Stoks va Gauss-Ostrogradskiy formulalari.
bo`lib, bo`lakli silliq egri chiziq va ning tekisligiga proyeksiyasi bo`lsin.
Faraz qilaylik, (S) sirtda uzluksiz ![](data:image/png;base64,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) funksiyalar aniqlangan bo`lib, bu funksiyalarning barcha birinchi tartibli xususiy hosilalari (S) sirtda uzluksiz bo`lsin.
Teorema. (Stoks). Agar yuqoridagi shartlar bajarilsa, u holda ushbu
Stoks formulasio`rinli bo`ladi.
Shunday qilib, Stoks formulasi (S) sirt bo`yicha olingan 2-tur sirt integrali bilan shu sirtning chegarasi bo`yicha olingan egri chiziqli integralni bog`lovchi formuladir.
8. Kompleks sonlarning moduli va argumenti. Kompleks sonlar ustida amallar. Kompleks sonning trigonometrik va koʻrsatkichli shakli.
Ta`rif: kompleks son deb ma`lum bir tartibda berilgan bir juft va haqiqiy sonlarga aytiladi va quyidagicha yoziladi: .
Yoki ko`rinishidagi songa ham kompleks son deyilib, bu kompleks sonning algebraik ko`rinishi deyiladi. Bunda va haqiqiy sonlar mos ravishda kompleks sonning haqiqiy va mavhum qismi deb yuritiladi va quyidagicha simvol bilan belgilanadi: , (Realis va Imaginarius – lotincha so`zlar bo`lib, haqiqiy va mavhum demakdir)
Ushbu va ko`rinishidagi sonlar o`zaro qo`shma kompleks sonlar deyiladi. – mavhum birlik bo`lib, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAARCAIAAAA61ZnRAAABJUlEQVR4nGP5//8/A70AC91swmLZ/v37Hz9+bG1traysTHPLtLW1bW1tq6urOzs7aWWZnZ3doUOHgAwxMbHbt2+bmJhQYijQhLCwsPPnz2O3DGITEPz48ePMmTORkZFk23Tq1Km5c+devHgRUwo9GGtra5mZmYFJNCoqijzLzMBg9uzZ2C1zc3NjYmLasWMHkN3d3Y2pSFFR8eHDh3CuuLj48+fPyXAHyLLS0lJ4MGIF9+/fJ8No7JadPn3a1NSUPP1onpaWlgbmHAKWJSYmEm8icjCS5GmoZTk5OWvXrsWliCQT16xZU1xcDGTIy8v39va2tbWdO3cOYdmTJ0+IN4sgCAEDCPvu3bufPn2CS9G2bAwPD1+xYgWdLAOWD8jcAS31aQoAjjp49sC5JPUAAAAASUVORK5CYII=) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAARCAIAAAA3y+mWAAABGklEQVR4nGP5//8/A+0BCx3swGLN/v37X758aWhoqK6uTkNrdHR07O3tq6qqOjo6qG+NnZ3doUOHgAxRUdHu7m5XV1eyTYQbhcUauAQwRZSWllZWVjo7O5NnDaYdDJiBtmDBAmlpaXl5efLswAVA1ri5uTExMe3YsQPITkhI+PXrF1AEWZGiouLDhw/hXHFx8efPn2M1DtkodGuAoQT3KSMjIzs7O5qi+/fvE+lqZKPQrTl9+rSpqSmRBiEDNF8CQzszMxOrUVBrEhMTiTcOHmiYvgwMDMRqFNSanJyctWvX4rKG+EBDNsrIyOjcuXMIa548eUKkKQQB3Ki7d+9++vQJLk6rMi08PHzFihU0t+bMmTPI3AEqoWkEAMsXdkSEASwGAAAAAElFTkSuQmCC) Shuning uchun: , , ,
Kompleks sonlar ustida amallar
Agar α=a+ib va β=c+id kompleks sonlar berilgan bo`lsa:
Qo`shish va ayirish.
α±β=(a+ib)±(c+id)=(a±c)+i(b±d)
Ko`paytirish va bo`lish
Agar va o`zaro qo`shma sonlar berilgan bo`lsa: ,
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