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Differensial tenglamalar

DT13409 · 4-semester · 60530500 Physics · 2024 intake

Credits
6
Total hours
180
Contact hours
72
Type
Compulsory
Block
Majburiy fanlar
Final assessment
Imtihon

Hours breakdown

  • Lecture36 h
  • Practical36 h
  • Independent study108 h

Topics · 51

Lecture · 36 h

  1. 1.Differensial tenglamalar faniga kirish. Oddiy differensial tenglamalar nazariyasining asosiy tushunchalari.2
  2. 2.Integral egri chiziqlar. Vektor maydon. Trayektoriya. Oddiy differensial tenglamalar orqali ifodalanuvchi ayrim fizik va geometrik masalalalar.2
  3. 3.Bir jinsli differensial tenglamalar. Bir jinsliga keltiriladigan differensial tenglamalar.2
  4. 4.Birinchi tartibli chiziqli differensial tenglamalar. Chiziqli differensial tenglamalar.2
  5. 5.Bernulli va Rikkati tenglamalari.2
  6. 6.To‘la differensial tenglamalar.2
  7. 7.Integrallovchi ko‘paytuvchi.2
  8. 8.Yechim va umumiy yechim tushunchasi. Koshi masalasi. Koshi masalasi yechimining mavjudligi va yagonaligi.2
  9. 9.n darajali birinchi tartibli chiziqli differensial tenglamalar va ularning umumiy xossalari. Maxsus yechimlar.2
  10. 10.Lagranj va Klero tenglamalari.2
  11. 11.Tartibi pasayadigan tenglamalar. Ketma-ket integrallash usuli.2
  12. 12.Noma’lum funksiya va uning hosilalariga nisbatan bir jinsli differensial tenglamalar. Umumlashgan bir jinsli differensial tenglamalar.2
  13. 13.O‘zgarmas koeffitsientli chiziqli bir jinsli differensial tenglamalar (Yuqori tartibli differensial tenglamada).2
  14. 14.O‘zgarmas koeffitsientli chiziqli bir jinsli bo‘lmagan tenglamalar (Yuqori tartibli differensial tenglamada). O‘zgarmasni variatsiyalash usuli.2
  15. 15.O‘zgarmas koeffitsientliga keltiriladigan tenglamalar. Eyler tenglamasi.2
  16. 16.O‘zgaruvchi koeffitsientli chiziqli differensial tenglamalar. Ostrogradskiy- Liuvill formulasi. Abel formulasi. Chegaraviy masalalar.2
  17. 17.O‘zgarmas koeffitsientli bir jinsli chiziqli sistemalar. Noma’lumlarni yo‘qotish usuli. O‘zgarmas koeffitsientli bir jinsli bo‘lmagan chiziqli sistemalar. Aniqmas koeffitsienlar usuli.2
  18. 18.Birinchi tartibli xususiy hosilali differensial tenglamalarning umumiy yechimini topish. Koshi masalasi.2

Practical · 36 h

  1. 1.Differensial tenglamalar faniga kirish. Oddiy differensial tenglamalar nazariyasining asosiy tushunchalari.2
  2. 2.O‘zgaruvchilari ajralgan differensial tenglamalar. O‘zgaruvchilari ajralgan differensial tenglamalarga keltiriladigan differensial tenglamalar2
  3. 3.Oʻzgaruvchilari ajralgan differensial tenglamalar. Oʻzgaruvchilari ajralgan differensial tenglamalarga keltiriladigan differensial tenglamalar.2
  4. 4.Bir jinsli differensial tenglamalar. Bir jinsliga keltiriladigan differensial tenglamalar.2
  5. 5.Chiziqli differensial tenglamalar.2
  6. 6.Bernulli tenglamasi.2
  7. 7.Rikkati tenglamasi.2
  8. 8.To‘la differensial tenglamalar.2
  9. 9.Integrallovchi ko‘paytuvchi.2
  10. 10.Yechim va umumiy yechim tushunchasi. Koshi masalasi. Koshi masalasi yechimining mavjudligi va yagonaligi.2
  11. 11.n darajali birinchi tartibli chiziqli differensial tenglamalar va ularning umumiy xossalari. Maxsus yechimlar.2
  12. 12.Lagranj tenglamasi. Klero tenglamasi.2
  13. 13.Tartibi pasayadigan tenglamalar. Ketma-ket integrallash usuli. Noma’lum funksiya va uning hosilalariga nisbatan bir jinsli differensial tenglamalar.2
  14. 14.O‘zgarmas koeffitsientli chiziqli bir jinsli differensial tenglamalar (Yuqori tartibli differensial tenglamada).2
  15. 15.O‘zgarmas koeffitsientli chiziqli bir jinsli bo‘lmagan tenglamalar (Yuqori tartibli differensial tenglamada). O‘zgarmasni variatsiyalash usuli. Eyler tenglamasi.2
  16. 16.O‘zgaruvchi koeffitsientli chiziqli differensial tenglamalar. Ostrogradskiy- Liuvill formulasi. Abel formulasi. Chegaraviy masalalar.2
  17. 17.O‘zgarmas koeffitsientli bir jinsli chiziqli sistemalar. Noma’lumlarni yo‘qotish usuli. O‘zgarmas koeffitsientli bir jinsli bo‘lmagan chiziqli sistemalar.2
  18. 18.Birinchi tartibli xususiy hosilali differensial tenglamalarning umumiy yechimini topish. Koshi masalasi.2

Independent study · 108 h

  1. 1.Differensial tenglamalar faniga kirish.8
  2. 2.Integral egri chiziqlar.8
  3. 3.O‘zgaruvchilari ajralgan va unga keltiriladigan differensial tenglamalar.8
  4. 4.To‘la differensial tenglamalar8
  5. 5.Birinchi tartibli tenglama uchun Koshi masalasi.8
  6. 6.Yechimning mavjudligi haqida teorema8
  7. 7.Yuqori tartibli tenglamalarning tartibini pasaytirish.8
  8. 8.O‘zgaruvchilarga nisbatan bir jinsli differensial tenglamalar8
  9. 9.Yuqori tartibli chiziqli differensial tenglamalar8
  10. 10.Bir jinsli bo‘lmagan chiziqli tenglamalar6
  11. 11.Bir jinsli bo‘lmagan o‘zgarmas koeffitsientli chiziqli differensial tenglamalar va ularning xususiy yechimlarini topish usullari6
  12. 12.Chiziqli differensial tenglamalar sistemasi.6
  13. 13.Ostragradskiy-Luivill formulasi6
  14. 14.Chiziqli bir jinsli bo‘lmagan tenglamalar sistemasi.6
  15. 15.Koshi masalasi6

Assessment (max score)

  • Final exam 5
  • Total 5
  • Midterm 1 5
  • Midterm 2 5

Source: HEMIS. Titles as in HEMIS (in Uzbek). Reading list and grading criteria are in the department's approved syllabus.

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