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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- fiO)git)
- 2 +4 s C. —— s 2 + 2
- 7T J U l-2rcos(4»-^)+r z C. 0)(z ) = Г
u(x,y) = ey sinx bo'lsa, /(z) funksiyani Gursa formulasi orqali toping.
u(x,y) = shx sin у bo'lsa, /(z) analitik funksiyani Gursa formulasi yordamida toping. u(x,y) = chx cos у bo'lsa, /(z) analitik funksiyani Gursa formulasi orqali toping. Agar u(x,y) = shx cosy bo'lsa, /(z) analitik funksiyani Gursa formulasi orqali toping. Agar u(x,y) = chx sin у bo'lsa, /(z) analitik funksiyani Gursa formulasi orqali toping. Markazi (0,0) nuqtada bo'lgan quyi yarim aylananing garmonik o'lchovini toping. Markazi (0,0) nuqtada bo'lgan yuqori yarim aylananing garmonik o'lchovini toping. Markazi (0,0) nuqtada bo'lgan ikkinchi chorak aylanasining garmonik o'lchovini toping. Markazi (0,0) nuqtada bo'lgan uchinchi chorak aylanasining garmonik o'lchovini toping. Markazi (0,0) nuqtada bo'lgan to'rtinchi chorak aylanasining garmonik o'lchovini toping. u'" +u' = f{x), x £ R s(x) £ C(R),f(x) = 0 agar |x| > const bo'lsa, tenglamaning xususiy yechimini toping. d.2 d A = —- — 2 1-1 operatoming fundamental yechimini toping. dx dx d2 d A = —- — 2 1-2 operatoming fundamental yechimini toping. dx dx 3u"(x) — u'(x) = 8(x),x £ R tenglamaning yechimini toping. и"(х) — 3и'(х) + 2и(х) = S(x) х Е R tenglama yechimini toping. Koeffitsientlari l2 fazo metrikasida taqribiy berilgan Fure qatorining jamlash masalasining korrekt emasligini isbotlang. dxt Au(x,y) = 0 u(x, 0) = f(x), —(x,0) = (pipe) masala yechimi korrekt emasligini isbotlang. Sohaning qismida berilgan analitik funksiyani butun sohaga davom ettirish masalasini korrekt emasligini isbotlang. Gravimetriya teskari masalasi yechimining korrekt emasligini isbotlang. Issiqlik tarqalishi tenglamasi uchun teskari vaqtli Koshi masalasini yechishning korrekt emasligini isbotlang. uxx Wyy 0 masalaning korrekt qo'yilmaganligini isbotlang. 36) utt = uxx tenglamaning xarakteristik to'rtburchakda berilgan Dirixle masalasini korrekt qo'yilmaganligini isbotlang. Ma'ruzalarni mustahkamlash uchun test savollari F(s) = /0°°e stf(t)dt Laplas almashtirishda originalni ко'rsating = X(-D 19 || 1| ~ ^ 31 \l, 0<(р<7Г 68 0, 123 1, 123 2,—<в<2п A 123 Agar fit) F(s), git) C(s) bo'lsa, Dyuamel integralini ko'rsating sF(s)G(s) -> fiO)git) + (/' * = flr(0)/(t) + Q7' * /) sFis)Gis) -> /(O)flf(t) sFis)Gis) = if'*g)it) sFis)Gis)^ig*f)it) - tasvirning originalini toping 1 t 1 - t t + 1 x(n) + a, x^-1) + ••• + anx = 1, x(0) = x'(0) + ••• + x(n-1}(0) = 0 masala echimi xt(t) bo'lsa, x^ + at + —I- anx = fit), x(0) = x'(0) = ••• = x(n-1)(0) = 0 masala echimi qanday aniqlanadi x(t) = Xl(t)f(0) + /0Сх{(т) ■ f(t - т)dx = т) ■ fit + r)dr x(t) = x(0)/'(t) + /0Сх1(т)/а - r)dt x(t) = x^t)/'(t) + /0Сх;(т)Г (t - T)dT *(t) = /0VW*i(t-T)dT f{t) = cost funksiyaning tasvirini toping s a. —— b. s2+l s s2-l s s2+ 4 s C' s2 + 2 /(t) = sint ning tasvirini toping l —— s2+1 s s2-l -f- s2+4 s C. —— s2 + 2 /(t) = sinlt originalning tasvirini toping 2 —— s2+4 1 s2 +1 -f- s2+l s C. —— s2+4 11. D sohada regulyar va analitik bo'lgan /(z) funksiya D da uzluksiz bo'lsa, u holda/(z) funksiyaning zeD dagi analitik davomini ko'rsating ь. с 1 12.Agar Z) markazi koordinata boshida bo'lib, radiusi birga teng bo'lsa, u holda yuqori yarim aylananing garmonik o'lchovini toping a)(z) = — Г —-—-dw v y 27Tj0 l—2rcos(w— 2 a)(z) = - f4 —-—-dbv 7TJU l-2rcos(4»-^)+rz C. 0)(z) = Г -dw v y J0 l-2rcos(v- 2 d. o)(z) = Гln —-— v y J0 l-2rcos(w-(o)+r2 13.Birlik aylana birinchi choragining garmonik o'lchovini toping
14.Birlik doirada Г1 f(z) < C, zeV1 да /(z) < s bo'lganda, analitik davom ettirish masalasi turg'unligini baholang |/(z)| < C1-^) ■ £"(z) |/(z)| < C1-^ \f{z)\<£^ \f(z)\ Download 391.68 Kb. Do'stlaringiz bilan baham: |
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