fx-72F

Size: px
Start display at page:

Download "fx-72F"

Transcription

1 SA1310-A JA fx-72f RJA V01

2 A!j(CLR)d(All)w SD/REG 45 PRGM 73 1

3 ! a s!s(sin 1 )bw b(contrast) fcde REPLAY 2

4

5 u u u u 4

6 u u 15 5

7 3 1 6

8 Ans M A B C D X Y π e

9 n ENG...40 CMPLX...41 SD/REG n BASE PRGM

10 O 11 A 1. 1N SETUP d1 Contrast u L I GHT DARK CASIO 2. d e 3. A 1p EXIT N +- A 1A OFF M M A x! LOGIC DT CL 9

11 M+ M 1 M a DT SD REG CL A SD REG 1 CMPLX 1 a A BASE LOGIC BASE A 2 ( 5+4 ) A 7 sin( 30) Deg 10

12 6 A 1., u u 1 2, d e COMP CMPLX BASE COMP CMPLX BASE n SD REG PRGM 1(COMP) 2(CMPLX) 3(BASE) 4(SD) 5(REG) 6(PRGM) u SD REG PRGM 4 5 6!, SETUP 6 e d 11

13 A 90 π 2 100!,1(Deg)!,2(Rad)!,3(Gra) A !,e1(Fix) 0(0 ) 9(9 )!,e2(sci) 1( 1 ) 9( 9 ) 0( 10 )!,e3(norm) 1(Norm1) 2(Norm2) Fix Fix Fix2 Sci

14 Sci Sci4 Norm1 Norm2 Norm x, x Norm x, x Norm1, Norm Norm Norm2 A!,ee1(ab/c)!,ee2(d/c) A!,eee1(a+bi )!,eee2(r θ ) A SD REG Frequency!,dd1(FreqOn)!,dd2(FreqOff) 13

15 ... COMP... Deg... Norm1... ab /c... a+bi... FreqOn!9(CLR)2(Setup)w w A w - 2 ( ) 2 ( 3 ) = 2*(5+4)- 2*y3E 2 ( 5+4 ) A sin, cos, ' ) sin(, cos(, tan(, sin 1 (, cos 1 (, tan 1 (, sinh(, cosh(, tanh(, sinh 1 (, cosh 1 (, tanh 1 (, log(, ln(, e^(, 10^(, '(, 3 '(, Abs(, Pol(, Rec(, arg(, Conjg(, Not(, Neg(, Rnd( 14

16 - sin 30 = s30)e sin( 30) 05 A ( 2 ( 5 4 ) 2 sin(30) 2 '(3) 2 h A 2 π A A sin sin π 6 2π 2 2'(2) 2 2' 2 4π 2π 4π 2π Pol Rec, A E ) = 15 (2+3)* (4-1E ( 2+3 ) ( E 15

17 A 16 > > e f c A I I A 16

18 1 2I I I 1Y(INS) A Y *13 Y I 369 1I I A d e Y Y **12 dd I 369 I12 17

19 Y 369**12 ddd Y 369 I A d e Y d e A d e E d e /0*2E ed d1 14 0I I0 2 Mat h ERROR E

20 e d A BASE + - * / = E = 36 7*8-4*5E { 7v3 2v1v3 7 { 3 2 { 1 { 3 2{4= 1{2 19

21 A 1 2 3v1v4+ 1v2v3E 4-3v1v2E = 7 d/c v3+1v2E 10 A 1v(d/c) A = = = = E v 3{1{4+1{2{3 4 3{1{2 2{3+1{2 4{11{12 1{2 7{6 15 1{1{2 20

22 v % % 1/100 A 2 1 2% = ((%)E 2% % = *20 1((%)E % 660/880 1((%)E % * 151((%)E % % % % * 251((%)E % % E

23 -G*201((%)E Ans Ans 20% g300g% ( ) /5001((%)E % 48 (46-40) /401( % E ( ) 500% 160 ( 46 40) 40% 15 eeeey8e ( 48 40) 40% A 60 { } e { } e { } e e30e30eE e e0e30e 22

24 A u 60 u = e20e30e+ 0e39e30eE = e20e*3.5E A e E e e COMP CMPLX BASE f

25 - 1+1E2+2E 3+3E f f c 1 O d e d e E = = 4.9 4*3+2.5E d I

26 YYYY -7.1E 4 3I Ans SD REG A B C D X Y 6 A Ans Ans A Ans/ Ans Ans SD REG Ans Ans 25

27 Ans CMPLX Ans A Ans *4E /30E Ans / Ans w+4wE E Ans 14 2 E Ans A Ans G A Ans G Ans '(Ans 5 26

28 E 789-GE 789 Ans w+4wE G)+5E '(Ans)+5 10 M M M M A M m 10M M 105/3m 105 3M+ 35 A M 1m(M ) 27

29 - 3 2 M 3*21m(M ) m 1m M M M 3 2M 6 m 1m M A tm(m) A 0 01t(STO)m(M) M A M 01t STO m M = m 53 6 = m ) 45 2 = 90 45*21m(M ) 99 3 = 33 99/3m () 22 tm(m) M A B C D X Y A B C D X Y 6 A - A t(STO)-(A) 28

30 A t - A t-(a) A - 5 A 5+S-(A)E A 0 - A 01t(STO)-(A) A - B C = *6+3 1t(STO)e(B) 5*81t(STO)w(C) Se(B)/Sw(C)E B 5 8 C B C (CLR)1(Mem)E E A 29

31 π e π e π e π e BASE π e(π) e Si(e) 40 π e BASE A 1. 17(CONST) u 1 mp m mn me mμ u 10 e d e d u mp m mn me mμ mpi u E mp

32 A 1 17(CONST) dddd4(c 0 )E C c 0 = 1/ ε 0 μ 0 1/1 17(CONST) ddd4( 0 ) 17(CONST) dd1(μ 0 )) E 1 '(I 1 '( ε0i 1 '( ε 0 μ0)i 1 '( ε 0 μ0) A No. 17(CONST) No. 1-1 m p kg 1-2 m n kg 1-3 m e kg 1-4 μ mμ kg 2-1 a m 2-2 h J s 2-3 μ N J T μ B J T H J s

33 No. 3-2 α r e m 3-4 λ c m 4-1 γ p s 1 T λ cp m 4-3 λ cn m 4-4 R m u kg 5-2 μ p J T μ e J T μ μ n J T 1 μ μ J T F C mol e C 6-4 N A mol k J K V m m 3 mol R J mol 1 K C m s C W m C m K σ W m 2 K ε F m μ N A φ Wb 9-3 g m s G S 32

34 No Z Ω 10-2 t K 10-3 G m 3 kg 1 s atm Pa u CODATA 2010 BASE A { } { } { } { } ( ) ( ) A sin(, cos(, tan(, sin 1 (, cos 1 (, tan 1 ( sin({n}), cos({n}), tan({n}), sin 1 ({n}), cos 1 ({n}), tan 1 ({n}) - sin 30 = 0.5 sin = 30 Deg sin( ( 30 ) s30)e 05 33

35 1s(sin 1 )0.5)E A CMPLX i sin(30) sin(1 i ) sin 1 ( 0.5) 30 1G(DRG') 1(D) D R G 2(R) (G) π Deg (1e(π)/2) 1G(DRG')2(R)E (π 2 ) r G(DRG') 3(G)E 50 g 45 sinh(, cosh(, tanh(, sinh 1 (, cosh 1 (, tanh 1 ( A sinh({n}), cosh({n}), tanh({n}), sinh 1 ({n}), cosh 1 ({n}), tanh 1 ({n}) 34

36 - sinh 1 = ws(sinh)1)e A w 1w s c t CMPLX A 10^(, e^(, log(, ln(, 10^({n}) {n} e^( log({n})... log 10 {n} log({m},{n})... log {m} {n} {m} ln({n})... loge{n} 1 log 2 16 = 4 log16 = sinh( 1 ) l2,16)e l16)e log ( 2,16) log ( 16) ln 90 (log e 90) = i90)e 3 e 10 = i(e x )10)E 35 In( 90) eˆ ( 10 )

37 A {n} x 2... {n} 2 {n} x 3... {n} 3 {n} x 1... {n} 1 x 2, x 3, x 1, ^(, '(, 3 '(, x '( 2 3 {(m)}^({n})... {m} {n} '({n})... {n} 3 '({n})... 3 {n} ({m}) x {m} '({n})... {n} 1 ('2 + 1) ('2 1) = 1 (1 + 1) 2+2 = 16 (12)+1) (12)-1)E (1+1)^2+ 2)E ('( 2 ) +1 )('(2 ) 1 ) 1 ( 1+ 1) ˆ ( 2+2 ) = y2^2v3)e A x 2 x 3 x 1 CMPLX CMPLX ^( '( 3 '( x '( Pol(, Rec( 2ˆ ( 2{3 )

38 o o (Rec) A Pol Pol( x, y ) x : x y : y Rec Rec( r, ) r : r : (Pol) 1 '2, '2 Deg 1+(Pol)12),12))E Pol('( 2 ),'(2 )) 2 t,(y) 2 2, 30 Deg 1-(Rec)2, 30)E Y Rec ( 2, 30) y t,(y) 37 Y 1

39 A COMP SD REG r x r x y X Y y Y r x Pol ('2, '2) + 5 = = 7 x!, Abs(, Ran#, npr, ncr, Rnd( x! npr ncr CMPLX A {n}! {n} 0 - (5 + 3)! (5+3) 1E(x!)E A Abs Abs( CMPLX 41 Abs ({n}) - Abs (2 7) = 5 1)(Abs)2-7)E A Ran# Ran# 38 (5+3 )! Abs ( 2 7 )

40 - 1000Ran# (Ran#) E E u A nprncr {n} P {m}, {n} C {m} *(nPr)4E 101/(nCr)4E A Rnd Rnd({n}) Norm1 Norm2 11 Fix Sci = /7*14E 3 1Ne1(Fix)3 1000Ran# 1000Ran# 10P4 10C

41 15 200/7E *14E Ans /7E (Rnd)E Rnd( Ans *14E Ans n ENG 3 ENG 2 ENG W ENG 1W( ) ENG Eng 1234E W

42 W Eng 123E 1W( ) W( ) CMPLX CMPLX N 2 A i CMPLX W i a+bi W i i 2+3W(i) A (r ) y( ) ii 5 30I θ 12 41

43 R I 1E(Re Im) ENG ENG i a+bi 1N(SETUP)eee1 a+bi 2+W(i)E 1E(Re Im) 2+ i 2+ i 2 1 i A b a + bi O a O 13 A (a+bi) 1N(SETUP)eee1 a+bi 42

44 1 2 ('3 + i) = 2'3 + 2i = i 2*(13)+W(i)) E 2 ('(3)+i ) E(Re Im) 2 ('(3)+i ) 2 2 '2 45 = 1 + 1i Deg 12)1y( ) 45E '(2) E(Re Im) A (r) 1N (SETUP)eee2 r 1 2 ('3 + i) = 2'3 + 2i = 4 30 '(2) *(13)+W(i)) E 2 ('(3)+i ) 4 1E(Re Im) 2 ('(3)+i ) i = Deg 1+1W(i)E 1+1 i E(Re Im) i 45

45 Conjg z = a+bi z = a bi i 1,(Conjg)2+3W(i) )E Conjg( 2+3 i ) 2 1E(Re Im) Conjg( 2+3 i ) - 3 Abs, arg z = a + bi zarg i Deg b = 2 O a = 2 1)(Abs)2+2W(i ) )E Abs ( 2+2 i ) ((arg)2+2W(i ) )E arg( 2+2 i ) 45 44

46 A 1-('a+bi) - 2'2 45 = 2 + 2i Deg 212)1y( )45 1-('a+bi)E 1E(Re Im) 2' ( 2 ) 45 a + bi A 1+('r) i = 2'2 45 = Deg 2 2' ( 2 ) 45 a + bi 2 2+2W(i)1+('r) E 2+2 i r θ E(Re Im) 2+2 i r θ 45 SD REG A FreqOn FreqOff FreqOn 13 A FreqOn FreqOff 45

47 FreqOn FreqOff SD REG A 1 SD N4 SD A FreqOn x1, x2 xn Freq1, Freq2 Freqn {x1}1,(;) {Freq1}m(DT) {x2}1,(;) {Freq2}m(DT) {xn}1,(;) {Freqn}m(DT) 1 {xn} m(dt) - (x) (Freq) ,(;) ; 4I 0 m(dt) 1 46 Line = 1

48 25.51,(;)6 m(dt) Line = ,(;)2 m(dt) FreqOff x1, x2 xn {x1}m(dt) {x2}m(dt) {xn}m(dt) A c - FreqOn A Line = I 3 0 c c c c x 1= Freq 1= x 2= Freq 2 =

49 FreqOn x1, Freq1, x2, Freq2 FreqOff x1, x2, x3 f A E -Freq3 2 3 Af 3E A 1m(CL) -x 2 Accc 1m(CL) x1: 24.5 Freq1: 4 x1: 24.5 Freq1: 4 x2: 25.5 Freq2: 6 x2: 26.5 Freq2: 2 x3: 26.5 Freq3: 2 FreqOn x Freq A 19(CLR)1(Stat)E 48 Freq 3 = Freq 3 = x 2= Line =

50 E A A E o 12(S-VAR) 1E A SD Σx 2 11(S-SUM)1 2 Σx 2 = 2 Σx i Σx n o σx x x σx sx (S-SUM)2 Σx = Σx i 11(S-SUM)3 12(S-VAR)1 x = Σx i n 12(S-VAR)2 σx = sx 12(S-VAR)3 sx = 49

51 minx maxx (S-VAR)e1 12(S-VAR)e2 REG N5 REG A REG 7 y = a + bx y = a + bx + cx 2 y = a + b lnx e y = ae bx ab y = ab x y = ax b y = a + b/x REG 1. N5 REG REG u 2 d e Lin Log Exp Pwr e ab Inv Quad AB Exp (Lin) 2(Log) 3(Exp) 4(Pwr) e1(inv) e2(quad) e3(ab-exp)

52 REG 12(S-VAR)3(TYPE) 1 A FreqOn (x1, y1), (x2, y2) (xn, yn) Freq1, Freq2 Freqn {x1}, {y1} 1,(;) {Freq1}m(DT) {x2}, {y2} 1,(;) {Freq2} m(dt) {xn}, {yn} 1,(;) {Freqn} m(dt) 1 {xn}, {yn} m(dt) FreqOff (x1, y1), (x2, y2) (xn, yn) {x1}, {y1} m(dt) {x2}, {y2} m(dt) {xn},{yn} m(dt) A c FreqOn x 1, y 1, Freq1, x 2, y 2, Freq2FreqOff x 1, y 1, x 2, y 2, x 3 f 51

53 A E A 1 m CL A 48 A E o p 12(S-VAR)1(VAR) x σx sx E 12(S-VAR)1(VAR)e x y σy 115 sy A REG S-SUM Σx 2 11(S-SUM)1 x Σx 2 = Σx i 2 Σx y 1E 14 11(S-SUM)2 x Σx = Σx i 52

54 n Σy 2 11(S-SUM)3 11(S-SUM)e1 y 2 Σy 2 = Σy i 2 Σy y Σxy x y Σx 2 y { x 2 y } Σx 3 11(S-SUM)e2 Σy = Σy i 11(S-SUM)e3 Σxy = Σx i y i 11(S-SUM)d1 Σx 2 y = Σx i 2 yi 11(S-SUM)d2 x 3 Σx 3 = Σx i 3 Σx 4 11(S-SUM)d3 x 4 Σx 4 = Σx i 4 VAR o 12(S-VAR)1(VAR)1 x σx x sx x x = Σx i n 12(S-VAR)1(VAR)2 σx = Σ(x i x) 2 n 12(S-VAR)1(VAR)3 sx = 53

55 p y σy y sy y 12(S-VAR)1(VAR)e1 12(S-VAR)1(VAR)e2 12(S-VAR)1(VAR)e3 VAR 55 a a b b r r m 12(S-VAR)1(VAR)ee1 12(S-VAR)1(VAR)ee2 12(S-VAR)1(VAR)ee3 12(S-VAR)1(VAR)d1 y x n σy = sy = y = Σy i n 12(S-VAR)1(VAR)d2 x y 54

56 VAR a 12(S-VAR)1(VAR)ee1 a b 12(S-VAR)1(VAR)ee2 b c 12(S-VAR)1(VAR)ee3 c m 1 12(S-VAR)1(VAR)d1 y x 1 m 2 12(S-VAR)1(VAR)d2 y x 1 n 12(S-VAR)1(VAR)d3 x y MINMAX minx 12(S-VAR)2(MINMAX)1 x maxx 12(S-VAR)2(MINMAX)2 x miny 12(S-VAR)2(MINMAX)e1 y maxy 12(S-VAR)2(MINMAX)e2 y A 55

57 a b a = Σy i b. Σx i n n b. Σx = i y i Σx i. Σyi n. 2 Σxi (Σx i ) 2 n r r. Σx = i y i Σx i. Σyi {n. 2 Σx i (Σx i ) 2 }{n. 2 Σy i (Σy i ) 2 } y a m m = b n = a + bx n a 2 Σy Σx i Σx a = i b ( ) c( i n n n ) Sxy. Sx2 x 2 Sx 2 y. Sxx 2 b = b Sxx. Sx2 x 2 (Sxx 2 ) 2 Sx 2 y. Sxx Sxy. Sxx 2 c = c Sxx. Sx 2 x 2 (Sxx 2 ) 2 (Σx i ) Sxx 2 = Σx i2 n (Σx i. Σyi ) Sxy = Σx i y i n m1 m1 = m2 m2 = b + b 2 4c(a y) 2c b b 2 4c(a y) 2c n n = a + bx + cx 2 Sxx (Σx. i Σx i2 ) 2 = Σx i3 n Sx 2 x 2 4 = Σx i (Σx i 2 ) 2 n Sx 2 2 y = Σx i y i (Σx i 2. Σyi ) n 56

58 a b Σy a i b. Σlnx i = n n. Σ(lnx i )y i Σlnx i. Σyi b = n. Σ(lnx i ) 2 (Σlnx i ) 2 r r = m n n. Σ(lnx i )y i Σlnx i. Σyi {n. Σ(lnx i ) 2 (Σlnx i ) 2 }{n. 2 Σy i (Σy i ) 2 } y a b m = e n = a + blnx e a a = Σlny i b. Σx exp( i n ) b r r = m m = n n. Σx i lny i Σx i. Σlnyi b = n. Σx i 2 (Σx i ) 2 n = ae bx n. Σx i lny i Σx i. Σlnyi {n. 2 Σx i (Σx i ) 2 }{n. Σ(lny i ) 2 (Σlny i ) 2 } lny lna b ab a b a = Σlny exp( i lnb. Σx i n ) n b = exp(. Σx i lny i Σx i. Σlnyi n ). 2 Σx i (Σx i ) 2 r r = n. Σx i lny i Σx i. Σlnyi {n. 2 Σx i (Σx i ) 2 }{n. Σ(lny i ) 2 (Σlny i ) 2 } 57

59 m m = n n = ab x lny lna lnb a a = Σlny i b. Σlnx exp( i ) n b b = n. Σlnx i lny i Σlnx i. Σlnyi n. Σ(lnx i ) 2 (Σlnx i ) 2 r r = ln y ln a m b m = e n. Σlnx i lny i Σlnx i. Σlnyi {n. Σ(lnx i ) 2 (Σlnx i ) 2 }{n. Σ(lny i ) 2 (Σlny i ) 2 } n n = ax b a b Σy a = i b. 1 Σx i n Sxy b = Sxx Sxy r r = Sxx. Syy 1 (Σx Sxx = i ) 2 1 Σ(x i ) 2 n m b m = y a (Σy i ) Syy 2 = Σy i2 n Σx i 1. 1 Σyi Sxy = Σ(x i )y i n n n = a + x b 58

60 SD N4(SD) FreqOn 1N(SETUP)dd1(FreqOn) 55m(DT) 571,(;)2m(DT) 591,(;)2m(DT) 611,(;)5m(DT) 631,(;)8m(DT) 651,(;)9m(DT) 671,(;)8m(DT) 691,(;)6m(DT) 711,(;)4m(DT) 731,(;)3m(DT) 751,(;)2m(DT) 12(S-VAR)1(o)E x (S-VAR)3(sx)E sx

61 2 g REG N5(REG)1(Lin) FreqOff 1N(SETUP)dd2(FreqOff) 20,3150m(DT)50,4800m(DT) 80,6420m(DT)110,7310 m(dt)140,7940m(dt)170,86 90m(DT)200,8800m(DT)230, 9130m(DT)260,9270m(DT)29 0,9310m(DT)320,9390m(DT) a 12(S-VAR)1(VAR)ee 1(a)E b 12(S-VAR)1(VAR)ee 2(b)E 12(S-VAR)1(VAR)ee 3(r)E 60 a b r

62 12(S-VAR)3(TYPE) 2(Log) a A12(S-VAR)1(VAR) ee1(a)e b 12(S-VAR)1(VAR) ee2(b)e 12(S-VAR)1(VAR)ee 3(r)E x 1 = a b r x = 350n y 12(S-VAR)1(VAR)d 2(n)E nbase BASE N3 n A DEC w x ' HEX 10 x BIN e x M l i OCT e 61

63 10 w(dec) d 16 ^(HEX) H 2 l(bin) b 8 i(oct) o A n Al(BIN)1+1E Ai(OCT)7+1E Syntax ERROR BASE A A B C D E F 1 1 b b 10 o { }{A} y {B} e {C} w sin -1 {D} s cos -1 E c tan -1 F t F F+ 1 A^(HEX)1t(F)+1E 20 H 62

64 A 2 0 x x x x x x 7FFFFFFF x FFFFFFFF Math ERROR n w DEC^ HEXl BINi OCT Aw(DEC)30E l(bin) i(oct) ^(HEX) d b 36 o 1E H LOGIC BASE E BASE LOGIC LOGIC 3 d e 63

65 a nd o r x no r d h b o x o r No t Neg A 10 3 E(LOGIC)d1(d)3 A Al(BIN)E(LOGIC)d1(d) 5+E(LOGIC)d2(h)5 E d3i d5+h l BIN A and 1010 b and = E(LOGIC) 1(and)1100E 1010and b 64

66 A or or = E(LOGIC) 2(or)11010E A xor xor = or b 1010E(LOGIC)e 1(xor)1100E 1010xor b A xnor xnor = E(LOGIC) 3(xnor)101E A Not 1111xnor b - Not( ) = E(LOGIC)e2(Not) 1010)E A Neg 2 No t ( 1010) b - Neg( ) = E(LOGIC)e3(Neg) )E Neg ( ) b 65

67 23 COMP A 1. G u Formula No.? u 68 Formula No.? Q 06 0 A 1. G 2. c f A Gccc 03:HeronFormula E a a 0 a 8 8E 66 b 0

68 b 5 c 5 5E 5E c s 0 03:HeronFormula 12 E A a b c r t v ρ 1j CLR b Mem 1j CLR d All 2 E a a E E a 8 a 8 67

69 A 1G LOOK a 0 1G(LOOK) 03: S= ' (s ( s a )(s 1 e 1p(EXIT) A No. 01 a b c ax 2 + bx + c = 0 a 0, b 2 4ac 0 No b, c 2 1 a a = b 2 +c 2 2bc cos b, c 0,

70 No a b c S S = s(s a)(s b)(s c), s = (a+b+c) (a + b > c > 0, b + c > a > 0, c + a > b > 0) No. 04 P(x) x P(x) Hastings 2 1 x P(x) = e dt 2π t 2 2 P x (0 x < ) x No. 05 Q(x) x Q(x) Hastings 1 x 2 2π 0 Q(x) = e dt t 2 Q x (0 x < ) x No Q, q r F F = 1 Qq (r > 0) 4πε 0 (ε r 0 : ) Q, q: Cr: m 2 69

71 No. 07 S ρ R R = ρ S (S,, ρ > 0) : m, S: m 2, ρ : Ω m, R : Ω No. 08 B I F F = IB sin θ ( > 0, 0 90 ) θ B : T, I : A, : m, θ :, F : N No. 09 RC R RC R C V t R VR VR = V e t/cr (C, R, t > 0) R : Ω, C : F, t :, V V R : V No. 10 G E E ( ) [db] E' G[dB] = 20 log10 (E E >0) E E E : VG : db No. 11 LRC f LRC R L C Z 2 Z = R π f L = ( 2π f C ) R ( ωc ) 2 + ωl ' / ( ) (R, f, L, C > 0) f : HzL : HC : FR Z : Ω 70

72 No. 12 LRC f LRC R L C Z Z = π f C ( R ) ( 2π f L ) 2 (R, f, L, C > 0) f : HzC : FL : HR Z : Ω No. 13 L C f 1 1 f 1 = (L, C > 0) L : HC : Ff 1 : Hz 2π LC No. 14 v 1 t S 1 S= v 1 t + gt 2 (g : t 0) 2 v 1 : m st : S : m No. 15 T T = 2π g (g : > 0) : mt : No. 16 m k T T = 2π m k (m k > 0) m : kgk : N/mT : No. 17 f1 v v1 u f 71

73 v u v v 1 f = f 1 (v v 1, f 1>0, (v u)/(v v 1) >0) vv 1 u : m/sf 1 f : Hz No. 18 n T V P P nrt = (R n T V > 0) V n : molt : KV : m 3 P : N/m 3 No. 19 m v r F F = m v 2 r (m v r >0) m : kgv : m/sr : mf : N No. 20 k x U 1 2 U = kx 2 (k, x > 0) k : N/mx : mu : J No. 21 v z ρ P C 1 C = v P 2 + +gz 2 ρ (g v, z, ρ, P > 0) v : m/sz : mρ : kgf/m 3 P : kgf/m 2 C : m 2 /s 2 72

74 No. 22 h 1 h = K sin2 θ +Csin θ 2 (K C 0 < θ 90, > 0) : mθ : h : m No. 23 S S = K cos 2 θ +Ccos θ (K C 0 < θ 90, > 0) PRGM PRGM,6 PRGM COMP CMPLX BASE SD REG A PRGM PRGM 1 COMP, CMPLX, BASE, SD, REG A : mθ : S : m

75 A - 1 inch = 2.54cm? A : A ,6(PRGM) PRGM ED I T RUN DEL (EDIT) EDIT Prog ram P P1 P4 3. u e /d 1 2 MODE : COMP CMPLX 1 2 MODE : BASE SD REG u 1 1 (COMP) COMP I

76 5.? A : A u? A : A (P-CMD)1(?) 1t( )y(a)e Sy(A)*2.54 u 1 3 (P-CMD) A 1p EXIT u E RUN Program u, 1 COMP A 1.,6 PRGM 1 EDIT EDIT Program e /d u f/c / 4. A 1p EXIT PRGM PRGM 75

77 A PRGM 1. p P1 P2 P3 P A PRGM 1., 6 PRGMPRGM 2. 2 RUN u RUN Program RUN P r o g ram P P1 P u A d e A 1., 6 PRGMPRGM 76

78 2. 3 DEL DELETE Prog ram P P1 P u DELETE Prog ram P A 1. 13(P-CMD) u 1? : ^ e d w A 78 77

79 g 1 3 (P-CMD) p A g (??? A? A + 5 A? A A 2 Ans 2 ^ ^ Q? A A 2^Ans 2 A g Goto Lbl Goto nlbl n Lbl ngoto n n 0 9 Goto n Lbl n? A Lbl 1? B A B 2^Goto 1 Goto n Lbl n Syntax ERROR 78

80 A g Lbl 1? A A 0 (A) ^ Goto 1 If While If While Ans A /If g If If u If Then Syntax ERROR 79

81 u Then Else * Goto Break u 84 If Then ( Else) IfEnd IfThen *Else *IfEnd u If Then Else IfEnd If Else IfEnd u Else { } u IfEnd:{ } If 1? A If A 10 Then 10A ^ Else 9A ^ IfEnd Ans ? A If A 0 Then A 10 A IfEnd Ans 1.05 A / For g For For Next For u For Next Syntax ERROR u 84 For To Next For To Next For Next 1 Next Next For 1 A To 10 A 2 B B ^ Next 80

82 For To Step Next For To StepNext For Next For To Next For 1 A To 10 Step 0.5 A 2 B B ^ Next A / While g u 84 While WhileEnd While WhileEnd While 0 While WhileEnd While 0WhileEnd? A While A 10 A 2 ^ A+1 A WhileEnd A While While WhileEnd WhileEnd A g Break Then Else Break For While Then Break? A While A 0 If A 2 Then Break IfEnd WhileEnd A ^ A 11 81

83 Deg, Rad, Gra (COMP, CMPLX, SD, REG) Deg Rad Gra 1,(SETUP)1(Deg) 1,(SETUP)2(Rad) 1,(SETUP)3(Gra) Fix (COMP, CMPLX, SD, REG) Fix n n 0 9 1,(SETUP)e1(Fix) Sci (COMP, CMPLX, SD, REG) Sci n n 0 9 1,(SETUP)e2(Sci) Norm (COMP, CMPLX, SD, REG) Norm 1 2 1,(SETUP)e3(Norm)1 2 Norm1 Norm2 FreqOn, FreqOff (SD, REG) FreqOn FreqOff 1,(SETUP)d1(FreqOn) 1,(SETUP)d2(FreqOff) 82

84 FreqOn FreqOff A ClrMemory (COMP, CMPLX, BASE) ClrMemory 19(CLR)1(Mem) A B C D X Y M 0 0 ClrStat (SD, REG) ClrStat 19(CLR)1(Stat) A M+, M (COMP, CMPLX, BASE) M+ M m 1m(M ) M M+ / M M A Rnd Rnd( (COMP, CMPLX, SD, REG) Rnd(Ans 10(Rnd) A Dec, Hex, Bin, Oct (BASE) Dec Hex Bin Oct w DEC) ^(HEX) l(bin) i(oct) n 83

85 A DT (SD, REG) { x } ; { Freq } DT { x } DT SD FreqOn SD FreqOff { x }, { y } ; { Freq } DT { x }, { y } DT REG FreqOn REG FreqOff 1,(;),, m DT 1 DT SD REG m DT A u ENG ENG u 1E Re Im u 19 CLR 3 All E u 19(CLR)2 Setup E A IfForWhile u If If u For While u While For u u 84

86 1 Pol(, Rec( sin(, cos(, tan(, sin 1 (, cos 1 (, tan 1 (, sinh(, cosh(, tanh(, sinh 1 (, cosh 1 (, tanh 1 ( log(, ln(, e^(, 10^(, '(, '( 3 arg(, Abs(, Conjg( Not(, Neg(, Rnd( 2 x 2, x 3, x 1, x!,,, r, g ^(, x '( % 3 a b / c 4 ( ) d, h, b, o n 5 m, n, m1, m2 6 π, e, (2π, 5A, πa, 3mp, 2i ) 2 ' 3, Asin(30) 7 npr, ncr 8, 9 +, 0,, >, <,,! or, xor, xnor u 2 2 x 2 ( ) ( 2) 2 y2we 2 2 = 4 (y2)we ( 2) 2 = 4 85

87 u 1 2π = 1/(2π) = π = (1/2) π = Stack ERROR CMPLX 1 2 CMPLX 5 86

88 A DEG 0 < x < sin x RAD 0 < x < GRA 0 < x < DEG 0 < x < cos x RAD 0 < x < GRA 0 < x < DEG sin x x = (2n 1) 90 tan x RAD sin x x = (2n 1) π / 2 GRA sin x x = (2n 1) 100 sin 1 x cos 1 x 0 < x < 1 tan 1 x 0 < x < sinh x cosh x 0 < x < sinh 1 x 0 < x < cosh 1 x 1 < x < tanh x 0 < x < tanh 1 x 0 < x < log x / ln x 0 < x < x < x < e x < x < 'x 0 < x < x 2 x < /x x < ; x 0 3 'x x <

89 x! 0 < x < 69 x : npr ncr Pol(x,y) Rec(r,θ) ^(x y ) x 'y a b / c 0 < n < , 0 < r < n n, r : 1 < {n!/(n r)!} < < n < , 0 < r < n n, r : 1< n!/r! < < n!/(n r)! < x, y < ' x 2 + y 2 < < r < : sinx a, b, c < < b, c x < < x < x > 0: < ylogx < 100 x = 0: y > 0 m x < 0: y = n, 2n+1 m, n : < y log x < 100 y > 0: x 0, < 1/x logy < 100 y = 0: x > 0 y < 0: x = 2n+1, 2n+1 m m 0; m, n : < 1/x log y < ^(x y ), x 'y, 3 ', x!, npr, ncr 1 Mat h ERROR A 88

90 d e 18 A A Math ERROR u u u 0 u u 87 Stack ERROR u u

91 Syntax ERROR Argument ERROR Data Full SD REG 45 Go ERROR PRGM Goto n Lbl n Goto n Lbl ngoto n 90

92 O O 19 CLR 2 Setup E LR44 2 TWO WAY POWER A 91

93 u k l u A O

94 1. 1A OFF O k CLR 3 All E A k l A 10 O G13 LR C 40 C mm 95g 93

95 ? A B c B A C b B C a < sin b c cos a c tan b a θ θ >sin = b c cos = a c b = c sin a = c cos Deg b = 10 sin 60 10s60)w a = 10 cos 60 10c60)w 10sin( 60 ) cos( 60 ) 5 94

96 b B a c b tanb sin a B b c a tana cos P(x,y) y 10m 60 0 x Deg 10, 60 1-(Rec)10,60)w Rec ( 10,60 ) 5 Yy t,(y) Y ? 2 a b B < sin b c θ cos a c tan b a 95

97 > tan = b a = tan 1 b a Deg tan t(tan 1 ) 5/8)w 60 e tan -1 ( 5 8 ) tan -1 ( 5 8 ) a c cos 1 a c b c sin 1 b c 5m r P(8,5) 8m Deg 8, 5r 1+(Pol)8, 5)w Y 0 θ Pol ( 8,5) t,(y) Y e Y

98 ? C D A X X < > Deg A sin C X sin 180 C D C D C D 501t(STO)y(A) 61e32e1t(STO)w(C) 49e25e1t(STO)s(D) Sy(A)sSw(C))/s180- Sw(C)-Ss(D))w? > C (61 32 ) (49 25 )D A (50m) 20W 60kg0.3 P P θ (20 ) Deg W (60kg) Asin( C ) sin( < P W sincos 60(s20)+ 0.3*c20)) w 97 60( sin( 20) +0.3 c

99 ? V 0 30m/s 50 3 h < > θ Deg 30*3* s50)- 2E*9.8* 3ww h V 0 t sin 1 2 gt2 g9.8m/s sin( 50 )

fx-3650P_fx-3950P_J

fx-3650P_fx-3950P_J SA1109-E J fx-3650p fx-3950p http://edu.casio.jp RCA500002-001V04 AB2 Mode

More information

fx-370ES_912ES_UsersGuide_J02

fx-370ES_912ES_UsersGuide_J02 Eng Eng 3 A Eng 1 1,234 Eng a 1234= W W 2 123 Eng a 123= 1W( ) S-D S-D π 72 A S-D π π nπ n d π c a b π c π ' f ' A S-D 1 A '5c6= f f f 73 2 π A 15(π)*'2c5= f 3 ' A!2e*!3= f 74 (CMPLX) 15 CMPLX N2 A u u

More information

36.fx82MS_Dtype_J-c_SA0311C.p65

36.fx82MS_Dtype_J-c_SA0311C.p65 P fx-82ms fx-83ms fx-85ms fx-270ms fx-300ms fx-350ms J http://www.casio.co.jp/edu/ AB2Mode =... COMP... Deg... Norm 1... a b /c... Dot 1 2...1...2 1 2 u u u 3 5 fx-82ms... 23 fx-83ms85ms270ms300ms 350MS...

More information

26.fx95MS_Etype_J-cover_SA0311D

26.fx95MS_Etype_J-cover_SA0311D P fx-95ms fx-100ms fx-570ms fx-912ms (fx-115ms) fx-991ms English Manual Readers! Please be sure to read the important notice on the inside of the front cover of this manual. J http://www.casio.co.jp/edu/

More information

6.fx570MS-Atype_J-cover_SA0403E

6.fx570MS-Atype_J-cover_SA0403E J fx-570ms fx-991ms CA 310029-001V06 http://www.casio.co.jp/edu/ Eng n 1 fx-95ms/fx-100ms/fx-570ms/ fx-912ms (fx-115ms)/fx-991ms 2 fx-570ms/fx-991ms COMP F 1 CMPLX F 2 SD F F 1 REG

More information

fx-JP500

fx-JP500 SA1409-A JA fx-jp500 http://edu.casio.jp RJA531983-001V01 1. 2. 1 2 15 31 + 3 ... 1... 3... 5... 5... 5... 7... 8... 9... 11... 14... 15... 17... 19... 19... 21... 26... 27... 27... 29 n... 33 /... 34...

More information

fx-JP700_fx-JP900

fx-JP700_fx-JP900 SA1412-A 1. 2. 1 2 15 31 + 3 ...1...3... 5... 5... 5...7...8... 9... 11...14... 15... 17... 18... 19... 21 QR fx-jp900... 25...26... 27...27... 29 n... 32 /...34... 35... 37... 38 fx-jp900...40 fx-jp900...

More information

fx-260A_Users Guide_J

fx-260A_Users Guide_J fx-260a http://edu.casio.jp J 1 5 2 Fl SD F0 COMP F4 DEG F5 RAD F6 GRA 3 F7 FIX F8 SCI F9 NORM COMP DEG, RAD, GRA COMP SD F0 SD SC FIX F9 SD DEG, RAD, GRA t SD COMP DEG RAD GRA COMP 23 4.5 53 23 + 4.5,

More information

I

I I 6 4 10 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............

More information

数学の基礎訓練I

数学の基礎訓練I I 9 6 13 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 3 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............

More information

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....

More information

c 2009 i

c 2009 i I 2009 c 2009 i 0 1 0.0................................... 1 0.1.............................. 3 0.2.............................. 5 1 7 1.1................................. 7 1.2..............................

More information

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............

More information

29

29 9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n

More information

Part () () Γ Part ,

Part () () Γ Part , Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35

More information

I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

I A A441 : April 15, 2013 Version : 1.1 I   Kawahira, Tomoki TA (Shigehiro, Yoshida ) I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17

More information

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s [ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =

More information

(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0

(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0 1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45

More information

70 : 20 : A B (20 ) (30 ) 50 1

70 : 20 : A B (20 ) (30 ) 50 1 70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................

More information

i

i i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,

More information

.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(

.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g( 06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,

More information

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y [ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)

More information

(u(x)v(x)) = u (x)v(x) + u(x)v (x) ( ) u(x) = u (x)v(x) u(x)v (x) v(x) v(x) 2 y = g(t), t = f(x) y = g(f(x)) dy dx dy dx = dy dt dt dx., y, f, g y = f (g(x))g (x). ( (f(g(x)). ). [ ] y = e ax+b (a, b )

More information

20 6 4 1 4 1.1 1.................................... 4 1.1.1.................................... 4 1.1.2 1................................ 5 1.2................................... 7 1.2.1....................................

More information

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,, 01 10 18 ( ) 1 6 6 1 8 8 1 6 1 0 0 0 0 1 Table 1: 10 0 8 180 1 1 1. ( : 60 60 ) : 1. 1 e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1,

More information

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) 4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7

More information

2011de.dvi

2011de.dvi 211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10

More information

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy z fz fz x, y, u, v, r, θ r > z = x + iy, f = u + iv γ D fz fz D fz fz z, Rm z, z. z = x + iy = re iθ = r cos θ + i sin θ z = x iy = re iθ = r cos θ i sin θ x = z + z = Re z, y = z z = Im z i r = z = z

More information

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 (

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 ( 1 1.1 (1) (1 + x) + (1 + y) = 0 () x + y = 0 (3) xy = x (4) x(y + 3) + y(y + 3) = 0 (5) (a + y ) = x ax a (6) x y 1 + y x 1 = 0 (7) cos x + sin x cos y = 0 (8) = tan y tan x (9) = (y 1) tan x (10) (1 +

More information

keisoku01.dvi

keisoku01.dvi 2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5 Mon, 2006, 401, SAGA, JAPAN Dept.

More information

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,. 9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,

More information

( )

( ) 18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................

More information

*3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i i r 3r + 4i 1 i 1 i *4 1 i 9 i 1 1 i i 3 9 +

*3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i i r 3r + 4i 1 i 1 i *4 1 i 9 i 1 1 i i 3 9 + 1 2 IT 1 *1 1 2 3 π i 1i 2i 3i πi i 2 1 *2 2 + 3 + 4i π ei 3 4 4 2 2 *1 *2 x 2 + 1 = x 2 + x + 1 = 2 3 1 2 2 2 2 *3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i 1 2 1 2 2 1 i r 3r + 4i 1

More information

meiji_resume_1.PDF

meiji_resume_1.PDF β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E

More information

untitled

untitled 1 ( 12 11 44 7 20 10 10 1 1 ( ( 2 10 46 11 10 10 5 8 3 2 6 9 47 2 3 48 4 2 2 ( 97 12 ) 97 12 -Spencer modulus moduli (modulus of elasticity) modulus (le) module modulus module 4 b θ a q φ p 1: 3 (le) module

More information

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b) 2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................

More information

pdf

pdf http://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg

More information

熊本県数学問題正解

熊本県数学問題正解 00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (

More information

1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2

1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2 θ i ) AB θ ) A = B = sin θ = sin θ A B sin θ) ) < = θ < = Ax Bx = θ = sin θ ) abc θ sin 5θ = sin θ fsin θ) fx) = ax bx c ) cos 5 i sin 5 ) 5 ) αβ α iβ) 5 α 4 β α β β 5 ) a = b = c = ) fx) = 0 x x = x =

More information

http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................

More information

4‐E ) キュリー温度を利用した消磁:熱消磁

4‐E ) キュリー温度を利用した消磁:熱消磁 ( ) () x C x = T T c T T c 4D ) ) Fe Ni Fe Fe Ni (Fe Fe Fe Fe Fe 462 Fe76 Ni36 4E ) ) (Fe) 463 4F ) ) ( ) Fe HeNe 17 Fe Fe Fe HeNe 464 Ni Ni Ni HeNe 465 466 (2) Al PtO 2 (liq) 467 4G ) Al 468 Al ( 468

More information

sikepuri.dvi

sikepuri.dvi 2009 2 2 2. 2.. F(s) G(s) H(s) G(s) F(s) H(s) F(s),G(s) H(s) : V (s) Z(s)I(s) I(s) Y (s)v (s) Z(s): Y (s): 2: ( ( V V 2 I I 2 ) ( ) ( Z Z 2 Z 2 Z 22 ) ( ) ( Y Y 2 Y 2 Y 22 ( ) ( ) Z Z 2 Y Y 2 : : Z 2 Z

More information

Note.tex 2008/09/19( )

Note.tex 2008/09/19( ) 1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................

More information

20 9 19 1 3 11 1 3 111 3 112 1 4 12 6 121 6 122 7 13 7 131 8 132 10 133 10 134 12 14 13 141 13 142 13 143 15 144 16 145 17 15 19 151 1 19 152 20 2 21 21 21 211 21 212 1 23 213 1 23 214 25 215 31 22 33

More information

30

30 3 ............................................2 2...........................................2....................................2.2...................................2.3..............................

More information

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a

More information

i

i 009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3

More information

chap1.dvi

chap1.dvi 1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f

More information

30 (11/04 )

30 (11/04 ) 30 (11/04 ) i, 1,, II I?,,,,,,,,, ( ),,, ϵ δ,,,,, (, ),,,,,, 5 : (1) ( ) () (,, ) (3) ( ) (4) (5) ( ) (1),, (),,, () (3), (),, (4), (1), (3), ( ), (5),,,,,,,, ii,,,,,,,, Richard P. Feynman, The best teaching

More information

64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k

64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k 63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5

More information

EL5250

EL5250 EL-5250 SHARP EL-5250 1 2 3 4 5 6 7 8 x @ "... i ;... @ F... k ;... i Q... @ ; j @ s ; A k S @ s@ ` ;; 5 NORMAL MODE 0. πrœ 10_ 9 10 y zall DATA CL?z z YES [DEL] z z NO [ENTER]z NORMAL MODE 0. @ o 0 +

More information

I 1

I 1 I 1 1 1.1 1. 3 m = 3 1 7 µm. cm = 1 4 km 3. 1 m = 1 1 5 cm 4. 5 cm 3 = 5 1 15 km 3 5. 1 = 36 6. 1 = 8.64 1 4 7. 1 = 3.15 1 7 1 =3 1 7 1 3 π 1. 1. 1 m + 1 cm = 1.1 m. 1 hr + 64 sec = 1 4 sec 3. 3. 1 5 kg

More information

i 6 3 ii 3 7 8 9 3 6 iii 5 8 5 3 7 8 v...................................................... 5.3....................... 7 3........................ 3.................3.......................... 8 3 35

More information

K E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................

More information

fx-991ES_J

fx-991ES_J J fx-991es RCA501267-001V01 http://www.casio.co.jp/edu/ A 19(CLR)3(All)=(Yes) 15 43 1 1 2 + -! A!2)+!3= 1 S sin 1 {D} s 1s(sin 1 )1= 1(Setup) fcde REPLAY 2 A a 16 z Z Deg Rad 16 3 4 u u 5 O fx-991es...

More information

2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a

2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a 009 I II III 4, 5, 6 4 30. 0 α β α β l 0 l l l l γ ) γ αβ ) α β. n n cos k n n π sin k n π k k 3. a 0, a,..., a n α a 0 + a x + a x + + a n x n 0 ᾱ 4. [a, b] f y fx) y x 5. ) Arcsin 4) Arccos ) ) Arcsin

More information

all.dvi

all.dvi 38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t

More information

K E N Z U 01 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.................................... 4 1..1..................................... 4 1...................................... 5................................

More information

untitled

untitled ( ) c a sin b c b c a cos a c b c a tan b a b cos sin a c b c a ccos b csin (4) Ma k Mg a (Gal) g(98gal) (Gal) a max (K-E) kh Zck.85.6. 4 Ma g a k a g k D τ f c + σ tanφ σ 3 3 /A τ f3 S S τ A σ /A σ /A

More information

2019 1 5 0 3 1 4 1.1.................... 4 1.1.1......................... 4 1.1.2........................ 5 1.1.3................... 5 1.1.4........................ 6 1.1.5......................... 6 1.2..........................

More information

4................................. 4................................. 4 6................................. 6................................. 9.................................................... 3..3..........................

More information

No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2

No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2 No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j

More information

LLG-R8.Nisus.pdf

LLG-R8.Nisus.pdf d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =

More information

ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d

ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9

More information

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi) 0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

More information

関数電卓 マニュアル

関数電卓 マニュアル 関数電卓 マニュアル EXE もくじ p EXE 電源の On/Off p3 EXE EXE S D 変換 p4 EXE リプレイ機能 p5 EXE 計算履歴 p6 EXE FUNCTION EXIT p7 EXE 微分 積分 p8 p9 EXE の計算 p0 EXE log の底の設定 p EXE 乗数 p EXE ソルブ機能 p3 EXE カルク機能 p4 EXE 内蔵公式 p5 EXE テーブルモード

More information

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f 22 A 3,4 No.3 () (2) (3) (4), (5) (6) (7) (8) () n x = (x,, x n ), = (,, n ), x = ( (x i i ) 2 ) /2 f(x) R n f(x) = f() + i α i (x ) i + o( x ) α,, α n g(x) = o( x )) lim x g(x) x = y = f() + i α i(x )

More information

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2 II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh

More information

t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z

t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z I 1 m 2 l k 2 x = 0 x 1 x 1 2 x 2 g x x 2 x 1 m k m 1-1. L x 1, x 2, ẋ 1, ẋ 2 ẋ 1 x = 0 1-2. 2 Q = x 1 + x 2 2 q = x 2 x 1 l L Q, q, Q, q M = 2m µ = m 2 1-3. Q q 1-4. 2 x 2 = h 1 x 1 t = 0 2 1 t x 1 (t)

More information

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59

More information

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B 9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A

More information

1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2

1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2 filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin

More information

2000年度『数学展望 I』講義録

2000年度『数学展望 I』講義録 2000 I I IV I II 2000 I I IV I-IV. i ii 3.10 (http://www.math.nagoya-u.ac.jp/ kanai/) 2000 A....1 B....4 C....10 D....13 E....17 Brouwer A....21 B....26 C....33 D....39 E. Sperner...45 F....48 A....53

More information

II 2 II

II 2 II II 2 II 2005 yugami@cc.utsunomiya-u.ac.jp 2005 4 1 1 2 5 2.1.................................... 5 2.2................................. 6 2.3............................. 6 2.4.................................

More information

211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,

More information

液晶の物理1:連続体理論(弾性,粘性)

液晶の物理1:連続体理論(弾性,粘性) The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers

More information

高校生の就職への数学II

高校生の就職への数学II II O Tped b L A TEX ε . II. 3. 4. 5. http://www.ocn.ne.jp/ oboetene/plan/ 7 9 i .......................................................................................... 3..3...............................

More information

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy f f x, y, u, v, r, θ r > = x + iy, f = u + iv C γ D f f D f f, Rm,. = x + iy = re iθ = r cos θ + i sin θ = x iy = re iθ = r cos θ i sin θ x = + = Re, y = = Im i r = = = x + y θ = arg = arctan y x e i =

More information

( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) =

( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) = 1 9 8 1 1 1 ; 1 11 16 C. H. Scholz, The Mechanics of Earthquakes and Faulting 1. 1.1 1.1.1 : - σ = σ t sin πr a λ dσ dr a = E a = π λ σ πr a t cos λ 1 r a/λ 1 cos 1 E: σ t = Eλ πa a λ E/π γ : λ/ 3 γ =

More information

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2 (2018 ) ( -1) TA Email : ohki@i.kyoto-u.ac.jp, ske.ta@bode.amp.i.kyoto-u.ac.jp : 411 : 10 308 1 1 2 2 2.1............................................ 2 2.2..................................................

More information

IA

IA IA 31 4 11 1 1 4 1.1 Planck.............................. 4 1. Bohr.................................... 5 1.3..................................... 6 8.1................................... 8....................................

More information

x (x, ) x y (, y) iy x y z = x + iy (x, y) (r, θ) r = x + y, θ = tan ( y ), π < θ π x r = z, θ = arg z z = x + iy = r cos θ + ir sin θ = r(cos θ + i s

x (x, ) x y (, y) iy x y z = x + iy (x, y) (r, θ) r = x + y, θ = tan ( y ), π < θ π x r = z, θ = arg z z = x + iy = r cos θ + ir sin θ = r(cos θ + i s ... x, y z = x + iy x z y z x = Rez, y = Imz z = x + iy x iy z z () z + z = (z + z )() z z = (z z )(3) z z = ( z z )(4)z z = z z = x + y z = x + iy ()Rez = (z + z), Imz = (z z) i () z z z + z z + z.. z

More information

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2 1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a

More information

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =

More information

I ( ) 2019

I ( ) 2019 I ( ) 2019 i 1 I,, III,, 1,,,, III,,,, (1 ) (,,, ), :...,, : NHK... NHK, (YouTube ),!!, manaba http://pen.envr.tsukuba.ac.jp/lec/physics/,, Richard Feynman Lectures on Physics Addison-Wesley,,,, x χ,

More information

ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +

ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + 2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j

More information

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C 0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,

More information

( ) : 1997

( ) : 1997 ( ) 2008 2 17 : 1997 CMOS FET AD-DA All Rights Reserved (c) Yoichi OKABE 2000-present. [ HTML ] [ PDF ] [ ] [ Web ] [ ] [ HTML ] [ PDF ] 1 1 4 1.1..................................... 4 1.2..................................

More information

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H 199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)

More information

IMO 1 n, 21n n (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a

IMO 1 n, 21n n (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a 1 40 (1959 1999 ) (IMO) 41 (2000 ) WEB 1 1959 1 IMO 1 n, 21n + 4 13n + 3 2 (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a = 4, b =

More information

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq 49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1 ... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =

More information

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t 1 1 2 2 2r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t) V (x, t) I(x, t) V in x t 3 4 1 L R 2 C G L 0 R 0

More information

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,. 24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)

More information

The Physics of Atmospheres CAPTER :

The Physics of Atmospheres CAPTER : The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(

More information

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π 4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan

More information

IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................

More information