O`zbekiston respublikasi aloqa, axborotlashtirish va telekommunikatsiya texnologiyalari davlat ko`mitasi
Yüklə 462,91 Kb.
|
solve(cos(x)=-sqrt(2)/2,x);3 p - 3 p _B1~ + 2 p _Z2~ 4 2 Misol 2.sin 2x cos x sin x2 tenglamaning [0;2] kesmada nechta ildizi bor? Maple dasturida yechish:_EnvAllSolutions:=true:solve(sin(2*x)=(cos(x)-sin(x))^2);1 p + p _Z3~, 5 12 12 p + p _Z3~ Transendent tenglamalarni yechishTransendent tenglamani yechishda, yechim aniq ko`rinishda bo`lishi uchun solve buyrug’idan avval _EnvExplicit:=true buyrug’ini ifodalash kerak. eq:={ 7*3^x-3*2^(z+y-x+2)=15, 2*3^(x+1)+3*2^(z+y-x)=66, ln(x+y+z)-3*ln(x)-ln(y*z)=-ln(4) }:_EnvExplicit:=true:s:=solve(eq,{x,y,z}):simplify(s[1]);simplify(s[2]);{x=2, y=3, z=1}, {x=2, y=1, z=3} Quyida keltirilgan ko’rsatkichli tenglama va tengsizliklarning yechimi Maple muhitida topilgan. Misol 1. Tenglamani yeching. 4x4 0,5 Maple dasturida yechish:eq:={4^(x-4)=0.5};eq := {4 (x - 4) = 0.5} _EnvExplicit:=true:s:=solve(eq,{x});s := {x = 3.500000000} Javob: x = 3,5 Misol 2. Tenglamani yeching. 3.5x-5 4 2 49 Maple dasturida yechish:eq:={3.5^(x-5)=(4/49)^2};eq : 3.5 ( x5) 16 _EnvExplicit:=true:s:=solve(eq,{x});2401 s := {x = 1.000000000} Javob: x = 1 Misol 3. Tenglamaning ildizi 10 dan qancha kam? Maple dasturida yechish:eq:={3^(x+1)*27^(x-1)=9^7};3x1 27x1 97 eq := {3 (x + 1) 27 (x - 1) = 4782969} _EnvExplicit:=true:s:=solve(eq,{x});s := {x = 4} assign(s); simplify(10-x);6Javob: 6
Misol 4. Tenglamani yeching. Maple dasturida yechish:22 x1 4 x1 8x1 64 eq:={(2^(2*x-1)*4^(x+1))/8^(x-1)=64};22 x1 4 x1 eq : 8x1 64 _EnvExplicit:=true:s:=solve(eq,{x});Javob: x = 2 s := {x = 2} Misol 5.ex 7ex 8 tenglamaning ildizlari yig’indisini toping. Maple dasturida yechish:eq:={exp(x)+7*exp(-x)=8};eq := {e x + 7 e (-x) = 8} _EnvExplicit:=true:s:=solve(eq,{x});Javob: x = ln 7 s := {x = ln(7)}, {x = 0} Misol 6.4x1 2x4 3 2x2 48 0 tenglamani yeching. Maple dasturida yechish:eq:={4^(x+1)-2^(x+4)+3*(2^(x+2))+48=0}; eq := {4 (x + 1) - 2 (x + 4) + 3 2 (x + 2) + 48 = 0} _EnvExplicit:=true: 2 2 s:=solve(eq,{x}); 2 2 ln 1 1 I 47 ln 1 1 I 47 s : x ln(2) , x ln(2) Turli ko’rinish va xarakterdagi tenglamalarni yechimini topishda INPAKX paketidadan foydalanib bajarish mumkin. Bizga interval sonlardan iborat bo’lgan sonlar berilsa, ular ustida ham har qanday arifmetik amallarni bevosita Maple dasturi tarkibida ishlovchi INPAKX paketi yordamida amalga oshirish mumkin. Maple dasturida interval arifmetik amallarni hisoblashda Inpakx paketi ishga tushirilib, so’ngra interval sonlar ustida amallar bajarish mumkin. Inpakx paketini ishga tushirish quyidagicha: restart;libname:="d:\\Maple\\Maple 9.5\\intpakX\\lib", libname;libname := "d:\Maple\Maple 9.5\intpakX\lib" , "d:\Maple\Maple 9.5\intpakX\lib" , "C:\Program Files\Maple 9.5/lib" with(intpakX);[&*, &**, &+, &-, &/, &Convex_Hull, &arccos, &arcsin, &arctan, &cabs, &cadd, &cdiv, &cdiv_opt, &cmult, &cmult_opt, &cos, &cosh, &csub, &exp, &intersect, &intpower, &ln, &sin, &sinh, &sqr, &sqrt, &tan, &tanh, &union, Evalf, Interval_Integerpower, Interval_Round_Down, Interval_Round_Up, Interval_add, Interval_arccos, Interval_arcsin, Interval_arctan, Interval_cos, Interval_cosh, Interval_divide, Interval_exp, Interval_hyp_rd, Interval_hyp_ru, Interval_intersect, Interval_ln, Interval_midpoint, Interval_option_zero, Interval_power, Interval_range_values, Interval_reciprocal, Interval_scale, Interval_sin, Interval_sinh, Interval_sqr, Interval_sqrt, Interval_subtract, Interval_tan, Interval_tanh, Interval_times, Interval_trig_rd, Interval_trig_ru, Interval_ulp, Interval_union, Interval_width, addinfinity, centred_form_eval, cexp, cni_range3d, complex_disc_plo,t complex_polynom_plot, compute_all_zeros, compute_all_zeros_with_plo,t compute_combined_range, compute_mean_value_range, compute_monotonic_range, compute_naive_interval_range, compute_range, compute_range3d, compute_taylor_form_range, construct, expinfinity, ext_int_div, horner_eval_cent, horner_eval_opt, ilog10, infinityln, init, interval_list_plo,t interval_list_plot3d, intpakX_greater, intpakX_ilog10, intpakX_max, intpakX_min, inv, is_in, max, max_abs_error, mid, midpoint, min, newton, newton_plot, newton_with_plot, powerinfinity, rd, rel_diam, ru, sqrinfinity, sqrtinfinity, subdivide_adaptive, subdivide_equi3d, subdivide_equidistan,t subtractinfinity, timesinfinity, ulp, width, x0_start] Quyida Inpakx paketida interval sonlar ustida interval arifmetik amallarning bajarilishi keltirilgan. A:=[2.,4.]; B:=[4.,5.];A := [2., 4.] B := [4., 5.] A &+ B;[5.999999999, 9.000000001] A &- B;[-3.000000001, 0.] A &* B;[7.999999999, 20.00000001] A &/ B;[0.3999999997, 1.000000001] is_in (A,B);false is_in (4.5,B);true K:=[1.,5.];K := [1., 5.] A &+ B &/ K;[1.199999998, 9.000000011] A &+ (B &/ K);[2.799999999, 9.000000007] Koeffitsiyentlari interval sonlardan iborat bo’lgan chiziqli tenglama quyidagi usulda yechiladi: C:=[1.,2.]; F:=[5.,7.];C := [1., 2.] F := [5., 7.] C * X = F;[1., 2.] [2.499999999, 7.000000008] = [5., 7.] X:=F &/ C;X := [2.499999999, 7.000000008] Koeffitsiyentlari interval sonlardan iborat bo’lgan kvadrat tenglama quyidagi usulda bajariladi: Misol 1.A:=[4.,5.]; B:=[14.,22.]; C:=[9.,9.]; A * X^2 + B * X + C =0;A := [4., 5.] B := [14., 22.] C := [9., 9.] [4., 5.] X 2 + [14., 22.] X + [9., 9.] = 0 disc:=(B &**2) &- (4 &* A &* C); positiveINT:=[0., infinity]; nepositiveINT:=[-infinity,0.];disc := [15.99999969, 340.0000004] positiveINT := [0., ¥ ] nepositiveINT := [-¥ , 0.] if is_in(disc, positiveINT) then X1:=(([-1.,-1.] &* B) &+ ((disc) &**(1/2))) &/ (2 &* A);X2:=(([-1.,-1.] &* B) &- ((disc) &**(1/2))) &/ (2 &* A);elif is_in(disc, nepositiveINT) then print("Yechimga ega emas");else X1:=(([-1.,-1.] &* B) &/ ([2.,2.] &* A)); print("Bitta yechimga ega"); end if;X1 := [-2.250000010, 0.5548861182] X2 := [-5.054886124, -1.799999991] Misol 2.A:=[1.,3.]; B:=[3.,6.]; C:=[4.,7.]; A * X^2 + B * X + C =0;A := [1., 3.] B := [3., 6.] C := [4., 7.] [1., 3.] X 2 + [3., 6.] X + [4., 7.] = 0 disc:=(B &**2) &- ([4.,4.] &* A &* C); positiveINT:=[0., infinity]; nepositiveINT:=[-infinity,0.];disc := [-75.00000009, 20.00000003] positiveINT := [0., ¥ ] nepositiveINT := [-¥ , 0.] if is_in(disc, positiveINT) then X1:=(([-1.,-1.] &* B) &+ ((disc) &**(1/2))) &/ (2 &* A);X2:=(([-1.,-1.] &* B) &- ((disc) &**(1/2))) &/ (2 &* A);elif (is_in(disc, nepositiveINT)) then print("Yechimga ega emas"); else X1:=(([-1.,-1.] &* B) &/ ([2.,2.] &* A)); end if;X1 := [-3.000000003, -0.4999999992] Xulosa.Hozirgi vaqtda kompyuterlarda ilmiy-texnikaviy hisoblashlarni bajarishda odatdagi dasturlash tillaridan va elektron jadvallaridan emas, balki Mathematica, MatLab, Maple, Gauss, Reduse, Eureka va boshqa turdagi maxsus matematik dasturlar keng qo’llanilyapti. Maple dasturining Inpakx yordamida turli kasb egalari o’z sohasi bo’yicha masalalarni hal etishi va kerakli grafiklarni, diagrammalarni olishi mumkin. Bu dastur imkoniyatlaridan kelib chiqib, uni tayyor paket deyish mumkin. Maple yuqori interfeysga ega bo’lib, turli matematik va texnik masalani tez yechish, ularning grafiklarini qurish va animatsiya effektlaridan foydalanish inkonini beradi. Maple tizimida masalalarni sonli yechish bilan bir qatorda analitik usulda yechish hisobga olinadi. Ushbu bitiruv malakaviy ishida Maple tizimining interfeysi, Maple tizimining funksiya va buyruqlari, Maple tizimida analitik hisoblashlarni bajarish, turli ko’rinish va xarakterdagi tenglamalarni Inpakx paketida yechish usullari, ya’ni tenglamalar va tenglamalar sistemasini yechish, tengsizliklar va tengsizliklar sistemasini yechish, trigonometrik va transendent tenglamalarni yechish kabi usullar haqida to’liq ma’lumot berilgan bo’lib, bu usullardan Maple tizimida hal etish misollar orqali tushuntirilgan. Shuning uchun, foydalanuvchilar bu dasturdan o’zlari yecha olmagan matematik masalalar uchun tayanch yechim ombori sifatida foydalanishlari mumkin. Shuningdek, differensial tenglamalarni yechish, statistika, termodinamika, boshqaruv nazariyasi kabi jarayonlarni geometrik tasvirlash va animatsiyalar orqali ijro etishni yuqori darajada amalga oshirish mumkin. Bu tizimdan tabiiy fanlar bo’yicha elektron darsliklar yaratishda asos dasturiy vosita sifatida foydalanishni tavsiya etish mumkin. Bularning barchasi o’quvchida ijodiy, mantiqiy va mustaqil fikrlashni rivojlanishiga, hamda yangi ob’ektlarni har tomonlama o’rganish va shu asosda o’zining mulohazalarini izhor etish imkonini beradi. Ushbu bitiruv malakaviy ishida yoritilgan tushunchalardan, taklif etilgan usullardan va yechilgan masalalardan aniq fanlarni o’qitishda, ilmiy tadqiqot va muhandislik ishlarini bajarishda foydalanish mumkin. Foydalanilgan adabiyotlar:I.A.Karimov Yangicha fikrlash va ishlash davr talabi. 5 tom.T. “O`zbekiston” 1997 y. D`yakonov V.P. Maple 6: uchebniy kurs. SPb.: Piter, 2001. Aloyev R.D Fan, texnika va ta`limda informatsion texnologiyalar. Buxoro, 2002 y. Fizika, matematika va informatika ilmiy-uslubiy jurnal. 4-son, T. 2003 y. Govoruxin V.N., Tsibulin V.G. Vvedenie v Maple V. Matematicheskiy paket dlya vsex. M.: Mir, 1997. Proxorov G.V., Ledenev M.A., Kolbeev V.V. Paket simvol`nix vichisleniy Maple V. M.: Petit, 1997. WWW.exponenta.ru internet sayti. G.N.Berman “Sbornik zadach po kursu matematicheskogo analiza” M. “Nauka” 1971 y. Zavarkin V.M. Jitomirskiy V.G. Lapchik M.P. Chislennie metodi M. “Prosveщenie” 1991 y. Xolmatov T.X. Tayloqov N.I. Nazarov U.A. Informatika va hisoblash texnikasi. “O’zbekiston milliy ensiklopediyasi” Davlat ilmiy nashriyoti, T. 2001 y . N.Pils, V.Slivina “Mathcad 2000” (Moskva, “Finans’ I statistika” 2000yil) Abduqodirov A.A., Fozilov F.I. Umurzaqov T.N. Hisoblash matematikasi va programmalash. Toshkent. O`qituvchi. 1989 y. D`yakonov V.P. Maple 6: uchebniy kurs. SPb.: Piter, 2001. D`yakonov V.P. Matematicheskaya sistema Maple V R3/R4/R5. M.: Solon, 1998. Manzon B.M. Maple V Power Edition. M.: Filin`, 1998. Govoruxin V.N., Tsibulin V.G. Vvedenie v Maple V. Matematicheskiy paket dlya vsex. M.: Mir, 1997. Proxorov G.V., Ledenev M.A., Kolbeev V.V. Paket simvol`nix vichisleniy Maple V. M.: Petit, 1997. Bugrov Ya.S., Nikol`skiy S.M. Elementi lineynoy algebri i analiticheskoy geometrii. M.: Nauka. 1989. Yüklə 462,91 Kb. Dostları ilə paylaş:
|