,K)A(I,K) A(I,K)X K Y1A(J,J) K1R1A(J,K)Y ~40 70009 5:"*** SIMULTANEOUS EQUATIONS ***"A :e "NUMBER OF EQUATIONS (9 MAX)";z R:R2R92040 :"COEFFICIENT MATRIX:" J1R "EQUATION ";J *I1R1 4IR12130 >" COEFFICIENT ";I; H2140 R" CO .S01100" 0R1(BR)(2A)6 2R2(BR)(2A)] 8:::"ROOTS (REAL): ";R1;", ";R2g B1110w LR1B(2A) PR2R(2A) T:::"ROOTS"::" (COMPLEX)";::R1;"+OR- ";R2 V::: `"MORE DATA"; jRE$ tRE$"Y"RE$"YES"10001RE540* _RE1000,2000,3000,4000,50004 7000 6:"ROOTS OF QUADRATIC EQUATIONS":5:"------------------------------" ::"EQUATION MUST BE IN THE FORM:AX^2+BX+C=0" ::"COEFFICIENTS A,B,C"; A,B,C S(B2)(4AC) $R((S))---"/ 2::"1. ROOTS OF QUADRATIC EQUATIONS"Z 7:"2. SIMULTANEOUS EQUATIONS (9 MAX)" <:"3. MATRIX ADDITION & SUBTRACTION--":" SCALAR MULTIPLICATION" F:"4. MATRIX MULTIPLICATION (10X10 MAX)" P:"5. QUIT" Z19:"WHICH ?";RE ]REѳ :255#A(10,10),B(10,10)L :7:"COMMON BASIC PROGRAMS--VOL.2"~:"ADAPTED FOR THE APPLE II BY JOSEPH BOLUS""JUNE 23,1978"#I13000:I(::"SIMULTANEOUS EQ. AND MATRIX OPERATIONS" -"------------------------------------   "ENTRY # ";J1;:A(I,J):J$HI:\ :10:"DO YOU WANT TO GO AGAIN ";:X$:X$"Y"1000d :2":#:10);"WHICH METHOD ";:XZX1X2ĺ:" **** WRONG NUMBER ****":1030iX100,200o>:"I WILL NOW ASK YOU FOR THE AUGMENTED":"COEFFICIENT MATRIX A ROW AT THE TIME. "C34,11:DI0N:10:"ROW # ";I1:FJ0N1:TIONS IS LESS THAN THE AC-":"CURACY FIGURE THEN THE ITERATIONS ARE":"STOPPED."::" ** HIT RETURN **";:X$:y'201::4:"* SIMULTANEOUS LINEAR EQUATION SOLVER *"1010);"1. GAUSS JORDAN METHOD":10);"2. GAUSS SEIDEL METHOD 2. A MAXIMUM NUMBER OF ITERATIONS":K" 3. AN ACCURACY FIGURE": ::"THE ACCURACY IS USED TO STOP THE":"ITERATIONS BEFORE THE MAXIMUM NUMBER.":" IF THE SUM OF THE ABSOLUTE DIFFERENCES"p""BETWEEN ENTRIES IN TWO SUCCESSIVE":"APPROXIMA RETURN TO CONTINUE **";:X$|I::"**** DESIRED ACCURACY NOT ATTAINED ****";::"HIT RETURN TO CONTINUE ";:X$:3000::5:" THE GAUSS-SEIDEL METHOD IS AN ITER-":"ATIVE ALGORYTHYM THAT REQUIRES :"::" 1. AN INITIAL GUESS":("T(A(J,N1)T)A(J,J):D(TY(J))D:Y(J)T:JQ:" ** ITERATION ";I;" **"::uJ0N:"X(";J1;") = ";Y(J):J:"ACCURACY : ";D::DACCĺ"*** DESIRED ACCURACY ATTAINED ***"::"HIT RETURN TO CONTINUE";:X$:3000:" ** HIT0N:" X(";I1;") = ";:Y(I):ITT(A(0,0)):I1N:(A(I,I))TT(A(I,I))I:T.00001ĺ:"*** GAUSS-SEIDEL NOT APPROPRIATE ! ***"::"HIT RETURN TO CONTINUE ";:X$:3000I1MAX:D0:J0N:T0:K0N:JKTA(J,K)Y(K)T,K:YOU WANT"; N* MMN)4 N088901> 21;H 958ER 3185Kz"THE POSSIBLE OUTCOMES IN ROLLING 2 DICE""ARE: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12"9000X(15),F(15),D(15),E(15)10,155279,155,,Z  21b 4)"1:";X(1);10)"2:";X(2);16)"3:";X(3);22)"4:";X(4);28)"5:";X(5);34)"6:";X(6)i It I16 F(I)(100X(I)M) I 23 "PCT."6)F(1)12)F(2)18)F(3)24)F(4)30)F(5)36)F(6) 24  M;" TRIALS. HOW MANY MORE DO & 0 1": 0,155279,155)D 54N I16?X X(I)0Fb IQq I1Ncv Y(6(1))1s{ X(Y)X(Y)1~ Z155X(Y) Y1ē34,Z47,Z Y2ē76,Z89,Z Y3ē118,Z131,Z Y4ē160,Z173,Z Y5ē202,Z215,Z Y6ē244,Z257 23) "PCT."6)F016)F126)F236)F31 24^ M;" TRIALS. HOW MANY MORE DO YOU WANT";e No MMN} N08890 21 958" 2200  "THE POSSIBLE OUTCOMES IN ROLLING ONE DIE" "ARE: 1, 2, 3, 4, 5, 6"  9000 X2X21+ 174,155X22187,155X225 2700A ( X3X31` 2 244,155X32257,155X32j < 2700r 21 2)"TTT ";X012)"TTH ";X122)"THH ";X232)"HHH ";X3 I F0(100X0M) F1(100X1M) F2(100X2M) F3(100X3M)X30:X00 z5 I1N- Y1((1).5)? Y2((1).5)Q Y3((1).5)` YY1Y2Y3n Y02300| Y12400 Y22500 Y32600 X0X01  34,155X0247,155X02  2700 ` X1X11 j 104,155X12117,155X12 t 2700M;" TRIALS. HOW MANY MORE DO YOU WANT";0 2N8 721B 9958L <MMNZ FN08890d P1160j  "THE POSSIBLE OUTCOMES IN TOSSING 3 COINS" "ARE: 3T; 2T,1H; 1T,2H; 3H"  9000 4 > H1 R0,155279,155 \X10:X20:1N Y(1) Y.512603 Y.5TT1:1240= HH1Z 181,155H2194,155H2d 1260 97,155T2110,155T2 21 9)"TAILS ";T21)"HEADS ";H I F1(100TM) F2(100HM) 22 "PCT."15)F127)F2 24) (ICE" 1 "ENTER THE NUMBER OF YOUR CHOICE"; TYPEY TYPE1000,2000,3000,4000_  "THE POSSIBLE OUTCOMES IN TOSSING ONE"  "COIN ARE: HEADS, TAILS"  9000 L V [1 `0,155279,155 y5 ~H0:T0 I <"THIS PROGRAM SIMULATES FOUR EXPERIMENTS"B(j2"WITH RANDOM OUTCOMES. THEY ARE:"p<F" 1. TOSS ONE COIN"PZ" 2. TOSS THREE IDENTICAL COINS"dn" 3. ROLL ONE DIE"x " 4. ROLL TWO IDENTICAL D     SSA(I,K)B(K,J)K!.S;" ";5J;BIH!P&:g0"MORE DATA ?";RE$:RE$"Y"RE$"YES"4000D4070009999Xb'PIb'PI J1R1""ROW ";J&,I1C1A6" VALUE COLUMN ";I;M@A(J,I)TJI[TJa^rh"MATRIX 2:"~rJ1R2|"ROW ";JI1C2" VALUE COLUMN ";I;B(J,I)IJI1R1J1C2S0K1C1*** MATRIX MULTIPLICATION ***"&:J"DIMENSION OF MATRIX 1 (R,C)";UR1,C1y"DIMENSION OF MATRIX 2 (R,C)";R2,C2C1R24110(7);(7);::"CANNOT BE MULTIPLIED"::"OTHER DIMENSIONS NECESSARY."4390"MATRIX 1:" D33310 K :J1R* I1C9 D23350L B(J,I)B(J,I)Z D33380s A(J,I)B(J,I);" ";}* 33904 A(J,I)S;" ";> IH R J\ :f "MORE DATA";p RE$z RE$"Y"RE$"YES"3000 4070005:" OF MATRIX (R,C)";8: R,C:R1R43120:C1C103120CD K12QN K23180bX "MATRIX 1:"lb 3190}l "MATRIX 2:"v J1R "ROW";J I1C "VALUE COLUMN";" ";I;" "; K23260 A(J,I) 3270 B(J,I) I J PE 'Y' TO CONTINUE,"?"'N' TO STOP. WHEN F(X) - L EXCEEDS"m"THE TOLERANCE EPSILON, YOU WILL HEAR A""SIGNAL. NOW ENTER DELTA."D$D(D$)N1"DELTA = ";D$,"EPSILON = ";E$"X0 = ";X0,"L = ";LM L BY"0R"MORE THAN EPSILON, CHOOSE A SMALL"[\"VALUE OF DELTA AND WE WILL EVALUATE"f"F(X) IN STEPS OF DELTA AWAY FROM X0.";pz"WE WILL EVALUATE F(X) AT X0-ND AND""X0+ND, WHERE D = DELTA AND N = 1,2,...""AFTER EACH PAIR, TYAND L YOU WILL ALLOW."B "ENTER A SMALL VALUE OF THE TOLERANCE"k"EPSILON (.1 OR .01, FOR EXAMPLE)";s E$%E(E$)*4"LET DELTA BE THE DIVERGENCE FROM X0.">"TO SEE HOW BIG DELTA CAN BE WITHOUT"H"PERMITTING F(X) TO DIFFER FROPPROACHES X0? (Y OR N)"; vA$1 A$"N"12007 Z "ENTER THE APPARENT LIMIT L";a Lg  "TO MAKE F(X) CLOSE TO L, X SHOULD BE" "CLOSE TO X0. HOW CLOSE SHOULD IT BE?" "WELL, THAT DEPENDS ON WHAT TOLERANCE""BETWEEN F(X) E" ZA$ ! "X","F(X)"' : X0A,F(X0A)@ S X0A,F(X0A)Y c AA2n I15t !{ "I #"(Y TO CONTINUE, N TO STOP)"; 7A$ :A$"N"600 D400 X b"DOES THERE SEEM TO BE A LIMIT " l"TO F(X) AS X A99İ2000 ^"ENTER A." hA% mU r"AFTER EACH TWO EVALUATIONS, THE DISTANCE" w"BETWEEN X AND X0 IS HALVED. TO EVALUATE" y |"F AT X0-A/2*N AND X0 + A/2*N TYPE 'Y'."  "TO STOP EVALUATING, TYPE 'N'." :"TYPE 'GO' TO CONTINUOOSE A NUMBER X0 AND A NUMBER A SO") ;Y @"THAT F IS DEFINED ON (X0-A,X0+A), THOUGH" J"NOT NECESSARILY AT X0 ITSELF. ENTER X0." N O"IF X0 IS INFINITE, ENTER -999 FOR MINUS" P Q"INFINITY, 999 FOR PLUS INFINITY." TX0 Y(X0)9T FUNCTION IS GIVEN BY:"! 300L "ENTER YOUR FUNCTION RULE BY TYPING:"R l "300 DEF FN F(X) = "r "FOLLOWED BY YOUR FUNCTION RULE." "THEN TYPE 'RUN 300' AND PRESS RETURN." ,F(X)(1X2)(1X) 1# 6"CHH d4n"THIS PROGRAM EVALUATES A FUNCTION OF "cx"YOUR CHOICE NEAR A POINT OF YOUR CHOICE""TO SEE WHETHER THE FUNCTION VALUES""APPROACH A LIMIT AS X APPROACHES YOUR""CHOSEN NUMBER X0 (OR GOES TO INFINITY)." "THE CURREN T" d#Nn#MNx# NT"; NMMN# N08890+215958?4175G":u(#"WE WILL PERFORM THE EXPERIMENT AS MANY"{2#<#"TIMES AS YOU WANT. THE RESULTS WILL BE"F#P#"REPORTED NUMERICALLY AND IN A BAR GRAPH."Z#"HOW MANY TRIALS DO YOU WAN):C317E(5):C420E(6):C523E(7)`C626E(8):C729E(9):C832E(10):C935E(11):CZ38E(12)h23"PCT."C0)F(2)C1)F(3)C2)F(4)C3)F(5)C4)F(6)C5)F(7)C6)F(8)C7)F(9)C8)F(10)C9)F(11)CZ)F(12)24M;" TRIALS. HOW MANY MORE DO YOU WAD(2))X(2)11D(3))X(3)14D(4))X(4)17D(5))X(5)20D(6))X(6)23D(7))X(7)26D(8))X(8)29D(9))X(9)32D(10))X(10)35D(11))X(11);38D(12))X(12)0I:I212DF(I)(100X(I)M)IF(I)9E(I)1NI"C08E(2):C111E(3):C214E(4S4ē84,W97,W&S5ē105,W118,W<S6ē126,W139,WRS7ē147,W160,WhS8ē168,W181,W~S9ē189,W202,WS10ē210,W223,WS11ē231,W244,WS12ē252,W265,WK212X(K)9D(K)1K22"FREQ."856I212@X(I)0!JI)O215PV212GQF(V)0:E(V)0NRV|T"SUM 2 3 4 5 6 7 8 9 10 11 12"hI1N|Y(6(1))1Z(6(1))1SYZX(S)X(S)1W155X(S)S2ē42,W55,WS3ē63,W76,W1ĺ"PRESS RETURN TO CONTINUE";:GO$4 NMANY1900h PMANY1ĺ"PRESS RETURN FOR ANOTHER GRAPH";:GO$ Q:21:"MORE PATIENCE, PLEASE..." SI0N XX(I)AI(BA)N ]Y(I)(SY)G(X(I))79 ^I _5 `970 a:21:310bMANY2ĺ"PR"ENTER YOUR CHOICE OF B";! B+ 1000< N(BA)SX2K &N99N99Q 3j 4PAUSE11000:PAUSE 521:"PATIENCE, PLEASE...I'M NOT AN IBM" :I0N ?X(I)AI(BA)N DY(I)(SY)F(X(I))79 II J2 K970 L21:300$ MMANYH(X)(X3.14162) J:* T300,320Y ^"HOW MANY OF THESE FUNCTIONS DO YOU WANT"v h"TO GRAPH (1, 2 OR 3)"; rMANY wSX20:SY30 | X(100),Y(100) "YOU MAY CHOOSE THE X-INTERVAL (A,B)." "ENTER YOUR CHOICE OF A"; A OU WANT TO GRAPH ONLY ONE"H " FUNCTION, USE LINE 300. USE 310"w " AND 320 FOR YOUR SECOND AND THIRD" " FUNCTIONS IF YOU WANT MORE THAN" " ONE GRAPH ON THE SAME AXES." " ,F(X)(X) 6G(X)(X3.14166) @"P"2000 x< "THERE ARE THREE FUNCTIONS CURRENTLY IN"j "THE PROGRAM AT LINES 300, 310 AND 320." "THEY ARE GIVEN BY:" 300,320 "RE-TYPE ANY THAT YOU WANT TO CHANGE NOW." "THEN TYPE 'RUN 300' TO CONTINUE."  "NOTE: IF Ya  ;2"THIS PROGRAM WILL PLOT GRAPHS OF UP TO"A7n<"THREE FUNCTIONS OF YOUR CHOICE ON THE"tAF"SAME AXES. "KP"WOULD YOU PREFER RECTANGULAR OR POLAR"UZ"COORDINATES (ANSWER R OR P)";dTYPE$ n(TYPE$,1)     2"01ĺ:"THAT LOOKS LIKE ENOUGH...":1 AN0700? B(AN)1K B$(B)r 1)N7)"-"8)(B$,(B$)1)25)SUM{ &340 BBAN1 B$(BB) 1)N8)(B$,(B$)1)25)SUM 340  1)"N"8)"N-TH TERM"25)"SUM OF N TERMS"  N0330& E1)N7)"-"8)(AN)25)SUM/ G340E J1)N8)AN25)SUMK Ti ^(N10)N10NN1:300s hNN1 r"TYPE 'N' TO STOP. TO SEE 10 MORE TERMS" t"JUST PRESS RETURN."; |Z$ Z$"N"490 1000 300 # (AN).000000IF YOU WANT TO CHANGE AN, RE-TYPE LINE"- sD x"300 AS FOLLOWS:"J }` " 300 AN = ..."f "TYPE RUN 200 TO CONTINUE." N1 SUM0 A(500) 1000 ,AN(1)(N1)2N 6A(N)AN ;SUMSUMAN @(AN).01500 BA 62"THIS PROGRAM COMPUTES TERMS OF A SERIES"<7k<"OF YOUR CHOICE AND PRINTS EACH TERM AND"qAF"THE SUM THROUGH EACH TERM, STARTING WITHP"N = 1. THE N-TH TERM OF THE SERIES "UZ"CURRENTLY IN MEMORY IS"d300' n"   300N1103"X = ";10N,"F(X) = ";F(10N):N@F Z (F(XL)L)E(F(XR)L)E1110.PBEEP158R(7)BTBEEPMVI15S`vj"(Y TO CONTINUE, N TO STOP)";~tA$~A$"N"1200NN11000X09992200N110"X = ";10N,"F(X) = ";F(10N)N2""X"10)"F(X)"26)"ERROR"($.&F.XLX0ND:XRX0NDX0V(F(XL)L)c2VVV1p4V$(VV)6P$(V$,(V$)1)8XL10)F(XL)25)P$:W(F(XR)L)<WWW1>W$(WW)@Q$(W$,(W$)1)BLXR10)F(XR)25)Q$ MX? (Y OR N)"; R$% R$"N"510@ "ENTER A VALUE OF X";G X` "F(";X;") = ";F(X) "DO YOU WANT ANOTHER ONE? (Y OR N)"; S$ S$"Y"450  "WHAT X-INTERVAL DO YOU WANT? ENTER A,B"; A,B SX20:SY40 &WIDTHBA 400 > "IF YOU WANT A DIFFERENT FUNCTION, TYPE:"Z " 400 DEF FN F(X) =" "FOLLOWED BY YOUR FUNCTION RULE IN BASIC" "THEN TYPE 'RUN 400' AND PRESS 'RETURN'." F(X)X22X  "DO YOU WANT TO EVALUATE F AT SOME ERO OF THE FUNCTION. WE WILL"L Z"THEN LOCATE THAT ZERO WITH AN ERROR OF"z d"LESS THAN .0001. IF THE SKETCH IS NOT" n"HELPFUL ENOUGH, YOU MAY CHANGE THE " x"HORIZONTAL SCALE SX OR THE VERTICAL" "SCALE SY AT LINE 540. F IS NOW GIVEN BY:"G  9"THIS PROGRAM SKETCHES THE GRAPH OF A"f("FUNCTION OF YOUR CHOICE AND FINDS THE"2"ZEROS, IF ANY, BY THE BISECTION METHOD."<"AFTER THE SKETCH IS COMPLETED, YOU WILL"F"BE ASKED TO 'EYEBALL' AN INTERVAL ABOUT" P"EACH Z     3220 R(J)H(.1J)4 X(J)SR(J)(.1J)139R Y(J)(S)R(J)(.1J)79Y J_ d,  1! 139,79279,792 I139279SA I,77I,81H IN Z J063& X(J)0X(J)279Y(J)0Y(J)15931300 X(J),Y(J)X(J)1,Y(J): JD  J063 Q3210,3213,3216 R(J)F(.1J) 3220 R(J)G(.1J)RETURN FOR ANOTHER GRAPH";# GO$A :21:"ONE MORE TIME..."H 6R 3200\ 3100l :21:2120 "PRESS RETURN TO CONTINUE"; GO$ :21 "SCALE = ";S;". TYPE 2300 S = YOUR CHOICE" "TO CHANGE IT. THEN TYPE 'RUN 2100'"T UE";:GO$ MANY12800" Q2I "PRESS RETURN FOR ANOTHER GRAPH";R GO$\ :21| "MORE PATIENCE, PLEASE..." 5 3200 3100 :21:2110 MANY2ĺ"PRESS RETURN TO CONTINUE";:GO$:2800 Q3 :21:2110 "PRESS O YOU WANT"(\"TO GRAPH (1, 2 OR 3)";2aMANY:bQ1QR(65),X(65),Y(65)ZS20d 3000nj :21t PAUSE11000:PAUSE~ "PATIENCE, PLEASE...I'M NOT AN IBM" 3200 2 3100 :21:2100  MANY1ĺ"PRESS RETURN TO CONTIN AND 2120 FOR YOUR SECOND AND THIRD";V" FUNCTIONS IF YOU WANT MORE THAN" " ONE GRAPH ON THE SAME AXES."4F(T)2(1(T))>G(T)2(1(T))HH(T)3(3T)M:R2100,2120 W"HOW MANY OF THESE FUNCTIONS D 2100, 2110 AND 2120."0"THEY ARE GIVEN BY:"?2100,2120o"RE-TYPE ANY THAT YOU WANT TO CHANGE NOW.""THEN TYPE 'RUN 2100' TO CONTINUE.""NOTE: IF YOU WANT TO GRAPH ONLY ONE"" FUNCTION, USE LINE 2100. USE 2110")" 1JJ79159SY*137,J141,J1JC J790(SY)T"137,J141,J[#Ja"DO YOU WANT TO DO ANOTHER GRAPH (Y/N)";M$(M$,1)"Y"80"THERE ARE CURRENTLY THREE FUNCTIONS IN""THE PROGRAM AT LINES J1I19X(J)139X(J)139Y(J)0Y(J)159985`139SXX(J),Y(J)140SXX(J),Y(J)gJmsy1139,0139,159140,0140,1590,79279,79J139278SXJ,77J,81JJ1390(SX)J,77J,8 :21?"THE SCALES HERE ARE SX = ";SX;", SY = ";SY;"."j"DO YOU WANT DIFFERENT SCALES (Y/N)";tANS$(ANS$,1)"N"ĉ::1950:21:"TYPE '375 SX = ... : SY = ... WITH YOUR""NEW SCALES. THEN TYPE 'RUN 300'"ESS RETURN TO CONTINUE";:GO$-cMANY2900Yd"PRESS RETURN FOR ANOTHER GRAPH";:GO$ce:21{f"ONE MORE TIME..."iI0NlX(I)AI(BA)NqY(I)(SY)H(X(I))79rIs6t970u21:320v"PRESS RETURN TO CONTINUE";:GO$      RETURN TO TRY AGAIN";>GO$(C240:YTT23T17@A$ :---CLS ON TRS-80- A$"Y"2403 = 1000U &:"THE ROOTS ARE:"[ 0h :J1I1v D10)X(J)} NJ  %"TO SOLVE ANOTHER EQUATION, RE-TYPE" *"LINE 1000. TYPE 'LIST 1000' TO VIEW IT." 49:"NO ROOT HERE. PRESS).00001450) r(RL).01(YM).18257 wTR:1000A |YRYTY "X = ";R,"Y = ";YRq (YM)(YR)1430y RM 330 LM 330 :"ROOT = ";M X(I)M II1 "TYPE 'Y' TO FIND ANOTHER ROOT OR" "TYPE 'N' TO STOP."; I1 : ---CLS ON TRS-80 * 1000: X14142H TX:1000Q YYTh "X = ";X,"Y = ";Yo "Xu , 6"ENTER THE ENDPOINTS OF AN INTERVAL TO BE SEARCHED." @L,R JM(LR)2 OTM:1000 TYMYT ^"X = ";M,"Y = ";YM h(YMES OF X SINCE THE"< "GRAPH MUST CROSS THE X-AXIS THERE."B q "YOU WILL BE ASKED TO TYPE THE ENDPOINTS" "OF SUCH INTERVALS TO BEGIN A SEARCH FOR" "CLOSER APPROXIMATIONS TO THE ROOTS." "PRESS RETURN TO CONTINUE."; G$ / P"I WILL PRINT A SET OF VALUES OF X AND Y"[ Z"WHICH I WOULD LIKE FOR YOU TO STUDY."a d n"EXAMINE THE LIST AND NOTE WHERE SIGN" x"CHANGES IN Y OCCUR. A CHANGE IN THE" "SIGN OF Y INDICATES A ROOT BETWEEN THE" "CORRESPONDING VALUA :---CLS ON TRS-80E"WE ARE GOING TO FIND THE ROOTS OF AN"n"EQUATION BY THE BISECTION METHOD."("THAT IS, WE WILL FIND THE VALUES OF X"2"THAT MAKE Y = 0, WHERE Y IS GIVEN BY:"<1000 F"WHEN YOU FINISH READING THIS MESSAGE, "D:DD2:1520@X<J(F(M)).001Ģ23:"NO ZERO HERE"FT1290T!FNU1ĺ"THE ZERO IS ";ROOT(1)0PNU11410CZ"ZEROS ARE ";OdK1NUbnROOT(K);" ";ixKo -- SCAN (A,B) FROM LEFT TO RIGHT D.1XABD(F(X)).000001MX:1290(F(XD))(F(X))1600AXMA(F(B)).00001MB7(F(M)).000011290V(F(M))(F(B))11260^BMsBA.000011290}1180AMBA.0000112901180 23"ZERO NUMBER ";J;" = ";MROOT(J)M(PAUSE11500:PAUSE2<218 BM$LM$"YES"ī20#V)`1j21^t"ENTER L,R AS ENDPOINTS OF AN INTERVAL"f~22"ABOUT ZERO NUMBER ";J;A,B:21:"DOES THE GRAPH LOOK TANGENT TO THE AXIS (Y/N)";:L$L$"Y"1500M(AB)2(F(A)).0000179,79J139278SX&J,77J,819J1,77J1,81@JSJ1390(SX)uJ,77J1,77J1,81J,81J,77|JJ79159SY137,J141,JJJ790(SY)137,J141,JJ$."DO YOU WANT TO DO ANOTHER GRAPH?"CH$"N"780  21I "TYPE '540 SX =...:SY =...'AND RUN 400"O U ] 21 "HOW MANY ZEROS DOES F APPEAR TO HAVE"; *NU 4 >J1NU H1120 RJ \ f p z1 139,0139,159 140,0140,1590,792 0N(WIDTH)101# :DLTAWIDTHN, D8703 N2> XIONM bXAIDLTAY lZF(X)h vXSXX139| X0X279ī680 YSY(Z)79 Y0Y159ī680 X,YX1,Y I  21 "DO YOU WANT DIFFERENT SCALES? (Y OR N)"; CH$ : - "ENTER DEGREE OF POLYNOMIAL ";KR :"NOW ENTER THE COEFFICIENTS."z "A(1) IS THE LEADING COEFFICIENT." "A("K1") IS THE CONSTANT TERM.": Q1K1 "A("Q") =";:" ";A(Q) Q p::"ENTER THE FIRST NUMBER TO BE USED":k  WRITTEN BY CHUCK FRIESEN: LINCOLN HIGH SCHOOLL MARCH, 1981:"THIS PROGRAM WILL ALLOW YOU TO"::"SYNTHETICALLY DIVIDE A POLYNOMIAL"::"BY CONSECUTIVE TERMS OF AN"::"ARITHMETIC SEQUENCE.":::"PRESS 'RETURN' TO CONTINUE." A$   936(Z15)15I 0+ J 2 P1 2MII1:I9M5(I): I90 I95W I9eK M(I)z39F(J)YS,38K JX1$" ": I139:X1$X1$"^":: X1$" FREQUENCY HISTOGRAM""TYPE ANY CHARACTER TO CONTINUE";: A$U WANT A HISTOGRAM";, A$: A$ "N" X  A$ "Y" "MUST BE Y OR N";: 1030`G1v I 4 P1 2$ F(I) G GF(I). I8G39YS39Gʫ1100BYS39GL936V ` 12j 0,390 t0,3939 ~ M5(Z)Z1 R I\:"VALUE ";1f"FREQ ";Dp"PCT ";Xz"CUM PCT ":bD 0v I 1 P 2A F(I)B F(I1)C0: X0 CABX100D D C P(A);10);P(B);20);P(C);30);P(D) I:"DO YO1 J I1 OBSB A(I) A(J) TA(J):A(J)A(I):A(I)TJ JR IXsP1:F(P)A(1):F(P1)1 I 2 OBSV A(I)  J 1 P 2K J 1  V F(J) F(K)F(K)1: 850* J4PP2>F(P)VHF(P1));P(KU)5:"TYPE ANY CHARACTER TO CONTINUE";:A$?936e: 9);"POPULATION PARAMETERS":"STD DEVIATION";20);P(D2)"VARIANCE";20);P(V2)"COEF OF VARIATION";20); P(C2) "STD ERROR";20);P(E2) I 1 OBS"MEAN";20);P(M1).D"MEDIAN";20);P(M2)QN"STD DEVIATION";20);P(D1) mX"VARIANCE";20);P(V1)b"AVG DEVIATION";20);P(D3)g"COEF OF VARIATION";20);P(C1)l"STD ERROR";20);P(E1)v"SKEWNESS";20);P(SK)"KURTOSIS";202)3* :"WANT FREQUENCY DISTRIBUTION";L  A$: A$ "Y" 750: 525w  A$ "N" "MUST BE Y OR N";: 520 936:  9);"DESCRIPTIVE STATISTICS": "MINIMUM";20);P(MIN) &"MAXIMUM";20);P(MAX) 0"RANGE";20);P(RG) : OBS X5 X5 (M1 A(I))'  I9 D3 X5 OBSE T1 M1W T2 X2 OBSi T3 X3 OBS{ T4 X4 OBS M3T33T1T22T13 M4T44T1T36T2T123T14  V1 0 SK0:KU0: 510 SK M3 (V11.5) KU M4 (V1! M2 (A(OBS2)A(1OBS2))28 V X2 X2 OBSM V1 V (OBS1)^ "V2 V OBSm ,D1 (V1)| 6D2 (V2) @E1 D1 (OBS) JE2 D2 (OBS) T M1 0 C10:C20: 370 ^C1 D1 M1 hC2 D2 M1 rX5 0 | I 1 X0:X20:X30:X40' I 1 OBS= "VALUE #";I;: NJ A(I) NX X X Nj X2 X2 N2| X3 X3 N3 X4 X4 N4 I 710 MINA(1):MAXA(OBS):RGMAXMIN M1XOBS OBS2 (OBS2) M2A((OBS2)1): 270 50. K A$ "N" "MUST BE Y OR N";: 70J P:"END PROGRAM": 1500j d:"HOW MANY OBSERVATIONS"; n OBS: OBS(OBS) "MUST BE AN INTEGER";: 110 x OBS 2 OBS 100 "MUST BE BETWEEN 2 AND 100";: 110 :"ENTER YOUR DATA:":  A(100),F(200) 936>"F R E Q U E N C I E S":~"ELEMENTARY DESCRIPTIVE STATISTICS":"FOR UNIVARIATE DATA"( P(Z)(Z103.5)(103.5)- M(Z1)(Z1)(Z140)(40)2 100<:"ANOTHER ANALYSIS"; F A$ : A$ "Y" Y(I1). IFI1ēH1DFX(I2),VCDFY(I2)\ F1DFA((I.95)DT):F2DFA((I.05)DT)n (F1)78550 (F2)78550 3 H2I1,VCF1H2I,VCF2 !J1DL:J &I 0:33,33:34,0 :22:5:"MORE"; DF$:F$"N"F$"Y"580X,VCTH:I DF1:FI1:LINP1* 7000` 21:"PRESS RETURN TO STOP":"OR RESTART ACTION."m IFILI{ J15:J 3 (F1)(F5)İ3000 (F2)(F4)İ3100 (F3)(F6)İ3200 H1DFX(I),VCDFY(I) IFIēH1DFX(I1),VCDF F6İ1350 ,F$"N"$ 6DL0:< @(F$,1)"Y"DL100E :3\ VC80:H185:H2155n H2,VC278,VC RTRR3:(F1)(F2)RTRR H23,VCRTH23,VCRT:H23,VCRTH23,VCRT H2,0H2,159 DX20:TH3 I16:H2IDX,VCTHH2IDN" :"2.) COS"$ :"3.) TAN"5 :"4.) SEC"F :"5.) CSC"W :"6.) COT"b 1000u F$:F(F$)48 F1F6210 216,0 ((F6)(F1))(F(F))İ1000 F1İ1100 F2İ1150 F3İ1200 F4İ1250 F5İ1300:Y(I1)RR(IDT) PI X2 Z" TRIGO"U \"---------------------------"[ ] ^"CIRCLE DEFINITIONS AND GRAPHS OF": `"TRIGONOMETRIC FUNCTIONS DEVELOPED": b"SIMULTANEOUSLY.": cAN$ d x"PICK A FUNCTION :" :"1.) SI  FOR INFORMATION APPLY TO M.J. CHRISTENSEN, C/O SCHOOL OF MATHEMATICS, GEORGIA INSTITUTE OF TECHNOLOGY, ATLANTA, GA. 30332 X(121),Y(121),W(121)NP121PI(1)12RR60(DTPI(NP1)2NM1NP1<I0NM1 FX(I1)RR(IDT)   P1024128C240C1CH:C(P):D"LOCK" K3B$"UNLOCK"3 K4B$"DELETE":S B$;:198::K$:K(K$)48h ,K17KT16130 6CH1:CVSTK16:1000:C194(B$"RUN"B$"LOAD")B$"B"B$ @CH639:1000:B$B$(C):CH:1:868:B$:D$;B$D:100 C1(CV8):C2CVC18: = 1 LOCK = 2 UNLOCK = 3 DELETE = 4 EXIT = 5...." B$"RUN":1:(A$,39);:A$(A$,2)(A$,1):K(16384):K128āK175:K:K(0):130 16368,O:KK176:K1K5300 1:868:K5Ā " PRESS 'LETTER' YOU WISH TO ";:K1B$"LOAD" K2B$!d::D$(4):D$"CATALOG":B(37)2:B22B22110T0:CH4:CV023:1000:C160ĹP1,219:P,T193:P1,221:TT1:SCV120CV:24:A$"nT0:CH4:CV023:1000:C160ĹP1,219:P,T193:P1,221:TT1:SCV1 xCV:24:A$"TYPE LETTER TO RUN, OR LOAD  3. EXIT FROM PROGRAM"::" RT3 RT1ė:112? RT29` RT3D$(4):D$;"RUN MENU"i 420 ***";:3771 uDP8(ZM)(GH)ZM0ĺ" ***";: y:D@ |F g "PRESS RETURN TO CONTINUE."o A$u ~ ZZ0 "SELECT ONE OF THESE OPTIONS:" ::"1. SAME POLYNOMIAL, DIFFERENT INTERVAL" :"2. DIFFERENT POLYNOMIAL" :"(J) J ZZ13495 **** PRINT TOP LINE ***B P1K1U 8P2);A(P);\ "Pd ,: \ *** PRINT OTHER LINES *** ](1000D.5)1000; ^R1K1 `C(R)(100C(R).5)100 h8R2);C(R); mR o