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10.2. Ãðàíèöÿ ³ íåïåðåðâí³ñòü ôóíêö³¿<br />
äâîõ çì³ííèõ............................................. 352<br />
10.2.1. Ãðàíèöÿ ôóíêö³¿ äâîõ çì³ííèõ .................. 352<br />
10.3. ×àñòèíí³ ïîõ³äí³ ........................................ 356<br />
10.3.1. ×àñòèíí³ ïîõ³äí³ ïåðøîãî ïîðÿäêó............. 356<br />
Âïðàâè .................................................................. 360<br />
10.3.2. Ïîõ³äí³ âèùèõ ïîðÿäê³â ............................ 360<br />
10.3.3. Ãåîìåòðè÷íèé òà åêîíîì³÷íèé çì³ñò<br />
÷àñòèííèõ ïîõ³äíèõ ................................... 362<br />
10.4. Äèôåðåíö³éîâí³ñòü ôóíêö³¿ ......................... 366<br />
10.4.1. Äèôåðåíö³éîâí³ñòü â òî÷ö³ ......................... 366<br />
10.4.2. Äèôåðåíö³àë ôóíêö³¿ .................................. 367<br />
10.4.3. Ïîõ³äíà çà íàïðÿìîì ................................. 368<br />
10.5. Ãðà䳺íò ôóíêö³¿ ....................................... 372<br />
10.5.1. Ïîíÿòòÿ ïðî ñêàëÿðí³ òà âåêòîðí³<br />
ïîëÿ .......................................................... 372<br />
10.5.2. Ãðà䳺íò ôóíêö³¿ ........................................ 373<br />
Âïðàâè .................................................................. 378<br />
10.6. Åêñòðåìàëüí³ çíà÷åííÿ ôóíêö³¿ áàãàòüîõ<br />
çì³ííèõ ..................................................... 378<br />
10.6.1. Åêñòðåìóì ôóíêö³¿ .................................... 378<br />
10.6.2. Íàéá³ëüø³ òà íàéìåíø³ çíà÷åííÿ<br />
ôóíêö³¿ ...................................................... 385<br />
Âïðàâè .................................................................. 388<br />
10.7. Óìîâíèé åêñòðåìóì .................................... 388<br />
10.7.1. Îñíîâí³ ïîíÿòòÿ ³ îçíà÷åííÿ...................... 388<br />
Âïðàâè .................................................................. 392<br />
10.8. Ïîíÿòòÿ ïðî åìï³ðè÷í³ ôîðìóëè ................ 392<br />
10.8.1. Ìåòîä íàéìåíøèõ êâàäðàò³â ó âèïàäêó<br />
ìîæëèâî¿ ë³í³éíî¿ çàëåæíîñò³ çì³ííèõ<br />
x òà y ....................................................... 396<br />
10.8.2. Ìåòîä íàéìåíøèõ êâàäðàò³â ìîæëèâî¿<br />
ñòåïåíåâî¿ çàëåæíîñò³ x òà y ................... 399<br />
ÒÅÌÀ 11. ÄÈÔÅÐÅÍÖ²ÀËÜͲ вÂÍßÍÍß<br />
11.1. Çàäà÷³ ïðèðîäîçíàâñòâà, ùî ïðèâîäÿòü<br />
äî äèôåðåíö³àëüíèõ ð³âíÿíü ....................... 402<br />
11.1.1. Íàéïðîñò³øà ìîäåëü íàêîïè÷åííÿ<br />
êàï³òàëó..................................................... 402<br />
11.1.2. Ïðî ðîçïàä ðàä³þ ...................................... 403<br />
11.1.3. Ïðî â³ëüíå ïàä³ííÿ ìàòåð³àëüíî¿<br />
òî÷êè ......................................................... 404<br />
11.2. Îcíîâí³ ïîíÿòòÿ òà îçíà÷åííÿ..................... 404<br />
11.2.1. Îçíà÷åííÿ .................................................. 404<br />
11.3. Ïðèêëàäè äèôåðåíö³àëüíèõ ð³âíÿíü, ðîçâ’ÿçêè<br />
ÿêèõ çíàõîäÿòüñÿ â ÿâíîìó âèãëÿä³<br />
çà äîïîìîãîþ åëåìåíòàðíèõ ïðèéîì³â<br />
......................................................... 405<br />
11.4. Äèôåðåíö³àëüí³ ð³âíÿííÿ ïåðøîãî ïîðÿäêó.<br />
Òåîðåìà Êîø³ ...................................... 409<br />
11.4.1. Ïîëå íàïðÿì³â (³çîêë³íè) ........................... 411<br />
11.4.2. Êëàñè íåë³í³éíèõ äèôåðåíö³àëüíèõ ð³âíÿíü<br />
ïåðøîãî ïîðÿäêó, ÿê³ ðîçâ’ÿçóþòüñÿ<br />
ó êâàäðàòóðàõ ............................................ 413<br />
Âïðàâè .................................................................. 416<br />
Âïðàâè .................................................................. 420<br />
11.5. ˳í³éí³ äèôåðåíö³àëüí³ ð³âíÿííÿ ïåðøîãî<br />
ïîðÿäêó ..................................................... 420<br />
11.5.1. Îçíà÷åííÿ .................................................. 420<br />
Âïðàâè .................................................................. 426<br />
11.6. ˳í³éí³ äèôåðåíö³àëüí³ ð³âíÿííÿ äðóãîãî<br />
ïîðÿäêó ..................................................... 427<br />
11.6.1. Îñíîâí³ ïîíÿòòÿ ³ îçíà÷åííÿ...................... 427<br />
11.6.2. ˳í³éí³ îäíîð³äí³ äèôåðåíö³àëüí³ ð³âíÿííÿ<br />
äðóãîãî ïîðÿäêó ................................... 428<br />
11.6.3. ˳í³éíî çàëåæí³ òà íåçàëåæí³ ôóíêö³¿<br />
íà ³íòåðâàë³ (a, b) ...................................... 429<br />
11.7. ˳í³éí³ äèôåðåíö³àëüí³ ð³âíÿííÿ äðóãîãî<br />
ïîðÿäêó ç³ ñòàëèìè êîåô³ö³ºíòàìè ............. 434<br />
11.7.1. Îäíîð³äí³ ð³âíÿííÿ .................................... 434<br />
Âïðàâè .................................................................. 436<br />
11.7.2. Íåîäíîð³äí³ ð³âíÿííÿ ................................. 437<br />
Âïðàâè .................................................................. 442<br />
11.8. Äèôåðåíö³àëüí³ ð³âíÿííÿ âèùèõ ïîðÿäê³â,<br />
ùî äîïóñêàþòü çíèæåííÿ ïîðÿäêó ....... 443<br />
11.8.1. гâíÿííÿ n-ãî ïîðÿäêó âèäó y (n) = f(x) ........ 443<br />
11.8.2. гâíÿííÿ äðóãîãî ïîðÿäêó.......................... 443<br />
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