ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ: Засвар хоорондын ялгаа
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| (13 завсрын хувилбар ижил хэрэглэгч харагдахгүй байна) | |||
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<div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'"> | <div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'"> | ||
'''ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ<sup>complex</sup> ᠲᠣᠭ ᠠ᠋''' ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠋ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ | '''ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ<sup>complex</sup> ᠲᠣᠭ ᠠ᠋''' ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠋ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ ᠥᠷᠭᠡᠵᠢᠭᠦᠯᠵᠦ᠂ <small><math>x ^ {2} + 1 = 0</math></small> ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠢ ᠰᠢᠢᠳᠦᠯ ᠲᠡᠢ ᠪᠣᠯᠭᠠᠭᠰᠠᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠶᠤᠮ᠃ | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ᠋ ᠢᠢ <span style="writing-mode: horizontal-tb;"><i>a + bi</i></span> ᠬᠡᠯᠪᠡᠷᠢ ᠪᠡᠷ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠡ ᠡᠭᠦᠨ ᠳᠦ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>a</i></span> ᠪᠣᠯᠤᠨ <span style="writing-mode: horizontal-tb;"><i>b</i></span> ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋᠂ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠨᠢ [[ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ]] | ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ᠋ ᠢᠢ <span style="writing-mode: horizontal-tb;"><i>a + bi</i></span> ᠬᠡᠯᠪᠡᠷᠢ ᠪᠡᠷ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠡ ᠡᠭᠦᠨ ᠳᠦ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>a</i></span> ᠪᠣᠯᠤᠨ <span style="writing-mode: horizontal-tb;"><i>b</i></span> ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋᠂ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠨᠢ [[ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ]] ᠪᠥᠭᠡᠳ <span style="writing-mode: horizontal-tb;"><i>i<sup>2</sup> = −1</i></span> ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠰᠢᠢᠳᠦᠯ ᠢ ᠬᠠᠩᠭᠤᠭᠰᠠᠨ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ | ||
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|[[File:Komplexe_zahlenebene.svg|thumb]] | |[[File:Komplexe_zahlenebene.svg|thumb]] | ||
|style = "height: 225px;"| | |style = "height: 225px;"|ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ᠢᠢ ᠲᠥᠯᠦᠭᠡᠯᠡᠵᠦ ᠪᠤᠶ ᠠᠷᠭᠠᠨ᠋ᠳ᠋ ᠤᠨ<sup>Argand</sup> ᠳᠢᠶᠠᠭ᠋ᠷᠠᠮ ᠳᠡᠭᠡᠷ ᠡ᠋ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ᠋ ᠢᠢ ᠸᠧᠺᠲ᠋ᠣᠷ<sup>vector</sup> ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠤᠶ ᠬᠣᠣᠰ ᠲᠣᠭ ᠠ᠋ ᠪᠠᠷ <span style="writing-mode: horizontal-tb;"><i>(a, b)</i></span> ᠳᠦᠷᠰᠦᠯᠡᠨ ᠦᠵᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨ ᠠ᠋᠃ | ||
ᠡᠭᠦᠨ ᠳ᠋ᠦ: <br><span style="writing-mode: horizontal-tb;"><i>Re</i></span> ᠢᠨᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩᠬᠡᠯᠢᠭ᠂ <br><span style="writing-mode: horizontal-tb;"><i>Im</i></span> ᠢᠨᠦ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠣᠯᠬᠤ ᠠᠭᠠᠳ <br><span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠢᠨᠦ <span style="writing-mode: horizontal-tb;"><i>i<sup>2</sup> = −1</i></span> ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠳ᠋ᠦ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠬᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠮᠥᠨ᠃ | ᠡᠭᠦᠨ ᠳ᠋ᠦ: <br><span style="writing-mode: horizontal-tb;"><i>Re</i></span> ᠢᠨᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩᠬᠡᠯᠢᠭ᠂ <br><span style="writing-mode: horizontal-tb;"><i>Im</i></span> ᠢᠨᠦ [[ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠊ᠠ᠋|ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ]] ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠣᠯᠬᠤ ᠠᠭᠠᠳ <br><span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠢᠨᠦ <span style="writing-mode: horizontal-tb;"><i>i<sup>2</sup> = −1</i></span> ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠳ᠋ᠦ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠬᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠮᠥᠨ᠃ | ||
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= ᠨᠡᠮᠡᠬᠦ = | = ᠨᠡᠮᠡᠬᠦ = | ||
ᠬᠣᠶᠠᠷ | ᠬᠣᠶᠠᠷ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠨᠡᠮᠡᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠦᠳ ᠢ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠨᠢ ᠨᠡᠮᠡᠵᠦ᠂ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ ᠦᠳ ᠢ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠨᠢ ᠨᠡᠮᠡᠨ ᠡ᠋᠃<ref name=":0">ᠰᠡᠷᠳᠠᠮᠪᠠ ᠪᠥᠬᠡᠪᠠᠲᠤ᠃ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠ᠃ Geogebra. https://www.geogebra.org/m/CwryWtd9?fbclid=IwAR0i1VN-HH5hegFJoWMjgCM9si7zH7x9hHDuEbU6iROuW3gbqIAeMGngvAs#material/nLiRDrsU ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/08/17</ref> | ||
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= ᠬᠠᠰᠤᠬᠤ = | = ᠬᠠᠰᠤᠬᠤ = | ||
ᠨᠢᠭᠡ | ᠨᠢᠭᠡ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠡᠴᠡ ᠨᠥᠭᠦᠭᠡ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠰᠠᠬᠤ ᠳ᠋ᠦ ᠪᠡᠨ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠪᠠ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ ᠦᠳ ᠢ ᠲᠤᠰ ᠪᠦᠷᠢ ᠬᠠᠰᠤᠶᠤ᠃<ref name=":0" /> | ||
| 50-р мөр: | 50-р мөр: | ||
= ᠦᠷᠡᠵᠢᠬᠦ = | = ᠦᠷᠡᠵᠢᠬᠦ = | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ᠦᠨ ᠰᠡᠯᠭᠦᠬᠦ (commutative)᠂ ᠪᠦᠯᠦᠭᠯᠡᠬᠦ (associatove)᠂ ᠵᠠᠳᠠᠯᠬᠤ (distributive) ᠴᠢᠨᠠᠷ ᠤᠳ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ ᠃<ref>''Виленкин Н. Я., Ивашов-Мусатов О. С., Шварцбурд С. И.'' Алгебра и математический анализ для 11 класса. Учебное пособие. — Изд. 6-е. — <abbr>М.</abbr>: Просвещение, 1998. — 288 с. — <nowiki>ISBN 5-09-008036-4</nowiki>.</ref> | |||
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|[[File:Complex_multi.svg|thumb]] | |[[File:Complex_multi.svg|thumb]] | ||
|style = "height: 225px;"|<span style="writing-mode: horizontal-tb;"><i>2 + i</i></span> ᠬᠡᠮᠡᠬᠦ ᠲᠣᠭ ᠠ᠋ ᠢᠢ (ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ) | |style = "height: 225px;"|<span style="writing-mode: horizontal-tb;"><i>2 + i</i></span> ᠬᠡᠮᠡᠬᠦ ᠲᠣᠭ ᠠ᠋ ᠢᠢ (ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ) <span style="writing-mode: horizontal-tb;"><i>3 + i</i></span> ᠬᠡᠮᠡᠬᠦ ᠲᠣᠭᠠᠨ ᠳᠤ (ᠤᠯᠠᠭᠠᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ) ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ᠢ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠢᠨᠦ᠃ | ||
ᠤᠯᠠᠭᠠᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠢ ᠡᠷᠭᠢᠭᠦᠯᠵᠦ ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠣᠷᠤᠶ ᠲᠠᠢ ᠲᠠᠭᠠᠷᠠᠭᠤᠯᠵᠤ᠂ <span style="writing-mode: horizontal-tb;"><i>√5</i></span> ᠢᠢᠠᠷ ᠰᠤᠩᠭᠠᠨ ᠠ᠋᠃ ᠡᠨᠡ ᠢᠨᠦ ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠾᠢᠫᠣᠲ᠋ᠧᠨᠦᠽ ᠤᠨ<sup>hypotenuse</sup> ᠤᠷᠲᠤ ᠪᠣᠯᠠᠢ᠃ | ᠤᠯᠠᠭᠠᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠢ ᠡᠷᠭᠢᠭᠦᠯᠵᠦ ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠣᠷᠤᠶ ᠲᠠᠢ ᠲᠠᠭᠠᠷᠠᠭᠤᠯᠵᠤ᠂ <span style="writing-mode: horizontal-tb;"><i>√5</i></span> ᠢᠢᠠᠷ ᠰᠤᠩᠭᠠᠨ ᠠ᠋᠃ ᠡᠨᠡ ᠢᠨᠦ ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠾᠢᠫᠣᠲ᠋ᠧᠨᠦᠽ ᠤᠨ<sup>hypotenuse</sup> ᠤᠷᠲᠤ ᠪᠣᠯᠠᠢ᠃ | ||
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| 66-р мөр: | 66-р мөр: | ||
= ᠬᠤᠪᠢᠶᠠᠬᠤ = | = ᠬᠤᠪᠢᠶᠠᠬᠤ = | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠳᠤ ᠬᠤᠪᠢᠶᠠᠬᠤ ᠦᠢᠯᠡᠳᠦᠯ ᠭᠦᠢᠴᠡᠳᠬᠡᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠬᠤᠪᠢᠶᠠᠭᠴᠢ ᠢᠢᠨ ᠬᠣᠣᠰᠮᠠᠭ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃ ᠬᠤᠪᠢᠶᠠᠷᠢ ᠢᠢᠨ ᠬᠣᠣᠰᠮᠠᠭ ᠢᠢᠠᠷ ᠬᠦᠷᠲᠡᠪᠦᠷᠢ ᠪᠠ ᠬᠤᠪᠢᠶᠠᠷᠢ ᠢᠢ ᠦᠷᠡᠵᠢᠭᠦᠯᠳᠡᠭ᠃ | |||
| 75-р мөр: | 75-р мөр: | ||
==ᠻᠸᠠᠲᠷᠠᠲ ᠵᠡᠷᠭᠡ== | ==ᠻᠸᠠᠲᠷᠠᠲ ᠵᠡᠷᠭᠡ== | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠻᠸᠠᠲᠷᠠᠲ<sup>quadrate</sup> ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠥᠪᠡᠷ ᠢ ᠢᠨᠦ ᠥᠪᠡᠷ ᠲᠦ ᠢᠨᠦ ᠦᠷᠡᠵᠢᠭᠦᠯᠦᠨᠡ᠋᠃<ref>Math is Fun. https://www.mathsisfun.com/algebra/complex-number-multiply.html ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/09 01</ref> | |||
| 82-р мөр: | 82-р мөр: | ||
==ᠻᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ== | ==ᠻᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ== | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ <span style="writing-mode: horizontal-tb;"><i>a + bi</i></span> <span style="writing-mode: horizontal-tb;"><i>(b ≠ 0)</i></span> ᠢᠢᠨ ᠻᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ ᠠᠨᠤ | |||
<math> \pm (\gamma + \delta i)</math> ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ | <math> \pm (\gamma + \delta i)</math> ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ | ||
<math>\gamma = \sqrt{\frac{a + \sqrt{a^2 + b^2}}{2}}</math> ᠪᠠ <math>\delta = (\sgn b)\sqrt{\frac{-a + \sqrt{a^2 + b^2}}{2}}</math> ᠪᠣᠯᠤᠮᠤᠢ᠃ | <math>\gamma = \sqrt{\frac{a + \sqrt{a^2 + b^2}}{2}}</math> ᠪᠠ <math>\delta = (\sgn b)\sqrt{\frac{-a + \sqrt{a^2 + b^2}}{2}}</math> ᠪᠣᠯᠤᠮᠤᠢ᠃ | ||
<span style="writing-mode: horizontal-tb;"><i>sgn b</i></span> ᠭᠡᠭᠴᠢ ᠢᠨᠦ <math>\sgn b = \begin{cases} \ \ 1, & b > 0 \\ \ \ 0, & b = 0 \\ -1, & b < 0 \end{cases}</math> ᠭᠡᠵᠦ ᠲᠠᠢᠢᠯᠠᠭᠳᠠᠨᠠ᠃ | <span style="writing-mode: horizontal-tb;"><i>sgn b</i></span> ᠭᠡᠭᠴᠢ ᠢᠨᠦ <math>\sgn b = \begin{cases} \ \ 1, & b > 0 \\ \ \ 0, & b = 0 \\ -1, & b < 0 \end{cases}</math> ᠭᠡᠵᠦ ᠲᠠᠢᠢᠯᠠᠭᠳᠠᠨᠠ᠃ | ||
ᠡᠭᠦᠨ ᠢ ᠪᠠᠲᠤᠯᠠᠬᠤ | ᠡᠭᠦᠨ ᠢ ᠪᠠᠲᠤᠯᠠᠬᠤ ᠢᠢᠨ ᠲᠤᠬᠠᠢᠢᠲᠠ ᠳ᠋ᠤ <math> \pm (\gamma + \delta i)</math> ᠲᠣᠭᠠ ᠢᠢ ᠻᠸᠠᠲᠷᠠᠲ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠵᠦ <span style="writing-mode: horizontal-tb;"><i>a + bi</i></span> ᠲᠣᠭᠠ ᠢᠢ ᠭᠠᠷᠭᠠᠵᠤ ᠢᠷᠡᠬᠦ ᠶᠣᠰᠤᠲᠠᠢ᠃ | ||
| 105-р мөр: | 105-р мөр: | ||
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ᠤᠨ<sup>Mandelbrot</sup> ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ᠳ᠋ᠤ ᠡᠭᠦᠰᠬᠡᠳᠡᠭ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠨ<sup>fractal</sup> ᠲᠦᠭᠡᠭᠡᠮᠡᠯ ᠵᠡᠰᠱᠢᠶ ᠡ᠋ ᠶᠤᠮ᠃ | ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ᠤᠨ<sup>Mandelbrot</sup> ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ᠳ᠋ᠤ ᠡᠭᠦᠰᠬᠡᠳᠡᠭ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠨ<sup>fractal</sup> ᠲᠦᠭᠡᠭᠡᠮᠡᠯ ᠵᠡᠰᠱᠢᠶ ᠡ᠋ ᠶᠤᠮ᠃ | ||
ᠡᠨᠡ ᠬᠦ ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;"><i>z = 0</i></span> ᠡᠴᠡ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠢᠲ᠋ᠧᠷᠠᠼ ᠬᠢᠬᠦ ᠳ᠋ᠦ <span style="writing-mode: horizontal-tb;"><i>f<sub>c</sub>(z)=z<sup>2</sup>+c</i></span> ᠹᠦᠨ᠍ᠻᠼ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠢᠢᠬᠤ ᠨᠥᠬᠦᠴᠡᠯ ᠪᠦᠬᠦᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠤ ᠣᠯᠠᠨᠯᠢᠬ ᠪᠠᠢᠢᠳᠠᠭ᠃ | ᠡᠨᠡ ᠬᠦ ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;"><i>z = 0</i></span> ᠡᠴᠡ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠢᠲ᠋ᠧᠷᠠᠼ<sup>iteration</sup> ᠬᠢᠬᠦ ᠳ᠋ᠦ <span style="writing-mode: horizontal-tb;"><i>f<sub>c</sub>(z)=z<sup>2</sup>+c</i></span> ᠹᠦᠨ᠍ᠻᠼ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠢᠢᠬᠤ ᠨᠥᠬᠦᠴᠡᠯ ᠪᠦᠬᠦᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠤ ᠣᠯᠠᠨᠯᠢᠬ ᠪᠠᠢᠢᠳᠠᠭ᠃ | ||
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ᠤᠨ | ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ᠤᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ ᠪᠠᠢᠢᠭᠠᠯᠢ ᠢᠢᠨ ᠭᠠᠢᠢᠬᠠᠮᠰᠢᠭᠲᠤ ᠳᠦᠷᠰᠦ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ᠦᠨ ᠰᠠᠢᠢᠬᠠᠨ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠶᠡᠷᠦ ᠪᠤᠰᠤ ᠢᠢᠨ ᠭᠣᠶᠤᠮᠰᠠᠭ ᠬᠣᠣᠰᠯᠠᠯ ᠢ ᠢᠯᠡᠷᠬᠡᠶ᠋ᠢᠯᠡᠳᠡᠭ᠃<ref>ᠷᠡᠨᠴᠡᠨ ᠦ ᠡᠩᠬᠡᠪᠠᠲᠤ᠃ '''ᠫᠢᠲ᠋ᠾᠠᠭᠣᠷ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌'''᠃ ᠮᠣᠩᠭᠤᠯ ᠤᠯᠤᠯᠰ ᠊ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ᠪᠠ ᠲᠣᠭᠠᠨ ᠲᠧᠻᠨᠣᠯᠣᠭᠢ ᠢᠢᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ https://imdt.ac.mn/c/1013874?content=1150891&fbclid=IwAR1HVqeXwT-h7dijj9EeIUzDvFustH99GAr9LHYQIU61XIByuBHCkSm10So 2020</ref> | ||
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ᠤᠨ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠨ ᠵᠠᠭᠠᠭ ᠢ ᠳᠠᠪᠠᠬᠤ ᠳᠤ ᠪᠠᠨ ᠵᠦᠯᠢᠶ ᠠ᠋ ᠢᠢᠨ<sup>Julia</sup> ᠹᠷᠠᠻᠲᠠᠯ ᠤᠳ ᠦᠷᠭᠡᠯᠵᠢ ᠬᠣᠯᠪᠤᠯᠲᠠ ᠪᠠᠨ ᠠᠯᠳᠠᠵᠤ᠂ ᠹᠠᠲᠣᠤ ᠢᠢᠨ<sup>Fatou</sup> ᠲᠣᠭᠤᠰᠤ ᠪᠣᠯᠤᠨ ᠬᠦᠪᠢᠷᠠᠳᠠᠭ᠃<ref>ᠨᠡᠭᠡᠭᠡᠯᠲᠡᠲᠡᠢ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠳ᠃ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠨ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠪᠠᠶ᠋ᠢᠳᠠᠯ᠃ ᠪᠢᠳᠡᠨ ᠦ ᠡᠷᠭᠢᠨ ᠲᠣᠭᠣᠷᠢᠨ ᠳ᠋ᠠᠬᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠬᠡᠷᠬᠢᠨ ᠠᠵᠢᠯᠯᠠᠳᠠᠭ ᠪᠤᠢ᠃ ᠹᠷᠠᠻᠲᠯᠠ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠶᠢᠨ ᠹᠷᠠᠻᠲᠯᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢ᠌ᠭ᠌᠃ https://ultrait.ru/mn/smartphones/otkrytie-fraktalov-beskonechnost-fraktalov-kak-ustroen-mir.html ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/10/02</ref> | ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ᠤᠨ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠨ ᠵᠠᠭᠠᠭ ᠢ ᠳᠠᠪᠠᠬᠤ ᠳᠤ ᠪᠠᠨ ᠵᠦᠯᠢᠶ ᠠ᠋ ᠢᠢᠨ<sup>Julia</sup> ᠹᠷᠠᠻᠲᠠᠯ ᠤᠳ ᠦᠷᠭᠡᠯᠵᠢ ᠬᠣᠯᠪᠤᠯᠲᠠ ᠪᠠᠨ ᠠᠯᠳᠠᠵᠤ᠂ ᠹᠠᠲᠣᠤ ᠢᠢᠨ<sup>Fatou</sup> ᠲᠣᠭᠤᠰᠤ ᠪᠣᠯᠤᠨ ᠬᠦᠪᠢᠷᠠᠳᠠᠭ᠃<ref>ᠨᠡᠭᠡᠭᠡᠯᠲᠡᠲᠡᠢ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠳ᠃ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠤᠨ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠪᠠᠶ᠋ᠢᠳᠠᠯ᠃ ᠪᠢᠳᠡᠨ ᠦ ᠡᠷᠭᠢᠨ ᠲᠣᠭᠣᠷᠢᠨ ᠳ᠋ᠠᠬᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠬᠡᠷᠬᠢᠨ ᠠᠵᠢᠯᠯᠠᠳᠠᠭ ᠪᠤᠢ᠃ ᠹᠷᠠᠻᠲᠯᠠ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠶᠢᠨ ᠹᠷᠠᠻᠲᠯᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢ᠌ᠭ᠌᠃ https://ultrait.ru/mn/smartphones/otkrytie-fraktalov-beskonechnost-fraktalov-kak-ustroen-mir.html ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/10/02</ref> | ||
| 120-р мөр: | 120-р мөр: | ||
== ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ == | == ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ == | ||
ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌<sup>quantum mechanics</sup> ᠠᠲ᠋ᠣᠮ ᠠᠴᠠ ᠵᠢᠵᠢᠭ ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮᠰ᠂ ᠶᠠᠭᠤᠨ ᠤ ᠡᠮᠦᠨᠡ ᠪᠣᠽᠣᠨ<sup>boson</sup> (ᠵᠢᠱᠢᠶᠡ ᠨᠢ ᠹᠣᠲ᠋ᠣᠨ<sup>photon</sup>ᠪᠠ ᠹᠧᠷᠮᠢᠣᠨ ᠤ<sup>fermion</sup> (ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠨᠧᠦᠲ᠋ᠷᠣᠨ) ᠬᠥᠳᠡᠯᠭᠡᠭᠡᠨ᠂ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠦᠢᠯᠡᠴᠢᠯᠡᠯ ᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ | [[Квант механик|ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌]]<sup>quantum mechanics</sup> ᠠᠲ᠋ᠣᠮ ᠠᠴᠠ ᠵᠢᠵᠢᠭ ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮᠰ᠂ ᠶᠠᠭᠤᠨ ᠤ ᠡᠮᠦᠨᠡ ᠪᠣᠽᠣᠨ<sup>boson</sup> (ᠵᠢᠱᠢᠶᠡ ᠨᠢ ᠹᠣᠲ᠋ᠣᠨ<sup>photon</sup> ᠪᠠ ᠹᠧᠷᠮᠢᠣᠨ ᠤ<sup>fermion</sup> (ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠨᠧᠦᠲ᠋ᠷᠣᠨ) ᠬᠥᠳᠡᠯᠭᠡᠭᠡᠨ᠂ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠦᠢᠯᠡᠴᠢᠯᠡᠯ ᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ | ||
ᠴᠢᠩᠭᠢᠬᠦ ᠳᠦ ᠪᠡᠨ ᠲᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠦᠢᠯᠡ ᠬᠥᠳᠡᠯᠦᠯ ᠦᠨ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢᠭ᠌ ᠲᠣᠳᠣᠷᠬᠠᠶ᠋ᠢᠯᠠᠯᠲᠠ ᠶᠢ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠤᠳᠬᠠ ᠪᠠᠷ ᠭᠠᠷᠭᠠᠳᠠᠭ᠃ | |||
ᠴᠤᠬᠤᠮ ᠳᠠᠭᠠᠨ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠤᠨ ᠦᠨᠳᠦᠰᠦ ᠰᠠᠭᠤᠷᠢ ᠪᠣᠯᠳᠠᠭ᠃ | |||
ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠲᠤ ᠱᠷᠥ᠋ᠲᠢᠩᠧᠷ ᠤᠨ <sup>Schrödinger</sup> ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠠᠴᠢ ᠬᠣᠯᠪᠣᠭᠳᠠᠯ ᠨᠢ ᠰᠣᠩᠭᠣᠳᠠᠭ ᠹᠢᠽᠢᠻ ᠳ᠋ᠡᠬᠢ ᠨᠧᠧᠲ᠋ᠣᠨ᠍ ᠤ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠬᠠᠤᠯᠢ ᠶᠢᠨ ᠠᠳᠠᠯᠢ ᠶᠤᠮ᠃ | |||
ᠠᠯᠢ ᠠᠯᠢ ᠨᠢ ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠶ᠋ᠢᠷᠢᠯᠠᠯ᠂ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢ <sup>impuls</sup> ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠯᠠᠨ ᠲᠣᠳᠣᠷᠬᠠᠶ᠋ᠢᠯᠠᠳᠠᠭ᠃ | |||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠼ ᠢ<sup>function</sup> ᠢᠯᠡᠷᠬᠡᠶ᠋ᠢᠯᠡᠬᠦ ᠳᠦ ᠲᠣᠬᠢᠷᠠᠮᠵᠢ ᠲᠠᠢ ᠤᠴᠢᠷ ᠠᠴᠠ ᠹᠢᠽᠢᠻ ᠦᠨ ᠡᠨᠡ ᠰᠠᠯᠪᠤᠷᠢ ᠳᠤ ᠵᠠᠶ᠋ᠢᠯᠠᠰᠢ ᠦᠭᠡᠢ ᠱᠠᠭᠠᠷᠳᠠᠯᠭᠠ ᠲᠠᠢ ᠶᠤᠮ᠃ | |||
ᠴᠠᠭᠠᠰᠢᠯᠠᠪᠠᠯ᠂ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠤᠨ ᠰᠢᠭᠤᠳ ᠨᠥᠯᠥᠭᠡ ᠪᠡᠷ ᠬᠢᠮᠢ ᠶᠢᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠬᠥᠭᠵᠢᠯ ᠡᠷᠴᠢᠮᠵᠢᠭᠰᠡᠨ᠃ | |||
1927 ᠣᠨ ᠳᠤ ᠸᠠᠯᠲ᠋ᠧᠷ ᠾᠠᠢᠢᠲ᠋ᠯᠧᠷ<sup>Walter Heitler</sup> ᠂ ᠹᠷᠢᠼ ᠯᠣᠨ᠍ᠳᠣᠨ<sup>Fritz London</sup> ᠨᠠᠷ ᠸᠠᠯᠧᠨ᠍ᠲ ᠤᠨ<sup>valency</sup> ᠬᠣᠯᠪᠣᠭᠠᠰᠤ ᠶᠢᠨ ᠣᠨᠣᠯ ᠢ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃ | |||
ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠤᠨ ᠨᠢᠭᠡ ᠭᠣᠣᠯ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠪᠣᠯ ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮᠰ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠼ ᠢ ᠤᠯᠬᠤ ᠶᠠᠪᠤᠳᠠᠯ ᠶᠤᠮ᠃ | |||
ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠼ ᠭᠡᠳᠡᠭ ᠨᠢ ᠲᠣᠳᠣᠷᠬᠠᠢ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠵᠤᠷᠪᠤᠰ ᠲᠤ ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠶ᠋ᠢᠵᠤ ᠪᠣᠯᠬᠤ ᠪᠠᠶ᠋ᠢᠷᠢᠰᠢᠯ ᠤᠳ ᠤᠨ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠲᠠᠷᠬᠠᠯᠲᠠ ᠶᠤᠮ᠄ | |||
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<small><math>\frac{-\hbar}{2m}\frac{\partial^2\Psi(x,t)}{\partial x^2} + V(x,t)\Psi(x,t) = i\hbar\frac{\partial \Psi(x,t)}{\partial t}</math></small> | |||
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ᠻᠢᠨᠧᠲᠢᠭ<sup>kinetic</sup> ᠧᠨᠧᠷᠭᠢ<sup>energy</sup> | |||
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ᠫᠣᠲ᠋ᠧᠨ᠍ᠼᠢᠶᠠᠯ<sup>potencial</sup> ᠧᠨᠧᠷᠭᠢ | |||
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ᠨᠡᠢᠢᠲᠡ ᠧᠨᠧᠷᠭᠢ | |||
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ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠼ ᠲᠦ ᠰᠢᠲᠦᠭᠰᠡᠨ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠤᠨ ᠰᠠᠭᠤᠷᠢ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠨᠢᠭᠡ ᠪᠣᠯ ᠳᠡᠭᠡᠷᠡ ᠳᠤᠷᠠᠳᠤᠭᠰᠠᠨ ᠱᠷᠥ᠋ᠲᠢᠩᠧᠷ ᠤᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠶᠤᠮ᠃ | |||
ᠡᠨᠡᠬᠦ ᠲᠣᠮᠢᠶᠠ ᠶᠢ ᠠᠰᠢᠭᠯᠠᠭᠰᠠᠨ ᠢᠶ᠋ᠠᠷ ᠤᠰᠤ ᠲᠥᠷᠦᠭᠴᠢ ᠶᠢᠨ ᠮᠣᠯᠧᠻᠤᠯ<sup>molecule</sup> ᠳᠠᠬᠢ ᠬᠣᠶᠠᠷ ᠠᠲ᠋ᠣᠮ ᠨᠢ ᠻᠣᠸᠠᠯᠧᠨ᠍ᠲ<sup>covalent</sup> ᠬᠣᠯᠪᠣᠭᠠ ᠭᠡᠳᠡᠭ ᠢ ᠡᠭᠦᠰᠬᠡᠨ ᠧᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠨᠤᠭᠤᠳ ᠢᠢᠠᠨ ᠬᠤᠪᠢᠶᠠᠯᠴᠠᠵᠤ ᠪᠠᠶ᠋ᠢᠳᠠᠭ ᠢ ᠪᠠᠲᠤᠯᠠᠭᠰᠠᠨ᠃<ref>Josiah Wu. Real Life Applications of Complex Numbers. 2020 https://issuu.com/harrowhongkong/docs/final_scientific_harrovian_issue_vi-i/s/11488755</ref> | |||
== ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠢᠢᠨ ᠣᠨᠤᠯ == | |||
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|style = "height: 340px;"|ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠢᠢᠨ ᠲᠣᠭᠲᠠᠯᠴᠠᠭᠠᠨ ᠤ ᠡᠩ ᠦᠨ ᠪᠦᠳᠦᠭᠦᠪᠴᠢ᠃ <br><br><span style="writing-mode: horizontal-tb;"><i>X(s)</i></span> ᠣᠷᠤᠯᠲᠠ ᠢᠢᠨ ᠮᠡᠳᠡᠭᠡᠯᠡᠯ᠂ <br><br><span style="writing-mode: horizontal-tb;"><i>Y(s)</i></span> ᠭᠠᠷᠤᠯᠲᠠ ᠢᠢᠨ ᠮᠡᠳᠡᠭᠡᠯᠡᠯ᠂ <br><br><span style="writing-mode: horizontal-tb;"><i>G(s)</i></span> ᠤᠷᠤᠭᠰᠢ ᠳᠠᠮᠵᠢᠭᠤᠯᠬᠤ ᠹᠦᠨ᠍ᠻᠼ<sup>function</sup>᠂ <br><br><span style="writing-mode: horizontal-tb;"><i>H(s)</i></span> ᠡᠷᠭᠢᠬᠦ ᠬᠣᠯᠪᠤᠭᠠ | |||
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ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠶᠢ ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠶᠢᠨ ᠣᠨᠣᠯ᠂ ᠢᠯᠠᠩᠭᠤᠶᠠ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠶ᠋ᠢᠳᠠᠯ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠭᠡᠨ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠳᠡᠭ᠃ | |||
ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠶᠢᠨ ᠣᠨᠣᠯ ᠳᠤ 《ᠰᠢᠰᠲ᠋ᠧᠮ》 ᠭᠡᠳᠡᠭ ᠦᠭᠡ ᠶᠢ ᠲᠦᠭᠡᠭᠡᠮᠡᠯ ᠠᠰᠢᠭᠯᠠᠳᠠᠭ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠵᠠᠪᠠᠯ ᠴᠠᠬᠢᠯᠭᠠᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠢ ᠬᠡᠯᠡᠳᠡᠭ ᠦᠭᠡᠢ᠃ | |||
ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠡᠭᠦᠨ ᠢ ᠬᠥᠷᠥᠩᠭᠡ ᠶᠢᠨ ᠵᠠᠬᠠ ᠵᠡᠭᠡᠯᠢ ᠳ᠋ᠡᠬᠢ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ᠂ ᠬᠢᠮᠢ ᠶᠢᠨ ᠤᠷᠪᠠᠯ᠂ ᠦᠢᠯᠡ ᠶᠠᠪᠤᠴᠠ ᠶᠢ ᠰᠤᠳᠤᠯᠬᠤ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠵᠦ ᠪᠣᠯᠤᠨᠠ᠃ | |||
ᠲᠡᠭᠦᠨᠴᠢᠯᠡᠨ ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠶᠢᠨ ᠣᠨᠣᠯ ᠢ ᠷᠣᠪᠣᠲ ᠤᠨ ᠲᠧᠻᠨᠣᠯᠣᠭᠢ ᠳᠤ<sup>technology</sup> ᠥᠷᠭᠡᠨ ᠠᠰᠢᠭᠯᠠᠳᠠᠭ ᠲᠤᠯᠠ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠠᠨᠠᠯᠢᠽ ᠴᠤ ᠪᠠᠰᠠ ᠲᠡᠭᠦᠨ ᠳᠦ ᠬᠡᠷᠡᠭᠯᠡᠭᠳᠡᠨᠡ ᠭᠡᠰᠡᠨ ᠦᠭᠡ᠃<ref>Ujjvala Y. Gawarguru, Mitali K. Tibdewal, Rajashri A. Naphade, Rahul M. Jethwani. The Review of Introduction & Application of Complex Number in Engineering. 2nd National Conference Recent Innovations in Science and Engineering (NC-RISE 17). Volume: 5 Issue: 9. pp55 – 57. ISSN: 2321-8169. https://ijritcc.org/download/conferences/NC-RISE_17/Track_6_(ASH)/1506931102_02-10-2017.pdf</ref> | |||
ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠶᠢᠨ ᠣᠨᠣᠯ ᠳᠤ ᠵᠠᠷᠢᠮ ᠳᠤ ᠪᠠᠨ ᠯᠠᠫ᠊ᠯᠠᠰ ᠤᠨ<sup>Laplace</sup> ᠬᠤᠪᠢᠷᠠᠭᠠᠯᠲᠠ ᠶᠢ ᠠᠰᠢᠭᠯᠠᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠳ ᠢ<sup>system</sup> ᠴᠠᠭ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠮᠤᠵᠢ ᠠᠴᠠ ᠳᠠᠪᠲᠠᠮᠵᠢ ᠶᠢᠨ ᠮᠤᠵᠢ ᠳᠤ ᠰᠢᠯᠵᠢᠭᠦᠯᠳᠡᠭ᠃ | |||
ᠳᠠᠷᠠᠭᠠ ᠨᠢ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠲᠡᠭ ᠪᠠ ᠲᠤᠶ᠋ᠢᠯ ᠤᠳ ᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠤ ᠰᠢᠨᠵᠢᠯᠡᠨᠡ᠃ | |||
ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠮᠥᠷ ᠦᠨ (root locus) ᠠᠷᠭᠠ ᠪᠠᠷ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠳᠦ ᠲᠡᠭ ᠪᠠ ᠲᠤᠶ᠋ᠢᠯ ᠤᠳ ᠵᠡᠭᠦᠨ ᠬᠠᠭᠠᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠤ ᠪᠠᠶ᠋ᠢᠨᠠ ᠤᠤ᠂ ᠡᠰᠡᠪᠡᠯ ᠪᠠᠷᠠᠭᠤᠨ ᠬᠠᠭᠠᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠤ ᠪᠠᠶ᠋ᠢᠨᠠ ᠤᠤ ᠭᠡᠳᠡᠭ ᠨᠢ ᠴᠢᠬᠤᠯᠠ᠃ | |||
ᠥᠭᠡᠷᠡ ᠪᠡᠷ ᠬᠡᠯᠡᠪᠡᠯ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠨᠢ ᠲᠡᠭ ᠡᠴᠡ ᠶᠡᠬᠡ ᠪᠠᠢᠢᠨᠠ ᠤᠤ ᠡᠰᠡᠪᠡᠯ ᠪᠠᠭᠠ ᠪᠠᠶ᠋ᠢᠨᠠ ᠤᠤ ᠭᠡᠳᠡᠭ ᠨᠢ ᠴᠢᠬᠤᠯᠠ ᠶᠤᠮ᠃ | |||
ᠴᠠᠭ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠬᠤᠪᠢᠷᠠᠯᠲᠠ ᠦᠭᠡᠢ ᠱᠤᠭᠤᠮᠠᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠨᠢ᠄ | |||
- ᠪᠠᠷᠠᠭᠤᠨ ᠬᠠᠭᠠᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠤ ᠲᠤᠶ᠋ᠢᠯ ᠲᠠᠢ ᠪᠣᠯ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠦᠭᠡᠢ ᠪᠠᠶ᠋ᠢᠨᠠ᠂ | |||
- ᠵᠡᠭᠦᠨ ᠬᠠᠭᠠᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠤ ᠪᠦᠬᠦ ᠲᠤᠶ᠋ᠢᠯ ᠨᠢ ᠪᠠᠶ᠋ᠢᠪᠠᠯ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠶ᠋ᠢᠨᠠ᠂ | |||
- ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠲᠤᠶ᠋ᠢᠯ ᠲᠠᠢ ᠪᠣᠯ ᠶᠠᠯᠢ ᠦᠭᠡᠶ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠶ᠋ᠢᠨᠠ᠃ | |||
==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ - complex number - комплексное число | |||
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ - imaginary unit - мнимая единица | |||
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭᠠ - imaginary number - чисто мнимое число | |||
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ - imaginaty part - мнимая часть | |||
ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠ - real number - действительное число | |||
ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ - real part - действительная часть | |||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ - complex plane - комлексная плоскость | |||
ᠲᠡᠩᠬᠡᠯᠢᠭ - axis - ось | |||
ᠣᠯᠠᠨᠯᠢᠭ - set - множество | |||
ᠡᠶᠡᠷᠭᠦ - positive - положительный | |||
ᠰᠥᠷᠭᠦ - negative - отрицательный | |||
ᠲᠡᠭᠰᠢᠳᠬᠡᠯ - equation - уравнение | |||
ᠲᠣᠮᠢᠶ ᠠ᠋ - formula - формула | |||
ᠡᠷᠭᠢᠯᠲᠡ - rotation - поворот | |||
ᠮᠠᠭᠠᠳᠯᠠᠯ - probability - вероятность | |||
ᠬᠡᠮ - degree - градус | |||
ᠤᠳᠤᠷᠢᠳᠤᠯᠭᠠ ᠢᠢᠨ ᠣᠨᠤᠯ - control theory - теория управления | |||
ᠠᠲ᠋ᠣᠮ - atom - атом | |||
ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮ - elementary particle - элементарная частица | |||
ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠼ - wave function - волновая функция | |||
ᠳᠠᠪᠲᠠᠮᠵᠢ - frequency - частота | |||
ᠹᠷᠠᠻᠲ᠋ᠠᠯ - fractal - фрактал | |||
ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ - quantum mechanics - квантовая механика | |||
ᠰᠣᠩᠭᠣᠳᠠᠭ ᠹᠢᠽᠢᠻ - classical physics - классическая физика | |||
==ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ== | ==ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ== | ||
<div style="writing-mode: horizontal-tb; "><References/> | |||
[[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]] | |||