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3 i Editor JFEP:

4 ii Internet World Wide Web HTML HTML HTML

5 iii

6 iv D

8 World Wide Web Internet (literacy) World Wide Web (WWW) WWW WWW BASIC WWW (ubiquitous)

9 Napier Pascal 20 Boole (1854) 1936 von Neumann Turing (universal Turing machine) (1936) 1940 EDSAC EDVAC Gödel (1931) Gödel Hilbert (1917) Hilbert Cantor (1895) Cantor ( ) 1 ( ) ( )

10 (2004 ) IC 3 Web CPU micro computer mi-com my-com ( ) IBM personal computer PC CPU CPU ( ) PDA(Personal Digital Access) = +

11 4 1 ( ) ( (RAM ROM) ( CD-ROM) ) ( ) ( LAN ) 5 5 CPU(Central Processing Unit) = + + Operating System OS Web Windows OS (middle) 1.3 (Z: )

12 Web ( ) WindowsNT OS(Operating System ) OS ( ) ( ) GUI

13 6 1 GUI(Graphical User Interface) GUI GUI (mouse) ( ) Alt+F GRPH Alt F CTRL+x CTRL ( ) x I 1 3 ( ) 2

14 Word Word

16 Editor ( ) (F) (F) (N) (F) (O) (F) (A) (F) (S) (F) (P) null (F) (X) (E) (E) (T) (E)

17 10 2 (E) (T) (E) (P) (E) (C) (E) (P) (S) (R) JFEP: ( ) (FEP) ATOK FEP FEP ATOK DOS/V (MS IME) ATOK FEP ( ) FEP

18 2.2. JFEP: 11 ( ) 2 7 (7 ) 2 16 (16 2 ) 7 ASCII(American Standard for Communication and Information Industry) JIS SJIS, EUC JIS UTF FEP FEP 2 JFEP DOS/V MSIME HELP JFEP

19 12 2 ( ) Shift 1 1 Enter 2 ATOK MSIME Shift JFEP ATOK MSIME Shift MSIME FEP MSIME

20 (document processor) (word processor) WYSIWYG(What You See Is What You Get ) WYSIWYG TEX ( ) ( ) WYSIWYG WYSIWYG Internet HTML (DTP) Page Maker 1970 CRT ( ) ( ) ( )

21 14 2 ( ) ( ) ( )

22 ( ) roman bold gothic italic slanted Small Cap sans serif

23 WYSIWYG (1 ) 1 ( ) 1 (align)

24 OK ( ) ( ) 2,,,,,,,, JPEG(Joint Picture Expert Group) Word (RTF) WYSIWYG TEX L A TEX

25 18 2 L A TEX L A TEX M lim M 0 1 x dx = π 2 \[\lim_{m\to \infty}\int^m_0\frac{1}{x^2+1}\, dx=\frac{\pi}{2}\]

26 (1) ( ) (a) 1 ( : ) (b) (c) (d) (e) (f) (g) computer (h) (i) (26pt) (8pt) ( ) italic ( ) (j) (2) ( ) ( )

28 (spread sheet) 1981 AppleII VISICALC Excel Lotus1 2 3 Multiplan VISICALC

29 22 3 A B C ( ) A3 B , , /7 3/7 3 5/9 3 5/ e e6 3/ % 1.20% 1.234% 1.23% $ $ , ,752( ) 1 0

30 % % / /5/5 2000/5/5 6/4/2000 6/4/00 H H :50 12:50 12:50:47 12:50:47 4:37 PM 4:37 PM 99/12/31 23:59 99/12/31 23: /1/1 0:01 00/1/1 0: AM PM ( ) ( ) (1) (2) ( ) (3) 3 (4) 3.3 2

31 =( ) = : : C C10 C10 =C1+C2+C3+C4+C5+C6+C7+C8+C9 C1 C9 C10 : : : AM PM (1) (2) (3) (1) (2) : : C5 C10 ( ) E10 E10 =E1+E2+E3+E4+E5+E6+E7+E8+E9

32 : (1) B6 =SUM(B1:B5) (2) C1 =B1/B6 (3) C2 C1 C2 =B2/B7 (4) B7 B1 B6 $ B6 $B6 B$6 $B$6 4 C1 =B1/$B$6 =B1/B$ (1) f x Version (2) (3) (4)

33 26 3 (5) 2 (6) OK BASIC C Pacal SUM( ) SUM(C3:C9) AVERAGE( ) AVERAGE(D4:D10) MAX( ) MAX(D4:D10) MIN( ) MIN(D4:D10) RANK(,, ) RANK(D7,D4:D10,0) INT( ) INT(B5) MOD(, ) MOD(E5,D7) IF( ) IF(B5>59,, ) 1 SUM 2 RANK(x,y,z), x y, z IF IF 8 C1 80 A B C 59 E IF(C1>79, A,IF(C1>69, B,IF(C1>59, C, E )))

34 (1) (2) (3) (4) (5) (6) OK (7), : 2 : : : : : 2 3D 3D : 3 : 2 :

35 ( ) A, B, C 3.5 2

36 (1) 150,000 15% 50 50,000 23% 9,500 19% 5,000 13% 198,000 9% 389,000 11% 348,000 18% 2 OA 57,000 24% 28,900 24% 250,000 13% 1 HUB 28,000 17% 5 119,000 0% 1 N N N (a) (b) % 100 =100%-c5 =1-c5 (b) (c) % (d) ( )

37 30 3 (2) , , , ,000 80,000 70,000 90,000 80, , , , , , , , , , ,000 95, , , , , , , , , ,000 90,000 95,000 85,000 90,000 75,000 87,000 58,000 79,000 87, ,000 94, ,000 (a) (b) ( ) (c)

38 (3) 90 S A B C E 40 F PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM (a) AVERAGE(x y) x y (b) STDEV(x y) x y STANDARDIZE(X ) X (c) (1) (2) X ( ) ( =sheet1!$b$2:$b$19 ) (3) Y ( ) ( =sheet1!$d$2:$d$19 )

39 32 3 (4) km 13.2km 9.5km 14.0km 11.6km 12.3km 11.9km 19.1km 44 : : : : : : : 00 1 : 01 : : : : : : : : 19 1 : 00 : : : : : : : : 42 1 : 02 : : : : : : : : 11 0 : 59 : : : : : : : : 40 1 : 01 : : : : : : : : 10 0 : 58 : 16 (a) (b) SUM( ) MIN( ) X RANK(X ) 0 1 (c)

40 (5) ( (pivot) ) (a) 1/3

41 34 3 (b) (1) (2) (3) 4 : (c) 5 6 7

42 (d) OK OK (1) (2) OK

43 36 3 (e) (c) ( ) (e) (c) (d)

44 Internet WWW ( ) TV ( ) 1968 ARPANET(Advanced Research Project Agency NET) 1979 ICCB(The Internet Configuration Connection Board) 1981 CSNET(Computer Science NET) 1983 IAB(The Internet Activity Board)

45 JUNET(Japan University NET) NFSNET(National Science Foundation NET) 1986 JUNET 1988 NFSNET internet worm 1992 Internet Society e mail(sendmail) 1972 telnet 1973 TCP/IP ftp 1976 UUCP 1983 TCP/IP 1984 DNS 1990 WWW ntp DHCP ICMP POP IMAP MAC 1 ( ) 48 ID MAC(Media Access Control) ID 00 : 0e : 7f : 9a : 45 : 0d 8 IP IP 32 ID IP Internet IP IP Internet hostname..u tokai.ac.jp Web tokai.ac.jp ac academic jp japan u tokai.ac.jp dname.co.jp dname.go.jp dname.or.jp dname.ad.jp dname.ne.jp

46 city.hiratsuka.kanagawa.jp dname.edu nantoka.com IP ICANN(The Internet Corporation for Assigned Names and Numbers) JPNIC(Japan Network Information Center) JPRS(Japan Registry Service.JP ) IP IP IPv6 IP IP RFC IP DNS IP DNS(Domain Name System) ipconfig arp -a nslookup TV

47 40 4 Web group ware (BBS) (chat) Web (virus) (worm) Web Web PC OS PC Web Windows Update UCE(Unsolicited Commercial E- mail) SPAM 50% ( 70% )

48 Web PC CD CD DVD TV (1) (2) (3) (4) WWW Web Web

49 42 4 (1) ( keyaki.cc.u-tokai.ac.jp ) (2) keyaki.cc.u tokai.ac.jp (3) keyaki.cc.u tokai.ac.jp (4) Internet (5) (6) Internet Web (1) Internet Explorer Netscape Web (2) Web (3) (4) Activ ( ) ID( ) PC (5)

50 reply Subject Re: forward Subject Fwd: SPAM( ) (To) ( ) (Subject) (Cc) carbon copy 2 Bcc blinded carbon copy Cc Cc Bcc

51 JPEG 50kB 20kB Cc 4.4 World Wide Web World Wide Web ( WWW Web) Internet information system 1 WWW Information system Internet WWW killer software Windows OS WWW ( ) ( ) (browser) Netscape Navigator Internet Explorer URL WWW URL(Uniform Resource Location) :// / /.../ # http https ftp file mailto gopher news http https ftp URL

52 4.4. World Wide Web OK WWW URL URL plug in Web PDF plug in CGI(common gateway interface) SSI(server side inclusion) Web SSL(Secured Socket Layer) WWW Cooky IP Cooky Cooky

53 46 4 Web SSL(Secured Socket Layer) SSL http https s secured( ) Web PC http html WWW WWW

54 4.4. World Wide Web HTML WWW html html html html html Hyper Text Markup Language hyper text text text text hyper text hyper text markup WWW 200 WWW html view ( ) document source( ) html WWW HTML HTML <tgname> <tgname> </tgname> htm (DOS ) html (UNIX ) myhomepage.htm : ( ) <html> <head><title> </title></head> <body> </body> </html>

55 48 4 1:  <html> <head><title> My Home Page </title></head> <body> </body> </html> <hn> <h1> <h6> <h1> chapter <h2> section <h3> subsection <h1> </h1> <p> <p> </p> <br> browser html browser browser <br>(brake) <hr> <hr>(horizontal rule) <a> WWW ( ) <a href=" URL"> </a> URL

56 4.4. World Wide Web 49 href="linkfile.htm" linkfile.htm href="htmfiles/linkfile.htm" htmfiles linkfile.htm href="../linkfile.htm" linkfile.htm <a name="pname"> <a href="#pname"> </a> HTML 2:  <html> <head><title> My Home Page </title></head> <body> <h1><center> </center></h1> <br> Web <hr> <h2> WWW </h2> <p> WWW(World Wide Web) 1990 <a href=" CERN </a> </p> <p> WWW World Wide Web Consortium <a href=" </p> </body> </html> <img> http GIF JPEG GIF PNG GIF

57 50 4 BMP BMP Internet (1) ( ) (2) (3) gif jpeg (4) html (5) html <img src="gfile.gif"> (jpeg gfile.jpg ) <font> <center> <strong> <font color="#rrggbb"> </font> RRGGBB 3 FF FF FF red blue <center> </center> <strong> </strong> <blink> </blink> Netscape Internet Explorer Internet Explorer <marquee> </marquee> Netscape IE NS <h1> <big> </big> <small> </small> <font size="n"> </font> n <pre> HTML <pre> </pre>

58 4.4. World Wide Web 51 <PRE> miles (Mmiles) </PRE> (i) (ii) (iii) <ol> <ol> <li> <li>... </ol> <ul> <ul> <li> <li>... </ul> <dl> <table> <dl> <dt> <dd> <dt> <dd>... </dl> <table> </table> <table border> </table> border

59 52 4 <tr> </tr> <th> </th> <td> </td> <p> </p> <table border> <tr> <th> </th><th> </th> </tr> <tr> <td> 174 </td><td> 75 </td> </tr> </table> <p> </p> <table boder> <tr> <th> </th><td> 174 </td> </tr> <tr> <th> </th><td> 75 </td> </tr> </table> HTML (1) (2) mydoc.htm.htm HTML.txt.doc (3) (4) mydoc.htm OK (5) (6) (7) HTML

60 4.4. World Wide Web 53 3:  <html> <head><title> HTML Sample Document </title></head> <body> <h1><center>html </center></h1> <hr> <p> HTML </p> HTML HTML <a-tag> </p> <a name="top"> <h1><center> </center></h1> </a> <hr> <img src="sample.gif"> <ul> <li><a href="#rm"> </a> <li><a href="#kr"> </a> <li><a href="#ch"> <a> </ul> <a name="rm"> </a> <dl> <dt> <dd> <dt> <dd><a href="#ir"> </a> </dl> <hr> <a name="kr"> <font color="#ff0000"> </font> </a><br> <br> <hr> <a name="ch"> </a><br> <br> <hr> <a name="ir"> </a> <ol> <li> <li> <li> </ol> <hr> <a href="#top"> </a>

61 54 4 <hr> <center><h2> </h2></center> <table border> <tr> <th> </th><th> </th><th> </th> </tr> <tr> <td> </td><td> 450 </td><td> </td> </tr> <tr> <td> </td><td> 780 </td><td> </td> </tr> <tr> <td> </td><td> 840 </td><td> </td> </tr> </table> </body> </html>

62 (1) sugita@sm.u-tokai.ac.jp (2) browser A4 1

64 BASIC 1965 Kurtz, T.E. Kemeny, J.G. Beginner s All purpose Symbolic Instruction Code bits micro computer BASIC N88 BASIC Visual Basic BASIC.BAS Visual Basic 2 N88 BASIC 3

65 N88 BASIC N88 BASIC 2 (F) (N) (O)

66 (S) (W) (P) (G) (Q) NBASIC (R) (G) (H) (I) (R) (V) (P) (C) (L) BASIC 5.3 BASIC Return N88 BASIC BASIC (R) (G)

67 BASIC BASIC N88 BASIC MSIME N88 BASIC PRINT (1): SIMPLE EXAMPLE INPUT "Input two integers."; A, B 120 LET SUM = A + B 130 LET DIFF = A - B 140 LET PROD = A * B 150 PRINT A; "+"; B; "="; SUM 160 PRINT A; "-"; B; "="; DIFF 170 PRINT A; "*"; B; "="; PROD 180 END 100% (R) (G) (1) Input two integers.? (2) 2 572, 291 Enter (3) = = *291= ( ) ( ) ( )

68 INPUT A,B A B "Input two integers." ( ) SUM DIFF PROD 150 PRINT A; "+"; B; "="; SUM A + B = SUM 180 END (F) (W) A:\ (S) (F) (S) 1 (F) (N) (F) (X) 5.5 ( ) INPUT " "; INPUT " ", INPUT

69 62 5 INPUT "Input 2 integers."; A, B INPUT "Input 2 integers.", A, B INPUT A, B 123, 456, PRINT 1; 2;... PRINT 1, 2,... ;, 1 LET variable = variable LET NBSIC COS SIN TAN LOG EXP SQR ( ) ATN (ArcTangent) ABS ( ) RND ( ) RANDOMIZE (RND ) INT ( ) FIX ( ) DEF FNREIDAI( 1, 2,...) = : (+,-,*,/,^) * ^ ( )( ) ^( ), -( ), *( ), /( ), +( ), -( ) 2 2^(1/2) (-(2+3^4)*(6-5)/(7*(8+9)-10)^2), \, mod

70 : = < > <> ( ) <= ( ) >= ( ) : NOT AND OR XOR IMP EQV NOT(-3 <= VALUE AND 4 >= VALUE) ( ) 3 1 : LET X = 345 : LET Y = 279 : PRINT X + Y FOR WHILE FOR cvariable = TO STEP (2) : NEXT cvariable FOR NEXT cvariable 2... cvariable cvariable STEP 1 STEP NEXT cvariable JIJOU WA INPUT " Input integer."; N 120 LET SQWA = FOR I = 0 TO N

71 LET SQWA = SQWA + I^2 150 PRINT I; SQWA 160 NEXT I 170 END N I=0 I2 = N 2 I 1, 2,..., N SQWA (3) : *9 HYOU FOR I = 2 TO FOR J = 2 TO PRINT USING "######"; I*J; 140 NEXT J 150 PRINT 160 NEXT I 170 END I J 2 I 2 J I 3 J 3 9 (4): MATRIX I/O DIM A(3,3) 120 FOR I=1 TO FOR J=1 TO PRINT "A(";I;J;")="; 150 INPUT A(I,J) 160 NEXT J 170 NEXT I 180 FOR I=1 TO FOR J=1 TO PRINT USING "####";A(I,J); 210 NEXT J 220 PRINT 230 NEXT I 240 END DIM A(3,3) A ( ) A(11)=? (1, 1) (3, 3)

72 WHILE WEND (5) : MENOKO DE HEIHOU-KON NO SEISUU-BU WO MOTOMERU PRINT " INTEGRAL PART OF ROOT(A)" 120 INPUT " Input integer. "; A 130 LET I = WHILE A >= LET A = A - ( 2*I -1 ) : LET I = I WEND 170 PRINT I END A A IF THEN 1 IF THEN 1 ELSE 2 (6) : 1 2 ELSE THEN GOTO OTETUDAI PRINT "OTETUDAI SIMASU. BANGOU DE ERANDE KUDASAI." 120 INPUT "1:SOOJI, 2:SENTAKU, 3:RYOURI"; I 130 IF I = 1 THEN PRINT " SIRIMASEN." 140 IF I = 2 THEN PRINT " WAKARIMASEN." 150 IF I = 3 THEN PRINT " DEKIMASENN." 160 END (7) :

73 JI HOUTEISIKI PRINT " a x^2 + b x + c = 0" 120 INPUT " a = "; A 130 IF A = 0 THEN PRINT "DATA ERROR" : GOTO *EXIT 140 INPUT " b = "; B 150 INPUT " c = "; C 160 LET D = B * B - 4 * A * C 170 IF D >= 0 THEN *REAL ELSE *IMAGINARY 180 *REAL 190 PRINT (-B + SQR(D))/(2*A) 200 PRINT (-B - SQR(D))/(2*A) 210 GOTO *EXIT 220 *IMAGINARY 230 PRINT -B/(2*A);"+";SQR(ABS(D))/(2*A);"I" 240 PRINT -B/(2*A);"-";SQR(ABS(D))/(2*A);"I" 250 *EXIT 260 END 2 2 GOTO GOTO 5.6 N88 BASIC BASIC IBM PC (x ) (y )

74 ( ) 1 1 (pixel) : 1 : 2 : 4 : 3 = : 5 = : 6 = : 7 = : COLOR,,, ( ) CLS 1 CLS 2 CLS 3 ( ) ( ) POINT (px, py) (LP) (px, py) LP POINT LINE (0, 0)-(320, 200) : LINE -(0, 400) 2 LINE (320, 200)-(0, 400) 5.6.2

75 68 5 LINE (x1, y1)-(x2, y2), color (x1, y1) (x2, y2) color var (color) LINE (x1, y1)-(x2, y2), color, B (x1, y1) (x2, y2) color LINE (x1, y1)-(x2, y2), color, BF color (8): 100 LINE (0, 0) - (639, 399) : STOP 110 LINE (0, 399) - (639, 0), 2 : STOP 120 LINE (200, 100) - (400, 300), 3, B : STOP 130 LINE (250, 150) - (350, 250), 5, BF : STOP 140 LINE (20, 20) - (220, 170), 0, BF : STOP 1 CIRCLE (cx, cy), rad, color (cx, cy) rad color CIRCLE (cx, cy), rad, color, θ1, θ2 (cx, cy) rad θ1 θ2 θ1 θ2 2π 2π θ1 θ2 θ1 = π/2, θ2 = 3π/2 θ1 = 3π/2, θ2 = π/2 - θ1 = 0 θ2 = 2π CIRCLE (cx, cy), rad, color,,, ratio (cx, cy) ratio > 1 rad rad/ratio ratio < 1 rad rad ratio ratio 1( ),F

76 (9): 100 LET PI = CIRCLE (320, 200), 100 : STOP 120 CIRCLE (320, 200), 150, 6 : STOP 130 CIRCLE (320, 200), 100, 5,,,, F : STOP 140 CLS CIRCLE (320, 200), 50, 2, 0, PI : STOP 160 CIRCLE (320, 200), 100, 3, PI, 0 : STOP 170 CIRCLE (150, 100), 50, 4, -PI/2, PI : STOP 180 CIRCLE (450, 100), 60, 5, 0, -PI*3/2 : STOP 190 CIRCLE (150, 300), 50, 6, -PI/4, -PI*7/4 : STOP 200 CIRCLE (450, 300), 60, 1, -2, -5,, F : STOP 210 CLS CIRCLE (320, 200), 100, 7 : STOP 230 CIRCLE (320, 200), 100, 4,,, 2 : STOP 240 CIRCLE (320, 200), 100, 2,,, 0.5 : STOP 250 CIRCLE (320, 200), 200, 0,,, 2, F 1 1 PSET (px, py), color (px, py) color PRESET (px, py) (px, py) PAINT (px, py), pcolor pcolor (px, py) pcolor PAINT (px, py), pcolor, bcolor (10): bcolor (px, py) pcolor RANSUU NI YORU PAINT RANDOMIZE VAL(RIGHT$(TIME$,2))* CLS FOR I = 1 TO LET X = RND*640 : LET Y = RND*390

77 LET C = RND*6+1 : LET R = RND* CIRCLE (X, Y), R, C 170 PAINT (X, Y), C 180 NEXT I 190 END 5.7 y = f(x) x = φ(t), y = ψ(t) NBASIC y (11): graph y=f(x) cls def fnkansuu(x)=x^3+x^2-2*x 130 let wx1=-2:let wx2=2:let wy1=-5:let wy2=3 140 def fnpx(wx)=639*(wx-wx1)/(wx2-wx1) 150 def fnpy(wy)=399*(wy-wy1)/(wy2-wy1) 160 sstep=(wx2-wx1)/ point (fnpx(wx1),fnpy(-fnkansuu(wx1))) 180 for x=wx1 to wx2 step sstep 190 line -(fnpx(x),fnpy(-fnkansuu(x))) 200 next x 210 line (fnpx(wx1),fnpy(0))-(fnpx(wx2),fnpy(0)) 220 line (fnpx(0),fnpy(wy1))-(fnpx(0),fnpy(wy2) 230 end 130 (WX1, WY1) (WX2, WY2) , (12): parameter plot cls let pi= :let r=1 130 def fnx(t)=cos(t)*r*(1+cos(t)) 140 def fny(t)=sin(t)*r*(1+cos(t)) 150 let wx1=-3:let wx2=3:let wy1=-2:let wy2=2 160 def fnpx(wx)=639*(wx-wx1)/(wx2-wx1) 170 def fnpy(wy)=399*(wy-wy1)/(wy2-wy1) 180 point (fnpx(fnx(0)),fnpy(fny(0))) 190 for t=0 to 2*pi+0.1 step 0.05

78 line -(fnpx(fnx(t)),fnpy(fny(t))) 210 next t 220 line (fnpx(wx1),fnpy(0))-(fnpx(wx2),fnpy(0)) 230 line (fnpx(0),fnpy(wy1))-(fnpx(0),fnpy(wy2)) 340 end 130, 140 x = x(t) y = y(t) (13): (14): (15): CHOKUSENN ZUKEI CLS FOR Y=0 TO 395 STEP LINE (0,Y)-(639,0) 140 LINE (0,399)-(639,Y) 150 NEXT Y 160 END CHOKUSENN ZUKEI SCREEN 3: VIEW (0,0)-(639,399): CLS LINE (80,0)-(460,380),,B 130 FOR I=0 TO 370 STEP LINE (80,I)-(80+I,380) 150 LINE -(460,380-I) 160 LINE -(460-I,0) 170 LINE -(80,I) 180 NEXT I 190 END CHOKUSEN ZUKEI SCREEN 3: VIEW (0,0)-(639,399): CLS LET PI = INPUT "Input integer.(5-20)"; N 140 IF N MOD 2 =0 THEN LET M=N/2 ELSE LET M=N 150 LET ARG=PI/N 160 LET ROT=2*PI/(3*N) 170 FOR J=0 TO 3*M FOR I=1 TO N LET X1=COS(ARG*I)* LET Y1=SIN(ARG*I)*190

79 72 5 (16): (17): 210 LET PX1=X1*COS(ROT*J)+Y1*SIN(ROT*J) LET PY1=-X1*SIN(ROT*J)+Y1*COS(ROT*J) LET PX2=X1*COS(ROT*J)-Y1*SIN(ROT*J) LET PY2=-X1*SIN(ROT*J)-Y1*COS(ROT*J) LINE (PX1,PY1)-(PX2,PY2) 260 NEXT I 270 NEXT J 280 END EN ZEKEI SCREEN 3: VIEW (0,0)-(639,399): CLS FOR K=8 TO 1 STEP CIRCLE (320,200), *(1-K),7,,,8/K 140 CIRCLE (320,200), *(1-K),7,,,K/8 150 NEXT K 160 END EN ZUKEI SCREEN 3: VIEW (0,0)-(639,399): CLS LET PI= INPUT " Input integer.(3-20)"; M 140 LET N=150: LET TH1=0 150 LET TTH1=2*PI/N: LET TTH2=2*PI/M 160 FOR I=1 TO N 170 LET TH1=TH1+TTH1 180 LET Y1=SIN(TH1)*N/PI 190 FOR J=1 TO M 200 TH2=TTH2*J 210 LET X2=320+(I*COS(TH2)-Y1*SIN(TH2)) 220 LET Y2=200-(I*SIN(TH2)+Y1*COS(TH2)) 230 LET Y3=200+(I*SIN(TH2)+Y1*COS(TH2)) 240 PSET (X2,Y2),7: PSET (X2,Y3),5 250 NEXT J 260 NEXT I 270 END

80 I II 2 1 (I) (1) N N i=1 i3 = N 3 (2) N N! ( ) (3) N N (4) N N (5) 2 ( ) (6) 2 II (1) 2 (2) : r = a + b cos θ (a > 0, b > 0) x = a cos 3 θ, y = a sin 3 θ (a > 0) r = a sin θ 3 (a > 0) r = a cos θ (a > 0) 2 r = a sin 3θ (a > 0) x = cos θ, y = 2 sin 2θ r = a(1 + cos θ) x = a(t sin t) y = a(1 cos t) (3)

82 ( ) Mathematica APL REDUCE ( ) MACSYMA ( ) µ Math DERIVE( ) Maple ( ) Maple Mathematica Mathematica ( ) ( ) Mathematica Maple 1000 (Mathematica ) Mathematica 6.2 Mathematica Mathematica kernel notebook Mathematica

83 76 6 notebook Mathematica x.y (x.y version ) click Mathematica In[1]:=10! Shift + Enter Out[1]:= In[2]:= Shift + Enter Shift Enter Mathematica notebook Mathematica notebook ( ) null( ) notebook notebook 6.3 Mathematica a+b a-b a*b a b( ) a/b a^b a + b ( ) a b ( ) a b ( ) a b ( ) a b ( )

84 Pi E I Infinity π ( ) e ( ) i ( ) ( ) Sin[x] Cos[x] Exp[x] Log[x] Log[2,x] Sqrt[x] Sum[a[k],{k,m,n}] sin(x) cos(x) e x log(x) log 2 (x) x n k=m a(k) Mathematica [ ] Mathematica 3 ( ) { } [ ] ( ) (parenthese) { } (brace) 2 [ ] (bracket) ( ) <> (angle)

85 Mathematica = = object Mathematica object g1=plot[2 x,{x,-3,3}]; g2=plot[-x+3,{x,-3,3}]; Show[g1,g2] g1 g2 Plot graph object 3 Show g1 g2 == Solve[2 x^2-3 x+1==0,x] 2x 2 3x + 1 = 0 x % object Expand[(x+y)^5] Factor[%] (x + y) Mathematica 2 1 ( ) In[1]:=f1=x^3-x^2+x-3; In[2]:=g1=Exp[Sin[x]+Cos[y]]; In[3]:=f1/.{x->a} Out[3]= a 3 a 2 + a 3 In[4]:=g1/.{x->a,y->b} Out[4]= E Sin[a]+Cos[b]

86 , 4 ( ) x,y In[5]:=f2[x_]=x^3-2*x+3; In[6]:=g2[x_,y_]=Sqrt[Sin[2*x]*Cos[y]]; In[7]:=f2[a] Out[7]= a 3 2 a + 3 In[8]:=g2[b,c] Out[8]= Sqrt[Sin[2 b] Cos[c]] In[9]:=a//f2 Out[9]= a 3 2 a + 3 5, 6 7, 8 9 (postfix) 7 In[10]:={b,c}//g2 Out[10]= g2[{b,c}] f1, g1 f2[x], g2[x,y] In[11]:=h1=x^3 Out[11]= x 3 In[12]:=h1[a] Out[12]= (x 3 )[a] In[13]:=b//h1 Out[13]= (x 3 )[b] In[14]:=h2[x_]=x^2-1 Out[14]= x 2 1 In[15]:=h2/.{x->a} Out[15]= h2 In[16]:=D[h1,x] Out[16]= 3x 2 In[17]:=D[h1[x],x] Out[17]= (x 3 ) [x] In[18]:=D[h2[x],x] Out[18]= 2x

87 80 6 In[19]:=D[h2,x] Out[19]= , 18 17, h2 h2 x ( ) ( ) In[1]:=x=2 Out[1]= 2 In[2]:=f=x^2 Out[2]= 4 In[3]:=g[x_]=x^3 Out[3]= 8 In[4]:=x=. In[5]:=x Out[5]= x In[6]:=f Out[6]= 4 In[7]:=g[x] Out[7]:= 8 x 2 2, 3 x=2 f=4, g=8 4 x f, g 4, 8 6, 7 Mathematica Abc??Abc Abc Abc=. Clear[Abc]

88 Mathematica h In[1]:=h = #1^2-#2^3+1& In[2]:=h[x_,y_] = x^2 - y^3 +1 #1 #2 & a//function function a In[3]:=a//#^5+#^3+#& Out[3]= a 5 + a 3 + a {} In[4]:=h=#^3& In[5]:={h[1],h[2],3//h,h[c]} Out[5]= {1, 8, 27, c 3 } Mathematica Mathematica D diff In[6]:=diff[f_[x]]:=D[f[x],x] In[7]:=diff[Cos[x]] Out[7]=-Sin[x] 6.5

89 82 6 Basic Input ( ) d dx (cos(x2 + a)) x (Cos[x^2+a]) x + y y x y y((x+y)/(x-y)) 2, ( ) d 2 dx 2 cos(x2 + 1) x ( x (Cos[x^2+1])) x,x (Cos[x^2+1]) 2 x y log(x2 + y 2 ) x ( y (Log[x^2+y^2])) x,y (Log[x^2+y^2]) ( )d ( )d π Mathematica notebook

90 D[f[x],x] D[f[x],{x,n}] D[f[x,y],x] Integrate[f[x],x] Integrate[f[x],{x,a,b}] Integrate[Sin[x]/x,{x,0,Infinity}] Integrate[f[x,y],{x,a,b},{y,c,d}] f (x):f(x) f (n) (x):f(x) n n f(x, y) :f(x, y) x f(x)dx:f(x) b a 0 b f(x)dx:f(x) sin x dx x dx d a c f(x, y))dy 1( ) (1) 3x + 2 x 2 + x + 2 (2) (3x 2 2) 4 sin x2 (3) e (4) x x (5) log(f(x)) (6) f(g(x 2 )) (7) f(x 3 ) (3 ) (8) xa x (3 ) (9) 1 2 log(x2 + y 2 ) (2 ) 2( ) 3x 2 + 2x (1) x 3 dx (2) 1 x 1 1 x (4) dx (5) x x 1 x dx (3) 1 + x 1 x(1 + 3 x) dx (6) dx 2 sin x + 3 cos x + 4 x 1 + cos x dx 3( ) (1) 2 1 (x + 1)(x 2)dx (2) 1 0 log x dx (3) 1 x 4( ) (1) (x 2 y 3 )dxdy D = {(x, y) 0 x 1, 0 y 1} D (2) (x 2 1 2xy)dxdy D = {(x, y) 1 x 2, x y 2} D 0 sin x x dx Mathematica Solve Roots Reduce ==

91 84 6 In[1]:=eq=a+x^2+b*x+c==0; In[2]:=Solve[eq,x] Out[2]= {{x > b Sqrt[b2 4 a c] }, {x > b + Sqrt[b2 4 a c] } 2 a 2 a In[3]:=Roots[eq,x] Out=[3] x == b Sqrt[b2 4 a c] x == b + Sqrt[b2 4 a c] 2 a 2 a In[4]:=Reduce[eq,x] Out[4]= x == b Sqrt[b2 4 a c] && a! = 0 x == b + Sqrt[b2 4 a c] 2 a 2 a 0 a == 0 && b == 0 && c == 0 a == 0 && x == ( c ) && b! = 0 b && a! = NSolve Solve[p == 0,x] Solve[{p == 0,q == 0},{x,y}] NSolve[p == 0,x] NSolve[p == 0,x,n] p = 0 x p = 0, q = 0 x y p = 0 n Mathematica ( 1) 1 3 a + ib a + ib ComplexExpand In[5]:=ComplexExpand[(-1)^(1/3)] Out[5]= Sqrt[3] 5( ) (1) x 2 + x 1 = 0 (2) x 4 + 2x 2 4x + 8 = 0 (3) x 2 x 1 = 0 { x + 2y = 1 3x 2y + 7z = 80 3 x 3 ax + 6 = 0 (4) (5) 5x + 3y 4z = 2 (6) a, 3 3x + 5y = 4 2x + 5y + z = Mathematica v, w A, B I a, b, c, d, k n

92 v={a,b} v = (a, b) v+w v + w k*v k v ( ) kv v.w ( ) v w (v, w) ( ) a b A={{a,b},{c,d}} A = c d MatrixQ[A] A Transpose[A] t A A MatrixForm[A] ( A ) = {{a, b}, {c, d}} a b A = ( c d ) IdentityMatrix[n] n (n ) A+B k*a k A ( ) A.B ( ) MatrixPower[A,n] MatrixExp[A] Inverse[A] MatrixPower[A,-1] A + B ka AB A n (n ) e A = I + A + A2 2! + + Ak k! +... A A 1 A A Det[A] det(a) A Eigenvalues[A] A Eigenvectors[A] A Eigensystem[A] A

93 86 6 In[1]:=Eigensystem[{{1,2},{2,2}}] Out[1]= {{ 3 Sqrt[17] 2, 3 + Sqrt[17] }, {{ 2 1 Sqrt[17], 1}, { Sqrt[17], 1}}} 4 3 Sqrt[17] 3 + Sqrt[17], ( 2 ) 2 ( ) 1 Sqrt[17] 1 + Sqrt[17], 1,, (6.1) (6.2) In[2]:=a={{1,2},{2,2}} Out[2]= {{1, 2}, {2, 2}} In[3]:=p=Eigenvectors[a] 1 Sqrt[17] 1 + Sqrt[17] Out[3]= {{, 1}, {, 1}} 4 4 In[4]:=q=Transpose[p]; In[5]:=MatrixForm[Simplify[Inverse[q].a.q]] Out[5]// 3 Sqrt[17] Sqrt[17] 0 2 Mathematica 6( ) (1) (4) (1),(2) (3),(4) (5),(6) (2) (5) (3) (6) Mathematica

94 y = f(x) (a x b) Plot[f[x],{x,a,b}] Plot[(x+1)*x*(x-1),{x,-2,2}] Mathematica Plot[E^x,{x,-3,3}] 2 Plot[{Sin[x],x-x^3/(3!)+x^5/(5!)},{x,-2 Pi,2 Pi}] x = f(t), y = g(t) (a t b) ParametricPlot[{f[t],g[t]},{t,a,b}] ParametricPlot[{Cos[3 t],sin[5 t]},{t,0,10}] 2 ParametricPlot[{{Cos[t],Sin[t]},{t-Sin[t],1-Cos[t]}},{t,-Pi,2 Pi}] C : r = f(t) (a t b) <<Graphics Graphics ; (back quote) PolarPlot[f[t],{t,a,b}] PolarPlot[t,{t,0,2 Pi}] 2

95 f(x, y) = g(x, y) (a x b) <<Graphics ImplicitPlot ; ImplicitPlot[f[x,y]==g[x,y],{x,a,b}] ImplicitPlot[x^(2/3)+y^(2/3)==1,{x,-2,2}] 2 x y PlotStyle Plot[f[x],{x,a,b},PlotStyle -> parameter] parameter Thickness[0.007] Dashing[{0.01}] Hue, RGBColor, GrayLevel Plot[Sin[x],{x,-7,7},PlotStyle -> Dashing[{0.05}]] Plot[Cos[x],{x,-7,7}, PlotStyle -> Thickness[0.007]] Plot[{Sin[10*x]*Sin[0.9*x],Sin[0.9*x],-Sin[0.9*x]}, {x, -7, 7}, PlotStyle-> {Dashing[{}], Dashing[{0.05}], Dashing[{0.05}]}] Plot[{E^x,1+x+x^2/2!+x^3/3!+x^4/4!},{x,-4,4}, PlotStyle ->{Hue[2/3], Hue[1/3]}] Frame, GridLines Frame -> True GridLines -> Automatic (grid line) Plot[Sin[x],{x,-4,4},Frame -> True, GridLines ->Automatic]

96 z = f(x, y) x = f(u, v), y = g(u, v), z = h(u, v) z = f(r, θ) r = f(θ, φ) f(x, y) = const f z = f(x, y) (a x b, c y d) Plot3D[f[x,y],{x,a,b},{y,c,d}] Plot3D[Sin[2*Pi*Sqrt[x^2+y^2]],{x,-1,1},{y,-1,1}] Plot3D[x^2-2*x*y+y^2-x^4-y^4,{x,-1.5,1.5},{y,-1.5,1.5}] PLot3D ParametricPlot3D ViewPoint Mathematica ViewPoint -> {p,q,r} (p, q, r) 3D ViewPoint Selector (1) Input 3D ViewPoint Selector 3D ViewPoint Selector (2) Plot3D[f[x,y],{x,a,b},{y,c,d} (3) 3D ViewPoint Selector (4) View Selector r (5) Selector paste Plot3D ViewPoint -> {p,q,r} {p,q,r} (6) Shift + Enter Plot3D[f[x,y],{x,a,b},{y,c,d},ViewPoint -> {p,q,r}] 2

97 90 6 PlotPoints PlotPoints -> 50 2 Plot3D[Sin[x*Sin[x*y]],{x,0,4},{y,0,4}] Plot3D[Sin[x*Sin[x*y]],{x,0,4},{y,0,4},PlotPoints -> 50] ImageSize Mathematica ImageSize->n n 1 pt 1/72 inch n 288 pt 4 inchi 10 cm AspectRatio Mathematica ( ) AspectRatio->n n : n 1 1 n Automatic x = f(t), y = g(t), z = h(t) (a t b) ParametricPlot3D[{f[t],g[t],h[t]},{t,a,b}] ParametricPlot3D[{t*Cos[t]/3,t*Sin[t]/3,t/5},{t,0,20}] ParametricPlot3D[{Cos[t/3],Sin[t/7],Cos[t/5]},{t,0,100}] x = f(u, v), y = g(u, v), z = h(u, v) ParametricPlot3D[{f[u,v],g[u,v],h[u,v]},{u,a,b},{v,c,d}] ParametricPlot3D[{(3+Cos[s])*Cos[t],(3+Cos[s])*Sin[t],Sin[s]}, {s,0,2*pi},{t,0,2*pi},plotpoints -> 25]

98 z = f(r, θ) (a r b, c θ d) Plot <<Graphics ParametricPlot3D CylindricalPlot3D[f[r,t],{r,a,b},{t,c,d}] CylindricalPlot3D[Sqrt[r]*Sin[5*t],{r,0,2},{t,0,2*Pi},PlotPoints->{10,50}] ViewPonit r = f(θ, φ) (a θ b, c φ d) Plot SphericalPlot3D[f[s,t],{s,a,b},{t,c,d}] SphericalPlot3d[2+Sin[3*s]*Sin[3*t],{s,0,Pi},{t,0,2*Pi}, PlotPoint -> {40,50}] ViewPoint 6.10 Mathematica D 3 ContourPlot DensityPlot 3 (x, y, z) Mathematica Plot3D[Sin[x*y],{x,0,3},{y,0,3}] ContourPlot[Sin[x*y],{x,0,3},{y,0,3},PlotPoints -> 30]

99 92 6 DensityPlot[Sin[x*y],{x,-10,10},{y,-5,5} PlotPoints -> 500, Mesh -> False] DensityPlot PlotPoints Plot3D ContourPlot (3 ) Mathematica Plot g1=plot3d[-2*x+3*y,{x,-10,10},{y,-10,10}]; g2=plot3d[2*x+3*y-2,{x,-10,10},{y,-10,10}]; Show[g1,g2,ViewPoint -> {-3,-2,1}] Mathematica <<Graphics Animation Do Animate Do[ Plot[Sin[2*(x-a)],{x,0,2*Pi}], {a,1,2,0.2}] Animate[ Plot[Sin[2*(x-a)],{x,0,2*Pi}], {a,1,2,0.2}] Sin Plot ParametricPlot PolarPlot ImplicitPlot Animate[ PolarPlot[a*(1+Cos[t]),{t,0,2*Pi}, PlotRange -> {{-1,3},{-2,2}}], {a,1,1.1,0.02}]

100 Animate[ ParametricPlot3D[{(3+a*Cos[s])*Cos[t],(3+a*Cos[s])*Sin[t],a*Sin[s]}, {s,0,2*pi},{t,0,2*pi},plotpoint -> 50], {a,1.0,1.2,0.01}] z Plot3D[Sin[x*y],{x,0,3},{y,0,3},Axes -> None]; SpinShow[%] 6.11 Mathematica Mathematica C Fortran Pascal Java 3 ( ) drgn[func_,pos_,kaku_,updown_] := Module[{f = func,x = pos,th = kaku//n,us = updown,tmp,y,ly}, {s1,s2} = us; tmp = Map[{Insert[#[[1]],f[#,th,s1,s2][[1]] + #[[1,1]],2], Insert[#[[2]],f[#,th,s1,s2][[2]] + #[[2,1]],2]}&,x]//Simplify; tmp = tmp//flatten[#,1]&; y = Map[Partition[#,2,1]&,tmp]//Simplify; ly = {Re[#],Im[#]}&/@(y//Flatten);Show[Graphics[Line[ly]]];y] kaiten[t_] := 1/(2 * Cos[t])*(Cos[t]+I*Sint[t]) tst[x_,t_,s1_,s2_] := {kaiten[s1*t],kaiten[s2*t]}x.{-1,1} pl = {{{0,1/2-I/2},{1/2-I/2,1}}}; Nest[drgn[tst,#,Pi/4,{-1,1}]&,pl,10]; 4 Mandelbrot mb[x_,y_,max_] := (z=c=x+i*y;i=0; While[Abs[z]<2.0 && i< max,z=z*z+c;i++]; Return[i]) DensityPlot[mb[x,y,60],{x,-2.25,0.75},{y,-1.5,1.5}, PlotPoints -> 150,Mesh -> False,ColorFunction -> Hue] 5 Julia

101 94 6 js[x_,y_,c_,max_] := (z=x+i*y;i=0; While[Abs[z]<2.0 && i<max,z=z*z+c;i++]; Reurn[i];) DensityPlot[js[x,y, *I,60],{x,-2.0,2.0},{y,-1.5,1.5}, PlotPonits -> 150,Mesh -> False, ColorFunction -> Hue] Mandelbrot Julia z n+1 = z 2 n + c z n Mandelbrot Julia c {c z 0 = 0, lim n z n < } {z 0 lim n z n <, c }

102 (1), (2), (3) Mathematica (1) (2) 1 (θ ) (a) r = a + b cos θ (a : b = 1 : 1, 1 : 2, 2 : 1, 2 : 3) ( ) (b) r = sin n θ (n = 2, 3, 4, 5) ( ) (c) x = sin θ, y = sin(n θ + π ) (n = 1, 2, 3, 4) ( ) 4 (3) 1 ViewPoint r (a) 2 3 (b) (c) Mathematica cai

sin x

sin x Mathematica 1998 7, 2001 3 Mathematica Mathematica 1 Mathematica 2 2 Mathematica 3 3 4 4 7 5 8 6 10 7 13 8 17 9 18 10 20 11 21 12 23 1 13 23 13.1............................ 24 13.2..........................