O'zbekiston respublikasi oliy va o'rta maxsus talim vazirligi samarqand davlat universiteti haydarov Akram matematik fizika va analizning zamonaviy usullari va nokorrekt masalalari
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S2+C02 S + Ct)
S2 + C02 6V./(t) = со scot funksiya tasvirini toping s S2 + C02 /(t) F(s) bulsa, to'g'ri munosabatni ko'rsating f(t - a) e~asF(s) fit - a) easF(s) d. f(t - a) <- e^F (§) fit) = e~at sincot originalning tasvirini toping CO (s+a)2+co2 b 1 (s+a)2+co2 a (s+a)2+co2 ^ a+co (s+a)2+co2 x^ + —I- anx = fix) ko'phadning xarakteristik ko'phadini toping Lis) = sn + a1sn~1 + -- + an Lis) = sn_1 H 1-1 Lis) = sn + 1 Lis) = sn- 1 x" + 2x' + x = e_t, x(0) = 0, x'(0) = 0 masalaning xarakteristik ko'phadini toping a. s2 + 2s + 1 s2 — 2s + 1 s2 + 2s s2 + l x" + 2x' + x = e~z, x(0) = 0, x"(0) = 0 Koshi masalasi echimini toping x(t) = ^t2e_t x{t)=\t2 x(t) = x(t) = it2-e_t x" + 2x' + x = e~z, x(0) = 1, x'(0) = 0 masala tasvirlar sohasida qanday ko'rinishga keladi (s + l)2X(s) = -^+2 + s (5 + 1)2ВД = ^ (s + 1)2ВД = 2 + s (s + l)X(s) =7^7+2 fx' + у = 0 [x + у' = 0 fx + у = 0 75 {x + у' = о = = _1 бУлса' tasvirni toping qanday ko'rinishga ega bo'ladi? Г sX(s) + Y(s) = 1 a" U(s) + sY(s) = -1 Г ВД + 7(s) = 1 U(s)-sY(s) = -l ( sX(s) - Y(s) = 1 C" U(s) + sY(s) = -1 Г s*(s) - 7(s) = 1 U(s) - sY(s) = -1 rx' + у = 0 l — s-1 -2- d. S + 1 s2+l 1 fx' + у = 0 76.) x(0) = 1, y(0) = — 1 булса, 7(s) tasvirni toping "T" у — U a. s+1 fx' + у = 0 74.) , x(0) = 1, y(0) = —1 Koshi masalasi tasvirlar sohasida (x + у = 0 ^ s-1 s+1 d. -2- s—1 fx' + y = 0 [x + у' = 0 77. x(0) = 1, y(0) = —1 bo'lsa, x(t) originalni toping
fx' +y = 0 [x + у' = 0 e_t et 1 - ef l + et fx' +y = 0 [x +y' = 0 = X(-D 19 || 1| ~ ^ 31 \l, 0<(р<7Г 68 0, 123 1, 123 2,—<в<2п A 123 80.res 3i z2+ 9 ni toping a. 6e3 b. -i- 6e3 i C. - 6 ni toping ni toping d. -4 cos2z 81.res (z-l)3 ' —Icosl = X(-D 19 || 1| ~ ^ 31 \l, 0<(р<7Г 68 0, 123 1, 123 2,—<в<2п A 123 3 ez2 82.res a. 3 b. 2 = X(-D 19 || 1| ~ ^ 31 \l, 0<(р<7Г 68 0, 123 1, 123 2,—<в<2п A 123 ni hisoblang 83 .res z — 0 2 tasvirning originalini toping s2 + 2S+5 —e^sinlt 2 — ~etsin2t 2 -etsin2t 2 -esint 2 F(s) = j- funksiya originalini toping - (s/it — sint) - (cht — sint) - (s/it — cost) - (cht + sint) F(s) = funksiya originalini toping tn = X(-D 19 || 1| ~ ^ 31 \l, 0<(р<7Г 68 0, 123 1, 123 2,—<в<2п A 123 etsin^t -etsinpt 84.F(s) = F(s) = tasvirning originalini toping a. ,at ^ ■ cos(3t eatsin(3t eatch(3t eatsh(3t /(t) = sin3t tasvirning originalini toping 6 a' (s2 + l)(s2+9) b 1 ' (s2 + l)(s2+9) 1 Q (s2 + 1)(s2+4) d 1 (s2-1)(s2-4) Laplas diskret almashtirishining chiziqlilik xossasini keltiring Z?=i cj fj(n) <- Tj=1ci 57=1c;/y(n) <- z?=1c;f;Q) C. /» <- J%=1Cj F/iq + 1) d. I?=1 Cj fj(n) <- n=1Cj F/(2q) Tasvirni differensiallash xossasini keltiring к a. nk/(n) <-(-i)*f-F*( dq к dq d к с. nk/(n) ^F*(q + 1) к d. nfc/(n) + f(n) n f(n) r oo 92.Tasvirni integrallash formulasini keltiring a- ^ ^ Lar(s)-/(0)]ds (n>l) 71 4. S,[F*(s)-f(0)]ds Tl c- ^ ^ ГГС^ + ЯО)]^ d-^ ^ JoV(s)-/(0)№ 93.Siljish xossasini keltiring eanf(ri) <- F*(q-a) ean/(n) F*(q + a) ean/(ri) <- F*(<7/a) ean/00 <- F*(q-a)f(n) <- F*(™?) 94.Diskret originalga ko'ra diskret tasvirni toping оЧ eq а" <- ^ eq-1 ГУ с аа еа eq+1 CLa ^ — 95.To'g'ri munosabatni keltiring eq eq+1 eq eq a • и <- b. n Download 391.68 Kb. Do'stlaringiz bilan baham: |
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