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35International journal of theoretical and practical research
Scientific Journal
Year: 2022 Issue: 1 Volume: 2 Published: 31.01.2022
http://alferganus.uz
Citation :
Mirzamakhmudova, N. T. (2022). Some methodological features of teaching the subject «Higher mathematics» in higher educational institutions. SJ International journal of theoretical and practical research, 2 (1), 186-192.
Mirzamaxmudova, N. T. (2022). Oliy talim muassasalarida "Oliy matematika" fanini oqitishning ayrim uslubiy xususiyatlari. Nazariy va amaliy tadqiqotlar xalqaro jurnali, 2 (1), 186-192.
Doi: https://dx.doi.org/10.5281/zenodo.6091655
DOI 10.5281/zenodo .60916 55
ISSN 2181-2357 T. 2. №1. 2022
ISJIF 2021:5.5
QR-Article
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Mirzamaxmudova Nilufar Tadjibayevna
katta o'qituvchi Farg'onapolitexnika instituti
UDC 372.8:51
OLIY TALIM MUASSASALARIDA "OLIY MATEMATIKA" FANINI OQITISHNING AYRIM USLUBIY XUSUSIYATLARI
Annotatsiya: Ushbu maqolada tayyorlanayotgan mutaxassisni zamon talablariga muvofiq o^qitish, bu jarayonda matematik model qurish, yechimni olishda zamonaviy texnologiyalardan foydalanish kabi masalalar ko^rib chiqilgan. Ishlab chiqarishda yuqori- samarali texnologiyalarni qollanilishning o^sishiprofessor-o^qituvchilar oldiga professional kompetentlikka ega, raqobatbardosh mutaxassislarni tayyorlash vazifasini qo^yadi. Masalalarni yechishda matematik modelni qurish mexanizmi, matematik apparatni qollay olish, olingan natijalarni tahlil qilish, yechimni olishda Maple dastur tizimidan foydalanish ko^rib chiqilgan.
Kalit so'zlar: Transport masalasi, sikl, potensiallar metodi, minimal element usul, tayanch yechim, Maple dastur tizimi, ta'lim sifati, Krivoshin-shatun mexanizmi, tezlik, egilish, differensial tenglama.
Mirzamakhmudova Nilufar Tadjibayevna
senior lecturer Fergana Polytechnic Institute
SOME METHODOLOGICAL FEATURES OF TEACHING THE SUBJECT «HIGHER MATHEMATICS» IN HIGHER EDUCATIONAL INSTITUTIONS
Abstract: This article discusses the training of modern specialists who meet modern requirements, the ability to build a mathematical model in the process, the use of modern technologies in obtaining solutions. The growth in the use of highly efficient technologies in production sets the task for teachers to prepare professionally competent, competitive specialists. The mechanism of constructing a mathematical model in solving problems,
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the use of the mathematical apparatus, the analysis of the results obtained, the use of the Maple software in solving the problem are considered.
Keywords: Transport problem, cycle, potential method, minimum element method, basic solution, Maple software package, learning quality, crank mechanism, speed, bending, and differential equation.
Мирзамахмудова Нилуфар Таджибаевна
старший преподаватель Ферганский политехнический институт
НЕКОТОРЫЕ МЕТОДИЧЕСКИЕ ОСОБЕННОСТИ ПРЕПОДАВАНИЯ ПРЕДМЕТА «ВЫСШАЯ МАТЕМАТИКА» В ВЫСШИХ ОБРАЗОВАТЕЛЬНЫХ УЧРЕЖДЕНИЯХ
Аннотация: В данной статье рассматривается подготовка современных специалистов, которые соответствуют к современным требованиям, умение построение математической модели в процессе, использование современных технологий при получении решений. Рост использования высокоэффективных технологий в производстве ставит перед педагогами задачу подготовки профессионально грамотных, конкурентоспособных специалистов. Рассмотрены механизм построения математической модели при решении задач, использование математического аппарата, анализ полученных результатов, использование программного обеспечения Maple при решении задачи.
Ключевые слова: Транспортная задача, цикл, потенциальный метод, метод минимального элемента, базовое решение, программный комплекс Maple, качество обучения, кривошипный механизм, скорость, изгиб, дифференциальное уравнение.
Tayyorlanayotgan mutaxassisni professional kompetentligi amaliy masalalarni yechishda matematik apparatni, informatsion texnologiyalarni qollay olish malakasiga bogliq. Oliy talimda kredit- modul tizimiga otish "Oliy matematika" fanidan maruza, amaliy mashgulotlarni kamaytirish, talabalarni mustaqil ishlash konikmalarini hosil qilishga asoslanadi.
Talabani ananaviy oqitib qolmasdan, mustaqil ishlashga jalb qilish asosida uni kelgusi amaliyotda informatsion texnologiyani qollab, yechimlar olish malakasini hosil qilish kerak.
"Oliy matematika" fani texnika yonalishidagi OTM larda birinchi va ikkinchi kursda o qitilishi sababli, o quv jarayonida maktabdagi ta lim davrida olgan bilim darajasiga qarab olib boriladi.
Talim sifati va effektivligi o'qitish jarayonida va mustaqil talimda yangi informatsion texnologiyalarni qo'llash, talim metodikasini intensifikatsiya qilishni taqozo etadi. Bu esa talabani nazariy va amaliy masalalar yecha oladigan, matematik apparatni mustaqil qo llaydigan va informatsion texnologiya asosida yechim olish malakasiga ega bo'lishini talab etadi.
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ISSN 2181-2357 T. 2. №1. 2022
Ushbu maqolada masalalarni yechishda Maple dastur tizimidan foydalanish uslubiyoti korib chiqilgan.
1-misol. Quyidagi transport masalasini korib chiqaylik.
1-jadval
30 10 20 40
35 1 3 2 4
50 2 1 4 3
15 3 5 6 1
Bu yerda a -yetkazib beruvchi, b. - iste'molchi. Berilganlarga kora masalaning matematik modelini quramiz.
m n
Ia=2>,
i—1 j—1
xii x12 xi3 x14 1 ( 1 3 2 41
x — x21 x22 x23 x24 С — 2 1 4 3
V x3i x32 x33 x34 V 3 5 6 1,
z (x) — x^ ^ + + I 4x^ I 2x2-^ I x^^ + I 3x24 I I 5x^2 I I x-^11 I ^12 I x^ 3 I ^14 — 35
34
X21 + X22 + X23 + X24 — 50
x^ I x^21 x^ I x^4 — 15 xn I x211 x31 — 30
x12 + x22 + x32 — 10
x^ I x^ I — 20
xi4 ^ x24 ^ x34 — 40
Masalani minimal element metodi yordamida yechsak, quyidagi natijaga ega bolamiz.
2-jadval
30 10 20 40
188
N =m +n -
1=3+4-1=6
Transport masalasini potensiallar metodi bilan yechamiz.
3-jadval
1 30 3 2 5 4 u = 0 1
2 1 10 4 15 3 25 u= 2 2
3 5 6 1 15 u =0 3
v =1 1 V = -1 2 v = 2 3 v =1 4
35 1 30 3 2 5 4
50 2 1 10 4 15 3 25
15 3 5 6 1 15
A12 = Ul +V2 -C12 = -4 Al4 = Ul +V4 -Cl4 = -3 A21 = U2 +V1 -C21 = 1 A31 = U3 +vi -C31 = -2 A32 = U3 +V2 -C32 = -6 A33 = U3 +V3-C33 = -4
A21>0
4-jadval
30 10 20 40
35 1 15 3 2 20 4
50 2 15 1 10 4 3 25
15 3 5 6 1 15
189
> with(simplex) : standardize({xll + xl2 + xl3 + xl4 = 35, x21 + x22 + x23 + x24 = 50, x31
+ x32 + x33 + x34 = 15,xll + x21 + x31 = 30, xl2 + x22 + x32 = 10, xl3 + x23 + x33 = 20,xl4 + x24 + x34 = 40});
{ -xll - x21 - x31 < -30,xll + x21 + x31 < 30, -xl2 - x22 -x32<-10, jc 12 + x22 + x32 < 10, -xl3 - x23 - x33 < -20, xl3 + x23 + x33 < 20, -xl4 - x24 - x34 < -40, xl4 + x24 + x34 < 40, -xll - xl2 - xl3 - xl4 < -35, xll + xl2 + xl3 + xl4 < 35, -x21 - x22 - x23 - x24 < -50, x21 + x22 + x23 + x24 < 50, -x31 - x32 - x33 — x34 < -15,x31 + x32 + x33 + x34 < 15}
>
with(simplex) : minimize(xll + 3-xl2 + 2-xl3 + 4-xl4 + 2-x21 + x22 + 4-x23 + 3-x24 + 3 ■x31 +5-x32 + 6 ■x33 + x34, { -xll - x21 - x31 < -30, xll + x21 + x31 < 30, -xl2 - x22 — x32 < -10,xl2 + x22 + x32 < 10, -xl3 - x23 - x33 < -20, xl3 + x23 + x33 < 20, -jc14 - x24 - x34 < -40,xl4 + x24 + x34 < 40, -xll - xl2 - xl3 - xl4 < -35, xll + xl2 + xl3 + xl4 < 35, -x21 - x22 - x23 - x24 < -50, x21 + x22 + x23 + x24 < 50, -x31 - x32 - x33 - x34 < -15, x31 + x32 + x33 + x34 < 15}, NONNEGA TIVE);
{xll = 15, xl2 = 0, xl3 = 20, xl4 = 0, x21 = 15, x22 = 10, x23 = 0, x24 = 25, x31 = 0, x32 = 0, x33 = Q,x34= 15}
>
+ 6 ■x33 + x34, [xll = 15, xl2 = 0, xl3 = 20, xl4 = 0, x21 = 15, x22 = 10, x23 = 0, x24 = 25, x31 = 0, x32 = 0, x33 = 0, x34 = 15 ]);
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2- misol.
Krivoshin- shatun mexanizmi berilgan. Uning aylanma chastotasi o'zgarishi co ga teng. Polzunning vaqtga bogliq tezligini toping.
Krivoshin
shatun
Polzunning harakatini organamiz. Buning uchun uning matematik modelini tuzamiz. Krivoshinning burilish burchagi vaqtga bog' liq bo' lib, <p(t) = ct ga teng.
Ma'lumki, koordinata boshida polzungacha bo'lgan masofa
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ß( ' ) =
arceos.
1 -
sin (p( t ))
V
Li
x (t )= L0 cos (p(t))+ L sinß(t)) Bu holda
v ( t ) = ^ v} dt
ISSN 2181-2357 T. 2. №1. 2022
2
> restart',
> f~ omega-1;
> betta ■■= arccos
M'-(^f)
f~ cot
betta := arccos
L&ún{(üty
LI2
> x{t) ■= L0-cos{f) + Ll-sin(betta);
x := t—>L0cos(f) + LI sin {betta)
> Diff(x(t),t)=diff(x(t),t);
t
T» I \ , T, ^sinícoí)2
LO cos( cot) +L1 -\—'—
J LI
= -ZOsin(ooi) co +
L02 sin(ö)f) cos(coi) ©
LI
L& sin(co¿)^
L1A
Bu ko rinishdagi uslubiyot bilan professional talimda matematik apparatni informatsion texnologiya bilan integratsiyasi malakasi hosil qilinadi.
Foydalanilgan adabiyotlar ro'yxati:
1. Abdurazakov, A., Makhmudova, N., & Mirzamakhmudova, N. (2021). On one method for solving degenerating parabolic systems by the direct line method with an appendix in the theory of filration.
2. Abdurazakov, A., Mirzamahmudova, N., Maxmudova, N. (2021). "Iqtisod" yo'nalishi mutaxassislarini tayyorlashda matematika fanini o'qitish uslubiyoti. Scientific progress. 7. URL: https://cyberleninka.ru/article/n7iqtisod-yo-nalishi-mutaxassislarini-tayyorlashda-matematika-fanini-o-qitish-uslubiyoti
3. Aybek, T., & Fozilov, A. (2021). Current Issues of Training Qualified Personnel. Central Asian Journal Of Innovations On Tourism Management And Finance, 2(11), 20-24.
4. Mirzamahmudova, N., Maxmudova, Nazarova, G. (2021). Matematik masalalarni yechishdagi ba'zi bir muammolar va ularni hal qilishda mantiqiy fikrlashning ahamiyati. Scientific progress. 7. URL: https://cyberleninka.ru/article/n/matematik-masalalarni-yechishdagi-ba-zi-bir-muammolar-va-ularni-hal-qilishda-mantiqiy-fikrlashning-ahamiyati
5. Nishonov, F. M., Ehsonova, N. T., & Tolibov, I. S. (2019). Professional growth of the teacher of mathematics of the academic lyceum in the conditions of technologies of the digital educational space. ISJ Theoretical & Applied Science, 03 (71), 534-537. Soi:
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http://s-o-i.Org/1.1/TAS-03-71-52 Doi: https://dx.doi.org/10.15863/TAS.2019.03.71.52
6. Nishonov, F. M., Shaev, A. K., (2021). Some questions of the organization of individual works of students in mathematics in the conditions of credit training. ISJ Theoretical & Applied Science, 04 (96), 1-7. Soi: http://s-o-i.org/1.1/TAS-04-96-1 Doi: https://dx.doi.org/10.15863/TAS.2021.04.96.1
7. Nishonov, F.M., and all. (2018). Some questions of design of tasks in mathematics. ISJ Theoretical & Applied Science, 09 (65): 41-44. Doi: https://dx.doi.org/10.15863/TAS.2018.09.65.7
8. Абдуразаков, А., Махмудова, Н. А., & Мирзамахмудова, Н. Т. (2021). Численное решение краевых задач для вырождающихся уравнений параболического типа, имеющих приложения в фильтрации газа в гидродинамических невзаимосвязанных пластах. Universum: технические науки, (10-1 (91)), 14-17.
9. Абдуразаков, А., Махмудова, Н., & Мирзамахмудова, Н. (2019). Решения многоточечной краевой задачи фильтрации газа в многослойных пластах с учетом релаксации. Universum: технические науки, (11-1 (68)), 6-8.
10. Qosimova, M. Y., Yusupova, N. X., & Qosimova, S. T. (2021). On the uniqueness of the solution of a two-point second boundary value problem for a second-order simple differential equation solved by the bernoulli equation. ACADEMICIA: An International Multidisciplinary Research Journal, 11(9), 969-973.
11. Fayzullayev, J. I. (2020). Mathematical competence development method for students through solving the vibration problem with a maple system. Scientific bulletin of Namangan state university, 2(8), 353-358.
12. Fayzullayev, J. I. (2021). Fundamental fanlar yordamida texnika oliy ta'lim muassasalari talabalarining kasbiy kompetentligini rivojlantirish. Oriental renaissance: Innovative, educational, natural and social sciences, 1(10), 454-461.
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