Ãëàâíàÿ      Ó÷åáíèêè - Ðàçíûå     Ëåêöèè (ðàçíûå) - ÷àñòü 50

 

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ÍÀÕÎÆÄÅÍÈÅ ÂÑÅÕ ÄÅÉÑÒÂÈÒÅËÜÍÛÕ ÊÎÐÍÅÉ ÀËÃÅÁÐÀÈ×ÅÑÊÎÃÎ ÌÍÎÃÎ×ËÅÍÀ ÌÅÒÎÄÎÌ ÄÅËÅÍÈß ÎÒÐÅÇÊÀ ÏÎÏÎËÀÌ (ÁÈÑÅÊÖÈÈ) È ÌÅÒÎÄÎÌ ÕÎÐÄ È ÊÀÑÀÒÅËÜÍÛÕ Ñ ÓÊÀÇÀÍÍÎÉ ÒÎ×ÍÎÑÒÜÞ È Ó×ÅÒÎÌ ÂÎÇÌÎÆÍÎÉ ÊÐÀÒÍÎÑÒÈ ÊÎÐÍÅÉ

 

             

ÍÀÕÎÆÄÅÍÈÅ ÂÑÅÕ ÄÅÉÑÒÂÈÒÅËÜÍÛÕ ÊÎÐÍÅÉ ÀËÃÅÁÐÀÈ×ÅÑÊÎÃÎ ÌÍÎÃÎ×ËÅÍÀ ÌÅÒÎÄÎÌ ÄÅËÅÍÈß ÎÒÐÅÇÊÀ ÏÎÏÎËÀÌ (ÁÈÑÅÊÖÈÈ) È ÌÅÒÎÄÎÌ ÕÎÐÄ È ÊÀÑÀÒÅËÜÍÛÕ Ñ ÓÊÀÇÀÍÍÎÉ ÒÎ×ÍÎÑÒÜÞ È Ó×ÅÒÎÌ ÂÎÇÌÎÆÍÎÉ ÊÐÀÒÍÎÑÒÈ ÊÎÐÍÅÉ

ÍÀÕÎÆÄÅÍÈÅ ÂÑÅÕ ÄÅÉÑÒÂÈÒÅËÜÍÛÕ ÊÎÐÍÅÉ ÀËÃÅÁÐÀÈ×ÅÑÊÎÃÎ ÌÍÎÃÎ×ËÅÍÀ ÌÅÒÎÄÎÌ ÄÅËÅÍÈß ÎÒÐÅÇÊÀ ÏÎÏÎËÀÌ (ÁÈÑÅÊÖÈÈ) È ÌÅÒÎÄÎÌ ÕÎÐÄ È ÊÀÑÀÒÅËÜÍÛÕ Ñ ÓÊÀÇÀÍÍÎÉ ÒÎ×ÍÎÑÒÜÞ È Ó×ÅÒÎÌ ÂÎÇÌÎÆÍÎÉ ÊÐÀÒÍÎÑÒÈ ÊÎÐÍÅÉ

Ôåäåðàë�E�E ÀâèàöèîûL�E Ñ�Eæá�EÐúBñè�E/b>

ÌÎÑÊÎÂÑÊÈÉ ÃÎÑÓÄÀÐÑÒÂÅÍÍÛÉ ÒÅÕÍÈ×ÅÑÊÈÉ ÓÍÈÂÅÐÑÈÒÅÒ ÃÐÀÆÄÀÍÑÊÎÉ ÀÂÈÀÖÈÈ

Êàôåäðà �Eèê�EäíüH �Eòå�Eòè�E

çàùèùåúü

�EúGåí�E�E_________________.

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ÐóêüAüCèòåë�E/b>

äîöåûQ, �E�E�EËóêèí�EÎ. Ï.

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ÍÀÕÎÆÄÅÍÈÅ ÂÑÅÕ ÄÅÉÑÒÂÈÒÅËÜÍÛÕ ÊÎÐÍÅÉ ÀËÃÅÁÐÀÈ×ÅÑÊÎÃÎ ÌÍÎÃÎ×ËÅÍÀ ÌÅÒÎÄÎÌ ÄÅËÅÍÈß ÎÒÐÅÇÊÀ ÏÎÏÎËÀÌ (ÁÈÑÅÊÖÈÈ) È ÌÅÒÎÄÎÌ ÕÎÐÄ È ÊÀÑÀÒÅËÜÍÛÕ Ñ ÓÊÀÇÀÍÍÎÉ ÒÎ×ÍÎÑÒÜÞ È Ó×ÅÒÎÌ ÂÎÇÌÎÆÍÎÉ ÊÐÀÒÍÎÑÒÈ ÊÎÐÍÅÉ

(Ï�Eñíèòåë�E�E çà�Eñê�E�E �EðñüAüH ðàáîòå �E äèñöèï�EûD «×èñ�EûLûå �Eòîäû»)

ÐàáúCó âû�E�Eèë�E/b>

ñòóäåíòû 5-ãî �Eðñ�E/b>

ñïåöèà�EûMñò�E 01.02

ÊüF�E�E Ñåðãå�EÀ�E�EàíäðüAè÷

/ÊüF�E�E Ñ.À./------------------------.

Ñåìåí÷èõè�E Â�Eäè�E�EÂ�Eäè�Eðîâè�E/b>

/Ñåìåí÷èõè�E Â.Â./------------------------.

28.X/1999 ãîäà.

ÌÎÑÊÂÀ - 1999

ÀÍÍÎÒÀÖÈß

 äàûLüH �EðñüAüH ðàáîòå ðàññ�Eòðåí �Eèíöè�Eúüõîæäåí�E �Eðíåé àëãåáðàè÷åñêüB�E�EüBúH�Eúü ñëåä�Eùè�E ÷èñëåíûZ�E �Eòîäà�E: �Eòî�Eáèñå�Eèè, �Eòî�Eõîðä �E�Eñàòå�EûZ�E �Eòî�EðàçëüEåí�E úü �EüEèòåë�E�Eó÷åòüK ú@ðåäå�EåìüH òî÷íúBòè �E�EüAåð�E �EàòûMñò�E�Eðíåé, �Eòà�E�E�Eñðåä�EVisual Basic for Applications 6.0 áû�E ðàçðàáúCàí�E�EüBðà�E�E ðåàëèç�Eùàÿ ýòî�E�Eèñ�E�E�EüAåð�E.  �Eÿñíèòåë�EüH çà�Eñê�E�EèâüCèò�E ú@èñàíèå �E�Eñà�E�E ÷èñëåíûZ�E�Eòîäî�E òà�E�E�EüBðà�E�E âê�E÷àÿ �Eèìåð�E�E«ý�EàíûZ�E�E�Eè».

1. ÒÅÕÍÈ×ÅÑÊÎÅ ÇÀÄÀÍÈÅ

Ðàçðàáîòàòü �EüBðà�E�Eäëÿ âû÷èñëåí�E �Eðíåé àëãåáðàè÷åñêüB�E�EüBúH�Eúü ñëåä�Eùè�E ÷èñëåíûZ�E �Eòîäà�E : �Eòîäî�E �E�EâèûLüB�Eäå�EûGÿ, �Eòîäî�Eõîðä �E�Eñàòå�EûZ�E �Eòîäî�EðàçëüEåí�E úü �EüEèòåë�E �Eòà�E�Eü@åñ�E÷èòü âû÷èñëåíèå çíà÷åíèé �Eðíåé �Eóêàçûâàå�E�E òî÷íúBòüþ �E�EüAåð�E �EàòûMñò�E�Eðíåé. Ñðåäà ðàçðàáúC�E �EüBðà�E�E�E�EüGçâüJ�E�E.

2. ÏÐÅÄÌÅÒÍÀß ÎÁËÀÑÒÜ

2.1. Î�EñàûG�E÷èñëåíûZ�E�Eòîäî�E/b>

×èñ�EûLûå �Eòîäû �EçâüJÿþ�Eúüéò�EðåøåûGÿ ú@ðåäå�EûLûõ çàäà�E çàðàûD�Eçí�E, ÷ò�E�E�E÷åûLûå ðåçó�Eòàòû áóäó�Eâû÷èñëåí�E�E ú@ðåäå�EûLüH �EãðåøûMñò�E, �Eýòî�E äëÿ �EüBèõ ÷èñëåíûZ�E�Eòîäî�EûDü@õîäè�E çàðàûD�E çíàò�E«óðüAåí�Eòî÷íúBòè», �Eòîðî�E áóäå�EñîúCâåòñòâüAàò�E�E�E÷åûLüD ðåøåûG�E

 ýòî�Eñâÿçè çàäà÷à úüõîæäåí�E �Eðíåé �EüBúH�Eúü âèäà (1)

F(x)=a0 +a1 x+a2 x2 +�Ean xn (1)

�Eåäñòàâ�Eåò úBü@ûé èíòåðå�E �E�E ôîðìóë�Eúüõîæäåí�E �Eðíåé äàæå �Eáè÷åñêüB�EóðàâûDûGÿ äîñòàòúHûM ñëüEûZ, �Eåñ�E ûDü@õîäè�E úCûñ�Eòü �Eðí�E �EüBúH�Eúü, ñòåïåí�E�Eòîðîãî ðàâí�E úü�Eèìåð, 5 �Eòî áå�E�E�Eùè ÷èñëåíûZ�E �Eòîäî�EûD ü@üHòèñü, òå�Eáî�E, ÷ò�EâåðîÿòíúBòü úü�E÷èÿ �Eòà�Eãî �EüBúH�Eúü úüòóðà�EûZ�E(èë�Eöå�E�E èë�Eòî÷íûõ �Eðíåé �E�E«�EðîòêüH» äðü@ûM�E÷àñò�E) äîâî�EûM �E�E, �Eôîðìóë äëÿ úüõîæäåí�E �Eðíåé óðàâûDûGÿ ñòåïåí�E �Eåâûø�Eùå�E4, ûD ñóùåñòâóåò. [1] Ä�Eôà�E�Eâñ�Eäà�EûDéøèå ú@åðàöèè áóäó�EñâüCèò�Eÿ �Eøü �EóòúHûDûGþ �Eðíåé, èíòåðâàë�E�Eòîðû�E�Eèá�Eçèòå�EûM èçâåñòûZ çàðàûD�E Ïðîùå âñåã�Eýòè «�Eèá�Eçèòå�EûZå» �Eðí�Eúüõîäèòü, èñ�E�Eçóÿ ãðàôè÷åñ�E�E�Eòîäû.

Ä�E úüõîæäåí�E �Eðíåé �EüBúH�Eúü ñóùåñòâóåò ûDñêüJ�E�E÷èñëåíûZ�E�Eòîäî�E ûM �E úBòàûMâè�Eÿ úü òå�Eèç ûG�E �Eòîäå èòåðàöèé, �Eòîäå õîðä �E�Eñàòå�EûZ�E�E�Eòîäå �E�EâèûLüB�Eäå�EûGÿ.

2.2.1. ÌåòüC õîðä �E�Eñàòå�EûZ�E (�E�EèíèðüAàíûZ�E

ÄàíûZ�E�Eòî�EúBûMâà�Eúü �Eñòðîåíèè ñõåìàòè÷åñ�Eãî ãðàôèê�EôóûIöè�E ú@ðåäå�EûG�EèíòåðâàëüA åã�E�Eðåñå÷åûGÿ �EúB�E àáñöèñ�E�E�Eñëåä�Eùè�E«ñæàòèå�E ýòîãî èíòåðâàë�E�E�E�E�Eùè ñòðîèìûõ õîðä �E�Eñàòå�EûZ�E �Eãðàôèê�Eýòî�EôóûIöè�E

Íàä�EúC�Eòèòü, ÷ò�Eñóùåñòâóþ�Eòà�E�E úCäå�EûM �Eòî�Eõîðä (äàåò çíà÷åíèå �Eðíÿ �EûDäîñòàò�E�E �E�Eòî�E�Eñàòå�EûZ�E(�E èçáûòêüK). Îäíàê�E�Eåè�Eùåñòâî �E�EèíèðüAàíûMãî �Eòîäà çà�Eþ÷àåò�E �E «äâóñòîðîûLåì ñæàòèè» ðàññ�Eòðèâàå�Eãî úCðåçê�E

ÐàññìúCðè�Eñëåä�Eùè�Eñëó÷àé:

- äàúü ôóûIöèÿ F(x) �E�Eñòðîåí åå ãðàôèê;

- ú@ðåäå�Eúü äî�Eñòèì�E�EãðåøûMñò�EQ

-

ðè�E1

- ñóùåñòâóåò �Eðåû[ ðàññ�Eòðèâàå�Eãî �EüBúH�Eúü. (ü@üFúü÷è�Eåã�E÷åðå�EA)

Äàë�Eåéøè�Eàëãîðèòì ñâüCèò�E �Eñëåä�Eùè�E äåéñòâ�E�E

1. ñòðîèì �Eñàòå�EûRþ �Eãðàôèê�EôóûIöè�E �Eòî÷ê�EF(b)

2. âû÷èñëÿåì �EúAäèúüòó �E�Eðåñå÷åûGÿ �Eñàòå�EûM�E�EúB�E àáñöèñ�E�E ôîðìóë�E(3) �Eü@üFúü÷àåì åå ÷åðå�Eb�E/p>

3. ñòðîèì �Eãðàôèê�E ôóûIöè�Eõîðä�E �EúFüCÿùóþ ÷åðå�Eòî÷ê�EF(a) �EF(b).

4. Âû÷èñ�Eåì òî÷ê�E �Eðåñå÷åûGÿ õîðä�E�EúB�E àáñöèñ�E�E ôîðìóë�E(2) �Eü@üFúü÷àåì åå ÷åðå�Ea'.

a�Ea- Da , ãä�E/b> (2)

b�Eb- Db , ãä�E/b> (3)

Òàêèì ü@ðàçî�E�E �E�E÷àåì ûMâû�E úCðåçî�E[a�E, b’], �EòðúV�E(�E ú@ðåäå�EûGÿ�E õîðä�E�E�Eñàòå�EûM�E �E-�EåæûD�E ñîäåðæ�EðåøåûG�EóðàâûDûGÿ A.

5. Òåïåð�E�Eèíèìàå�E úCðåçî�E [a�Eb’] çà ûMâû�EúCðåçî�E [a,b] �E�EâòúAÿåì øàãè 1-4 äî òå�E�E�E �E�E ðàçíúBòü F(b)-F(a) ûD ñòàíåò �Eû[øå �Eðâ�Eà÷àë�E�E çà�EæåûLüH �EãðåøûMñò�EQ. Îòìåòèì òà�E�E ÷ò�E�Eñë�Eýòîãî ðå�E�EûCóåòñÿ �E�E÷åñòâå èñ�E�Eãî ðåøåûGÿ âçÿòü ñðåäûD�Eàðèô�Eòè÷åñêüD F(a) �E F(b).

Çàìå÷àíèå �E�Eòîäó õîðä �E �Eñàòå�EûZ�E  ðàññ�EòðåíûM�Eñëó÷àå �EüGçâüCúüÿ F�Ex)>0, �E�E ãðàôèê «âû�E�Eûé» �Eb>a. Ïðè ðàáîòå �E�Eæäûì úCäå�EûZ�Eñëó÷àå�EûDü@õîäè�E úüõîäèòü �EüGçâüCûZ�EôóûIöè�E �EðâüB�E�EâòúAüB�E�E�EäêüA �E ñîü@ðàçóÿñü �Eåå çíàêüK, ú@ðåäå�Eòü a �Eb.

ÂüF�Eæí�E÷åòûðå ñëó÷�E:

y y

F(x) F(x)

x x

�E�E

y y

F(x) F(x)

x x �E�E

�E F�Ex) < 0

F’’(x) > 0

�E F�Ex) > 0

F’’(x) > 0

�E F�Ex) < 0

F’’(x) < 0

�E F�Ex) > 0

F’’(x) < 0

Ñ�Eñî�Eõîðä Ñ�Eñî�E�Eñàòå�EûZ�E/b>
F�Ex)F’’(x) > 0 Ñ ûDäîñòàò�E�E/td> Ñ èçáûòêüK
F�Ex)F’’(x) < 0 Ñ èáûò�E�E/td> Ñ ûDäîñòàò�E�E/td>

Òàêèì ü@ðàçî�E åñ�E õîðä�E(�Eñàòå�Eúüÿ) äàåò çíà÷åíèå �Eðíÿ �EèçáûòêüK, òî ýòî�E�Eðåû[ áåðåòñÿ �E�E÷åñòâå ûMâî�E�EàâüH ãðàíèö�E �Eåñ�E �EûDäîñòàò�E�E�Eòî �Eâî�E  ü@üG�Eñëó÷�E�Eòî÷íûé �Eðåû[ �Eæè�E �Eæä�Eòî÷êàì�E�Eðåñå÷åûGÿ õîðä�E�E�Eñàòå�EûM�E�EúB�E àáñöèñ�E

Çàìå÷àíèå 2 �E�Eòîäó õîðä �E �Eñàòå�EûZ�E Òàê �E�Eäëÿ ðåøåûGÿ �Eñòàâ�EûLüH çàäà÷è òðåáóåòñÿ úCûñ�EûG�E�EüGçâüCûM�EôóûIöè�EF(x), �Eòî�Eõîðä �E�Eñàòå�EûZ�EäîñòàòúHûM òðóäûM ðåàëèçóå�Eúü �EüBðà�EûM�EóðüAûD, �E�E �Eàâèë�Eâû÷èñëåí�E �EüGçâüCûZ�E�E ü@ùå�Eâèäå äîâî�EûM ãðüKüFäêè äëÿ «�EûG�EûGÿ» ÝÂÌ; �E�EûD�EñðåäñòâåûLüK óêàçàíèè �EüGçâüCûM�Eäëÿ �EæäüH ñòåïåí�E�EüBúH�Eúü �E�Eòü �E�E�Eòåðà ñåðüåçûM çàãðóæàåòñÿ, ÷ò�EúHåí�Eçà�Eäëÿåò ðàáîòó, �EçàäàûG�EôóûIöè�E�E ñîúCâåòñòâåíûM, åå �EüGçâüCûM�E ûD�EñðåäñòâåûL�E�E�EüBðà�EûM�E�Eäå �EûDäî�Eñòèì�E Îäíàê�E èñ�E�Eçóÿ äàûLûé �Eòî�E ñõüCèìúBòü èíòåðâàë�E�E�Eðíþ �EüGñõüCèò úüèáüJåå áûñòðî, úBü@åíûM åñ�E ñîâìåñòèòü �Eòî�Eõîðä �E�Eñàòå�EûZ�E�E�Eòîäî�Eáèñå�Eèè, �E�E ñåðåäèúü ûMâîãî úCðåçê�Eçà÷àñò�E äàåò âïüJûD óäüA�EòâúAèòåë�EüD ðåøåûG�E

2.2.2. ÌåòüC èòåðàöèé

Ïÿòû�Eøà�Eàëãîðèòì�Eõîðä �E �Eñàòå�EûZ�Eú@ðåäå�E�Eâîçâðà�E�E�EðâüK�Eøàãó �E�Eñëåä�Eùóþ öè�Eè÷ûMñò�Eõîäà, �E�E �Eòî�Eõîðä �E�Eñàòå�EûZ�Eÿâëÿ�Eÿ èòåðàöèîûLûì. Äðóãî�E�Eòî�E òà�E�EúBûMâàûLûé úü �EâòúAàõ òà�E�Eáû�Eúüçâàí �E«�Eòî�Eèòåðàöèé». Ñóò�Eåã�Eçà�Eþ÷àåò�E �Eñëåä�Eùå�E

- äàúü ôóûIöèÿ F(x);

- ú@ðåäå�Eúü äî�Eñòèì�E�EãðåøûMñò�EQ;

- ú@ðåäå�E�E ûD�Eòîðû�Eèíòåðâàë [ a , b ], òî÷í�Eñîäåðæàùèé ðåøåûG�EóðàâûDûGÿ.

- Î�Eåäåëåí�E ûD�Eòîðî�E÷èñë�Ez, �Eèíàä�Eæàùå�E[ a , b ] (úüçîâå�Ez «ûR�Eâû�E�Eèá�EæåûGåì»)

Ä�E �E�E÷åûGÿ ñëåä�Eùåãî �Eèá�EæåûGÿ �Eäñòàâè�E�Eôîðìóë�E(1) âìåñòî X Z, �E�E÷è�E

x1 =F(z) (4)

�E �EüCüJæàÿ àíàëüBè÷ûM,

x2 =F(x1 )

x3 =F(x2 ) (5)

�E/b>

xn =F(xn-1 )

Òàêèì ü@ðàçî�E �E�E÷àåì ûD�Eòîðóþ �EñëåäüAàòåë�EúBòü, �E åñ�E åå �Eåäåë (6)

limxn =A, n®v (6)

òî À ÿâëÿåò�E èñ�E�E�E�Eðíåì.

ÄàíûZ�E�Eòî�Eÿâëÿåò�E èñ�Eþ÷èòå�EûM àíàëèòè÷åñ�E�E ÷ò�Eóïðîùàåò åã�E�EøèûL�E ðåàëèçàö�E, üCúü�E ñîäåðæèò ñëåä�Eùè�E ûDäîñòàò�E:

- ûDü@õîäè�Eñò�E âûáîðà ûR�Eâîãî �Eèá�EæåûGÿ (âåäü òî, ÷ò�EèíòóèòèâûM äëÿ ÷å�Eâå�E, äëÿ ÝÂÌ �Eæå�Eñòàò�Eäîâî�EûM ñëüEûM�Eçàäà÷å�E

- úü�EûD�E �E�E÷åûL�E �EñëåäüAàòåë�EúBòü �EúBòî �Eæå�EûD ñõüCèò�Eÿ, �Eòîãä�EðåøåûG�E úüéäåí�EûD áóäå�E

Ýòè �EûQðàðãóìåíòû ñòàë�EúBûMâàûGåì äëÿ úC�E�Eåí�E �Eòîäà èòåðàöèé �E�Eâûáîðå àëãîðèòìèçèðóå�Eãî �Eòîäà.

2.2.3. ÌåòüC �E�EâèûLüB�Eäå�EûGÿ (�Eòî�E áèñå�Eèè)

ÌåòüC �E�EâèûLüB�Eäå�EûGÿ (èçâåñòûZ�E åù�E�E�E�E«�Eòî�Eäå�EûGÿ úCðåçê�E�E�E�E�E) òà�E�Eÿâëÿåò�E ðå�EðñèâûZ�E �E�E �Eåäóñ�Eòðèâàå�E�EâòúAåíèå �Eó÷åòüK �E�E÷åûLûõ ðåçó�Eòàòî�E

Ñóò�E�Eòîäà �E�EâèûLüB�Eäå�EûGÿ çà�Eþ÷àåò�E �Eñëåä�Eùå�E

- äàúü ôóûIöèÿ F(x);

- ú@ðåäå�Eúü äî�Eñòèì�E�EãðåøûMñò�EQ;

- ú@ðåäå�E�E ûD�Eòîðû�Eèíòåðâàë [ a , b ], òî÷í�Eñîäåðæàùèé ðåøåûG�EóðàâûDûGÿ.

1. Âû÷èñ�Eåì çíà÷åíèå �EúAäèúüòû Å, áå�E ñåðåäèûR úCðåçê�E[a , b], �E�E Å= (a + b ) / 2 (7)

2. Âû÷èñ�Eåì çíà÷åí�E F(a), F(b), F(E), �EúBóùåñòâ�Eåì ñëåä�Eùóþ �EüAåð�E: Åñë�EF(E)>Q, òî �Eðåû[ �EóêàçàíûM�Eòî÷íúBòüþ úüéäåí. Åñë�EF(E)<Q, �E�E ûDü@õîäè�Eÿ òî÷íúBòü åù�EûD äîñòèãûRòà, òî ôîðìèðóå�Eäâ�Eèíòåðâàë�E [a , E] �E[E , b] �EüAåðÿåì çíàê�EF(a), F(b), F(E). Í�E�EûUàõ üCûMãî èç ýòè�EèíòåðâàëüA çíàê�EôóûIöè�Eáóäó�EüCèíàêüA�E �Eúü äðóã�Eðàçëè÷ûZ (èíà÷�EÅ - èñ�E�E�E�Eðåû[). È èìåíûM òî èíòåðâàë, úü �EûUàõ�Eòîðîãî çíàê�Eðàçëè÷ûZ, �E áåðå�Eçà úBûMâó �E�Eñëåä�Eùå�Eèòåðàöèè, �E�E �EèðàâûGâàåì �EÅ �Eáî a, �Eáî b.

3. ÏåðåõüCèì �E �EûIòó 1.

Çàäà÷�E �Eæí�Eóïðîñòèò�E åñ�E ú@ðåäå�Eòü ãðàíèö�E�Eðíåé: ãðàíèö�Eàáñî�Eòíûõ çíà÷åíèé �Eðíåé âû÷èñëÿåò�E �E ôîðìóë�E(8)

: (8),

(9),

ãðàíèö�E�E�Eæèòå�EûZ�E�Eðíåé �E�E ôîðìóë�E (9):

�Eãðàíèö�EúCðèöàòå�EûZ�E�Eðíåé �E çà�EûG�E�EóðàâûDûG�E(1) �Eúü –õ.

Òàêèì ü@ðàçî�E �E �E�E÷àåì �Eòî�E õî�E �EäîñòàòúHûM �EäëåíûZ�E(âïðî÷å�E �E�EûDóäà÷ûM�Eâûáîðå ûR�Eâîãî �Eèá�EæåûGÿ �E�Eòîäå èòåðàöèé �Eèñ�EðåøåûGÿ �Eæå�Eçà�EûRòü�E úü åù�Eáî�E�Eäî�EüD âðåìÿ, äà �E�Eòî�E æå ûDèçâåñòûM, �Eèâåäåò �E âåñü õî�Eâû÷èñëåíèé �EúCâåòó), ûM çàòî âïüJûD úüäåæíûé �E�EúBòî�E�Eòî�E ûD òðåá�Eùè�EðåøåûGÿ äî�E�Eèòåë�Eûõ çàäà�E âðüC�Eâû÷èñëåí�E �EüGçâüCûM�E �Eðå�EðñèâûMñò�Eñà�Eãî àëãîðèòì�E�EçâüJÿåò �E�E÷èòü úHåí�E�E�Eàêòíûé �E�Eãê�E÷èòàåìûé �E�E È�EûL�E�Eýòî�E �Eòî�E �E�EâèûLüB�Eäå�EûGÿ �Eáû�Eâûáðàí äëÿ ðåàëèçàöèè úü �EüBðà�EûM�EóðüAûD.

2.2.4. ÌåòüC ðàçëüEåí�E úü �EüEèòåë�E/b>

ÄàíûZ�E�Eòî�Eÿâëÿåò�E �E�EúBòüþ àíàëèòè÷åñ�E�E üCúü�E �E�EúBòüþ çàâèñè�EúC äðóãèõ. Ã�Eâíûì åã�E�Eåè�Eùåñòâî�E ÿâëÿåò�E òî, ÷ò�E�EäàûLüK �Eòîäå ûD �EüGñõüCèò �Eòåðè �EàòûZ�E�Eðíåé. Ï�Eñíèì úü �Eèìåð�E

Ïóñòü äà�E�EüBúH�E�EF(x) = 2x3 -11x2 +20x-12 (11)

Åãî �Eæí�Eçà�Eñàòü �Eâèäå: F(x) = (x+2)2 (2x-3) (12)

Ó �EüBúH�Eúü n-ñòåïåí�E �E�EèçâåñòûM, n �Eðíåé, �Eèç (12) ñëåäóå�E ÷ò�E�Eðíÿ�E F(x) ÿâëÿþòñÿ �E �E1,5, �Eè÷åì �Eðåû[ �E ÿâëÿåò�E �EàòûZ�E �E�E ôà�Eè÷åñ�E ýòî äâ�EüCèíàêüAûõ �Eðíÿ. Ïðè úCûñ�EûG�Eæå �Eðíåé �Eáû�Eèç âûøåú@èñàíûZ�E�Eòîäî�E«âòúAüH» �Eðåû[ �E áóäå�E�Eòå�E�E �E�E ãðàôèê ôóûIöè�Eáóäå�Eèìåò�E�Eøü äâ�Eòî÷ê�E�Eðåñå÷åûGÿ �EúB�E àáñöèñ�E/p>

×òîáû èçáåæàòü ýòîãî �Eèìåíÿåò�E �Eòî�EðàçëüEåí�E úü �EüEèòåë�E Ñóò�Eåã�Eçà�Eþ÷àåò�E �Eñëåä�Eùå�E �Eæäûé �EüBúH�E�Eâèäà (1) �Eæí�E�Eåäñòàâèò�E�Eâèäå (x+h1 )(x+h2 )�Ex+hn )*H = 0 (13) ,

èë�E F(x) = (x+h)(bn-1 xn-1 +�E1 )+b0 (14)

ãä�Eh1�En �E�Eðí�EóðàâûDûGÿ, �EÍ �E�EüGçâåäåíèå �EüEèòåëåé �E âûûDñåûLûõ çà ñêü@�E ( Í ûG�E�EûD âë�Eåò úü óðàâûDûG�E �E�E úC ûDãî èçáàâëÿþòñÿ, äå�E úü Í ü@�E÷àñò�E (13). Ïðè ýòî�EûD èñ�Eþ÷åûM, ÷ò�EûD�Eòîðû�Eh �Eãó�Eáûòü âçàè�E�Eðàâí�E ÷ò�E�E ñâèäåòåë�Eòâóå�E�Eúü�E÷è�E�EàòûMãî �Eðíÿ.

Ä�E âû÷èñëåí�E çíà÷åíèé ûMâû�E�EýôôèöèåûQüA �E(14) èñ�E�Eçóþòñÿ ôîðìóë�E

bn =an

bn-1 =bn h+an-1 (15)

bn-2 =bn-1 h+an-2

�E

Òàêèì ü@ðàçî�E àëãîðèòì ýòîãî �Eòîäà âûãëÿäè�Eñëåä�Eùè�Eü@ðàçî�E

1. Î�Eåäåëèò�E ãðàíèö�E�Eðíåé óðàâûDûGÿ;

2. Ïðè �E�Eùè �Eáîãî èç âûøåú@èñàíûZ�E�Eòîäî�Eúüéò�EüCèí �Eðåû[ óðàâûDûGÿ;

3. Ïðè�E�Eÿ ôîðìóë�E (14) �E(15) ñôúA�Eðîâàòü ûMâû�E�EüBúH�E�Eñòåïåí�E úü 1 �Eû[øå�E�Eåäûäóùåã�E

4. ÂåðûRòü�E �E �EûIòó 2.

5. ÏüAòî�Eòü äî òå�E �E�E �E�E ñòåïåí�E�EüBúH�Eúü ûD ü@ûR�Eòñÿ.

Ýòî�E�Eòî�Eáû�EðåàëèçüAàí úü �EüBðà�EûM�EóðüAûD �Eâê�E÷å�E�E �EðñüA�E ðàáîòó.

3. ÎÏÈÑÀÍÈÅ ÑÒÐÓÊÒÓÐÛ ÏÐÎÃÐÀÌÌÛ

 ðà�Eàõ çàäàûGÿ úü �EðñüA�E ðàáîòó �E ñðåä�E�EüBðà�EèðüAàí�E Visual Basic for Applications áû�E ðàçðàáúCàí�E�EüBðà�E�E úüõî�Eùàÿ �Eðí�E�EüBúH�Eúü �Eóêàçûâàå�E�Eòî÷íúBòüþ.

3.1. Î�EñàûG�E�EüBðà�EûZ�E�Eäó�E�E/b>

Ðàçðàáîòê�E�EüBðà�E�Eâå�Eñü �Eó÷åòüK �EûUåïöè�Eü@úå�EûM-úAèåûQèðüAàíûMãî �EüBðà�EèðüAàí�E, �Eýòî�E ÷åòê�E ú@ðåäå�EûLüH �EñëåäüAàòåë�EúBòè äåéñòâèé �EûD�EûD�E Îäíàê�E ðàçáèð�E �EüBðà�E�E úü ñîñòàâ�Eþùè�E �Eæí�E�EúB�Eäèòü «�Eòü» àëãîðèòì�E�E�Eäå.

Â�E �EüBðà�E�EñîñòüG�Eèç ôîðì �E �Eäó�E�E ÌüCóëåé âñåã�Eäâ�E üCèí ñîäåðæèò ñòàíäàðòûRþ �EúGåäóð�Eàâòîçà�Eñê�E (åã�Eðàññ�Eòðèâàò�E�E ûD ñòàíåì), �EäðóãüH �Eâñ�E«�Eáëè÷ûZå» �EúGåäóð�E�E ôóûIöè�E

Public function F(x). Ôóí�E�E, âîçâðàùàþùàÿ çíà÷åíèå �EüBúH�Eúü äëÿ �EðåäàâàåìüB�E �E

Public function DetectBorders. ÂüFâðàùàå�Eãðàíèö�E�Eðíåé, ñîãëàñûM ôîðìóëàì ( 7 , 8, 9 ).

Public sub Gra �E�EúGåäóð�E «úCâåòñòâåíúüÿ» çà ñîñòàâ�EûG�Eãðàôèê�E

3.2. Î�EñàûG�Eôîðì

 ôîðìàõ çà�Eþ÷åúü úBûMâí�E ÷àñò�E �EüBðà�E�E �Eòî�E÷èñë�E�EñîáñòâåíûM àëãîðèòì �Eòîäà �E�EâèûLüB�Eäå�EûGÿ. Ðåøåíèå «óïàêüAàò�E ýòè ôóûIöè�E�Eôîðì�Eáû�E �EüCèêòîâàûM ñëåä�Eùè�E �Eè÷èíàì�E

- ñî�Eàùåíèå ü@úå�E çàûG�EåìüH �E�Eòè �E �E�Eñëåäñòâè�E óñ�EðåûG�Eðàáîòû çà ñ÷åò ñî�Eàùåí�E âðåìåí�E æèçí�E�Eðå�EûLûõ;

- ðàçãðàûG÷åûG�E äîñòóï�E(�E�E ûDü@õîäè�Eÿ ôóûIöèÿ èë�E�Eòî�E�Eãó�Eáûòü àêòèâèðîâàûZ èñ�Eþ÷èòå�EûM �Eäî�EñòèìüH ñèòóàöèè �Eýòî çíà÷èòåë�E�Eñíèæàå�EâåðîÿòíúBòü úIèáüI);

- �Eæä�E ôîðì�E ÿâëÿåò�E «âåùüþ �Eñåáå» �EûD çàâèñè�EúC úBòà�EûZ�E(�EüK�E«�EðíåâüH»

3.2.1. ÔúA�E Form_Main

ßâëÿåò�E �EðíåâüH ôîðìüH �EüBðà�E�E ñîäåðæèò Ã�EâíüD �E�E, �EçâüJÿþùå�E�E�Eáî�E�E�Eäê�Eâû�E�Eÿòü âñ�EûDü@õîäè�E�Eäåéñòâ�E, �Eòà�E�E ñîõðàíÿòü �Eçàâåðøàò�Eðàáîòó �EüBðà�E�E

3.2.2. ÔúA�E Form_Koeff

 ýòî�Eôîðì�Eçàäàþòñÿ �EýôôèöèåûQ�E�EüBúH�Eúü.

Çàìå÷àíèå. Ä�E çàäàûGÿ �EýôôèöèåûQ�E�Esub>0 ûDü@õîäè�E óêàçàò�Eçíà÷åíèå ñòåïåí�E�Eðàâíûì 0.

3.2.3.ÔúA�E Form_Mnogo

3.2.4.ÔúA�E Form_WP

Ýòà ôîðì�E�E ñóùåñòâó ÿâëÿåò�E �EûD�Eþ óïðàâëåí�E �Eðåæè�E ãðàôèê�E�E�EçâüJÿåò åã�Eðàñïå÷àòàò�Eèë�Eçà�Eûò�E

3.2.5. ÔúA�E Form_Korni

«ÎñíüAúüÿ ôîðìà» �EèìåíûM �EûD�Eçà�Eþ÷å�Eñà�Eàëãîðèòì �Eèñ�E �Eðíåé (Sub FindKor) �Eòîäà�E áèñå�Eèè �Eõîðä/�Eñàòå�EûZ�E

 �E÷åñòâå ñâüHñò�E�Eü@úå�E�E«ôîðìà» �Eèñóòñòâóþ�E òð�E�Eþ÷åâû�E�EúGåäóð�E ðåàëèç�Eùè�EñîáñòâåíûM àëãîðèòì�Eúüõîæäåí�E �Eðíåé �Eúüõîæäåí�E �EüGçâüCûM�E

Public sub FF* �E�EúGåäóð�E «úCâåòñòâåíúüÿ» çà úüõîæäåíèå �EüGçâüCûM�E

Public sub Horda_Kasatelnye �E �EúGåäóð�E ðåàëèç�Eùàÿ �Eèñ�E�Eðíåé �E àëãîðèòì�Eõîðä �E�Eñàòå�EûZ�E

Public sub Find_Kor �E�EúGåäóð�E ðåàëèç�Eùàÿ �Eèñ�E�Eðíåé �E àëãîðèòì�E�E�EâèûLüB�Eäå�EûGÿ úCðåçê�E

Çàìå÷àíèå. À�EúAèò�E úüõîæäåí�E �EûD�Eú@èñàí�E�E ãëàâ�E2. Ñóò�Eæå àëãîðèòì�Eúüõîæäåí�E �EüGçâüCûM�EñâüCèò�E �E�EúBòî�E �Eðå�EüEåí�E �EýôôèöèåûQ�E�Eñòåïåí�E�Eóìåí�Eåí�E çíà÷åí�E ñòåïåí�Eúü åäèíèö�E Ýòî �EçâüJÿåò �Eððåêòí�Eú@ðåäå�Eòü �EüGçâüCûRþ, �E�Eýòî�E�Eððåêòí�E«èçáàâèòü�E» úC �EûD÷íüH �EûPòàûQ�E

4. ÀÍÀËÈÇ ÐÅÇÓËÜÒÀÒÎÂ

 ðåçó�Eòàòå âû�E�Eåí�E çàäàûGÿ úü �EðñüA�E ðàáîòó áû�E ñîçäàí�E�EüBðà�E�EVI Function 2.0 , úüõî�Eùàÿ �Eðí�Eàëãåáðàè÷åñêüB�E �EüBúH�Eúü âèäà (1) �Eóêàçûâàå�E�Eòî÷íúBòüþ �Eñðåäñòâî�Eñëåä�Eùè�E�Eòîäî�E

· �Eòî�Eäå�EûGÿ úCðåçê�E�E�E�E�E

· �Eòî�Eõîðä �E �Eñàòå�EûZ�E(�E�EèíèðüAàíûZ�E

Òàêæå �E�Eñîñòàâ�EûG�E�EüBðà�E�Eáû�E ó÷òåúü âîçìüEûMñò�Eúü�E÷èÿ �E�EüBúH�Eúü �EàòûZ�E�Eðíåé, �Eñðåäñòâà èõ ü@úüðóæåûGÿ òà�E�Eâîøë�E�Eñîñòàâ �EüBðà�E�E

Ôàêòè÷åñêèå ðåçó�Eòàòû ñîâïàë�E�E ôîðìàë�Eûì�E

5. ÑÏÈÑÎÊ ËÈÒÅÐÀÒÓÐÛ

1. Ãóòåð Ð.Ñ. , Îâ÷èíñêèé Á.Â. «Ý�E�EûQ�E÷èñëåíûMãî àíàëèç�E�E�Eòå�Eòè÷åñêèé ü@ðàáîòê�E ðåçó�Eòàòî�Eú@ûòà». ÌúB�E�E «Íàó�E», 1979

2. Êàëèò�E�EÍ.Í. «×èñ�EûLûå �Eòîäû». ÌúB�E�E «Íàó�E», 1978

3. Êðû�E�EÂ.È., Áàá�EâÂ.Â., Ì�Eàñòûðñ�E�EÏ.È. «Âû÷èñ�Eòå�EûZ�E�Eòîäû». ÌúB�E�E «Íàó�E», 1976

4. Ï. Ñàíúü. «Visual Basic for Applications 6.0 «�E �EäëèíûG�E», Êèå�E BHV

6. ÏÐÈËÎÆÅÍÈß

6.1. Ïðè�E�Eàëãåáðàè÷åñêüB�E�EüBúH�Eúü �Eúüõîæäåí�E åã�E/p>

�Eðíåé

ÌûMãî÷ëåí F(x) = 3x2 +5x-8

Ãðàôè�E�Eåäñòàâ�E�Eúü ðè�E 6.1

ÒúHûMñò�EQ = 0,0001

ÍàéäåûLûå �Eðí�E x = -2,66666669921875 �Eòî�E/p>

x= 0,99991015625 áèñå�Eèè

ÍàéäåûLûå �Eðí�E x = -2,66667654214111 �Eòî�E/p>

x= 0,99981915025 õîðä �E�Eñàòå�EûZ�E/p>

ðè�E 6.1

6.2. Á�E�Eñõåì�Eàëãîðèòì�E�E�EâèûLüB�E äå�EûGÿ

A = �Eâàÿ ãðàíèö�E/p>

 = �Eàâ�E ãðàíèö�E

C �Eñåðåäèúü

F(x) - ôóûIöèÿ

6.3. Á�E�Eñõåì�Eàëãîðèòì�E�Eèñ�E �Eðíåé �Eòîäî�Eõîðä �E�Eñàòå�EûZ�E/p>

A = �Eâàÿ ãðàíèö�E/p>

 = �Eàâ�E ãðàíèö�E

F(x) - ôóûIöèÿ

6.4 ÐóêüAüCñòâî �E�Eçîâàòå�E.

ÏúB�E çà�Eñê�E�EüBðà�E�E�Eðå�EÂàì�E�Eÿâèòñÿ Ã�EâíüD �E�E, âê�E÷àþùå�E�Eñå�E ñëåä�Eùè�E�E�EüBðà�E�E

ÑÎÕÐÀÍÈÒÜ ÑúFðà�Eåò ôàéë ñî âñåì�EñäåëàíûZ�E èç�EûDûGÿ�E
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UNIT1

Dim curcell As Range

Dim ma As Double

Dim Ao As Double

Public Function F(x As Variant)

F = (x ^ 20 * Range("a20").Value) + (x ^ 19 * Range("a19").Value) + (x ^ 18 * Range("a18").Value) + (x ^ 17 * Range("a17").Value) + (x ^ 16 * Range("a16").Value) + (x ^ 15 * Range("a15").Value) + (x ^ 14 * Range("a14").Value) + (x ^ 13 * Range("a13").Value) + (x ^ 12 * Range("a12").Value) + (x ^ 11 * Range("a11").Value) + (x ^ 10 * Range("a10").Value) + (x ^ 9 * Range("a9").Value) + (x ^ 8 * Range("a8").Value) + (x ^ 7 * Range("a7").Value) + (x ^ 6 * Range("a6").Value) + (x ^ 5 * Range("a5").Value) + (x ^ 4 * Range("a4").Value) + (x ^ 3 * Range("a3").Value) + (x ^ 2 * Range("a2").Value) + (x * Range("a1").Value) + Range("a21").Value

End Function

Public Function F1(x As Variant)

F1 = (x ^ 20 * Range("j20").Value) + (x ^ 19 * Range("j19").Value) + (x ^ 18 * Range("j18").Value) + (x ^ 17 * Range("j17").Value) + (x ^ 16 * Range("j16").Value) + (x ^ 15 * Range("j15").Value) + (x ^ 14 * Range("j14").Value) + (x ^ 13 * Range("j13").Value) + (x ^ 12 * Range("j12").Value) + (x ^ 11 * Range("j11").Value) + (x ^ 10 * Range("j10").Value) + (x ^ 9 * Range("j9").Value) + (x ^ 8 * Range("j8").Value) + (x ^ 7 * Range("j7").Value) + (x ^ 6 * Range("j6").Value) + (x ^ 5 * Range("j5").Value) + (x ^ 4 * Range("j4").Value) + (x ^ 3 * Range("j3").Value) + (x ^ 2 * Range("j2").Value) + (x * Range("j1").Value) + Range("j21").Value

End Function

Public Function F2(x As Variant)

F2 = (x ^ 20 * Range("m20").Value) + (x ^ 19 * Range("m19").Value) + (x ^ 18 * Range("m18").Value) + (x ^ 17 * Range("m17").Value) + (x ^ 16 * Range("m16").Value) + (x ^ 15 * Range("m15").Value) + (x ^ 14 * Range("m14").Value) + (x ^ 13 * Range("m13").Value) + (x ^ 12 * Range("m12").Value) + (x ^ 11 * Range("m11").Value) + (x ^ 10 * Range("m10").Value) + (x ^ 9 * Range("m9").Value) + (x ^ 8 * Range("m8").Value) + (x ^ 7 * Range("m7").Value) + (x ^ 6 * Range("m6").Value) + (x ^ 5 * Range("m5").Value) + (x ^ 4 * Range("m4").Value) + (x ^ 3 * Range("m3").Value) + (x ^ 2 * Range("m2").Value) + (x * Range("m1").Value) + Range("m21").Value

End Function

Public Sub Gra()

Sheets("Ëèñ�E").Select

Range("e1").Select

For i = -10 To 10

ActiveCell.Value = F(i)

ActiveCell.Cells(2).Select

Next i

End Sub

Public Function DetectBorders()

' Ôóí�E�E ú@ðåäå�EûGÿ ãðàíèö äåéñòâèòåë�Eûõ �Eðíåé

ma = 0

For Each curcell In Range("Koeffs")

If curcell.Value > ma Then ma = curcell.Value

If curcell.Value <> 0 Then Ao = curcell.Value

Next curcell

DetectBorders = 1 + (ma * Ao)

End Function

UNIT2

Sub auto_open()

Sheets("Ëèñ�E").Select

Form_Main.Show

End Sub

FORM_ABOUT

Private Sub CommandButton1_Click()

Form_About.Hide

End Sub

FORM_KOEFF

Private Sub CommandButton1_Click()

ko = TextBox1.Value

st = TextBox2.Value

Select Case st

Case 0

Range("A21").Value = ko

Case 1

Range("A1") = ko

Case 2

Range("A2") = ko

Case 3

Range("A3") = ko

Case 4

Range("A4") = ko

Case 5

Range("A5") = ko

Case 6

Range("A6") = ko

Case 7

Range("A7") = ko

Case 8

Range("A8") = ko

Case 9

Range("A9") = ko

Case 10

Range("A10") = ko

Case 11

Range("A11") = ko

Case 12

Range("A12") = ko

Case 13

Range("A13") = ko

Case 14

Range("A14") = ko

Case 15

Range("A15") = ko

Case 16

Range("A16") = ko

Case 17

Range("A17") = ko

Case 18

Range("A18") = ko

Case 19

Range("A19") = ko

Case 20

Range("A20") = ko

Case Else

MsgBox ("ÂûõüC çà �Eåäåë�Eäî�Eñòèìûõ çíà÷åíèé")

st = st - 1

End Select

TextBox1.Value = 0

TextBox2.Value = st + 1

End Sub

Private Sub CommandButton2_Click()

Form_Koeff.Hide

End Sub

Private Sub CommandButton3_Click()

Range("a1").Value = 0

Range("a2").Value = 0

Range("a3").Value = 0

Range("a4").Value = 0

Range("a5").Value = 0

Range("a6").Value = 0

Range("a7").Value = 0

Range("a8").Value = 0

Range("a9").Value = 0

Range("a10").Value = 0

Range("a11").Value = 0

Range("a12").Value = 0

Range("a13").Value = 0

Range("a14").Value = 0

Range("a15").Value = 0

Range("a16").Value = 0

Range("a17").Value = 0

Range("a18").Value = 0

Range("a19").Value = 0

Range("a20").Value = 0

Range("a21").Value = 0

End Sub

Private Sub UserForm_initialize()

st = 0

ko = 0

TextBox1.Value = ko

TextBox2.Value = st

End Sub

FORM_KORNI

Private Sub CommandButton1_Click()

ListBox1.Clear

TextBox1.Value = 0

Form_Korni.Hide

End Sub

Private Sub CommandButton2_Click()

Range("Toc").Value = TextBox1.Value

Call FindKor

'Call Perenos

End Sub

Sub FindKor()

Range("Curright") = Range("Right").Value

Range("Curleft") = -Range("Right").Value - 0.333

'Range("right").Value = DetectBorders

Range("Stepleft").Value = Range("right").Value * (-1) - 0.333

Do

nashli = False

Call MoveLe

If Sgn(F(Range("curleft").Value)) = Sgn(F(Range("curright").Value)) Then

End If

If Sgn(F(Range("curleft").Value)) <> Sgn(F(Range("curright").Value)) Then

Do

' nashli = True

Range("Curcenter").Value = ((Range("curleft").Value) + (Range("curright").Value)) / 2

If Abs(F(Range("Curcenter").Value)) > Range("toc").Value Then If Sgn(F(Range("curleft").Value)) <> Sgn(F(Range("curcenter").Value)) Then Range("curright").Value = Range("curcenter").Value Else: Range("curleft").Value = Range("curcenter").Value

If Abs(F(Range("Curcenter").Value)) <= Range("toc").Value Then ListBox1.AddItem (Range("Curcenter").Value)

Range("Koren").Value = Range("Curcenter").Value

Loop Until Abs(F(Range("Curcenter").Value)) <= Range("toc").Value

End If

Loop Until Range("Stepleft").Value > Range("right").Value Or nashli = True

End Sub

Sub Horda_Kas()

'Sub FindKor()

Range("Curright") = Range("Right").Value

Range("Curleft") = -Range("Right").Value - 0.333

'Range("right").Value = DetectBorders

Range("Stepleft").Value = Range("right").Value * (-1) - 0.333

Do

MoveLe

If Sgn(F(Range("curleft").Value)) <> Sgn(F(Range("curright").Value)) Then

Do

' nashli = True

If F1(Range("curleft").Value) * F2(Range("curleft").Value) > 0 Then

Range("curleft").Value = Range("curleft").Value - ((Range("curright").Value - Range("curleft").Value) * (F(Range("Curleft").Value) / (F(Range("Curright").Value - F(Range("Curleft").Value)))))

Range("Curright").Value = Range("curright").Value - F(Range("curright").Value) / F1(Range("curright").Value)

End If

If F1(Range("curleft").Value) * F2(Range("curleft").Value) < 0 Then

Range("curright").Value = Range("curleft").Value - ((Range("curright").Value - Range("curleft").Value) * (F(Range("Curleft").Value) / (F(Range("Curright").Value - F(Range("Curleft").Value)))))

Range("Curleft").Value = Range("curright").Value - F(Range("curright").Value) / F1(Range("curright").Value)

End If

If Abs(Abs(F(Range("Curright").Value))) - Abs(F(Range("Curleft").Value)) <= Range("toc").Value Then

'MsgBox (Range("curleft").Value)

ListBox1.AddItem (Range("Curright").Value)

'If ((Range("Curleft").Value) + (Range("Curright").Value)) > 0 Then ListBox1.AddItem (((Range("Curleft").Value) + (Range("Curright").Value)) / 2)

'If ((Range("Curleft").Value) + (Range("Curright").Value)) < 0 Then ListBox1.AddItem (((Range("Curleft").Value) + (Range("Curright").Value)) / 2)

Range("Koren").Value = Range("Curleft").Value

End If

Loop Until Abs(F(Range("Curright").Value)) - Abs(F(Range("Curleft").Value)) <= Range("toc").Value

End If

Loop Until Range("Stepleft").Value > Range("right").Value Or nashli = True

End Sub

Sub MoveLe()

Range("stepleft").Value = Range("stepleft").Value + 0.333

Range("curLeft").Value = Range("stepleft").Value

Range("Curright").Value = Range("Curleft").Value + 0.333

Range("Curcenter").Value = ((Range("curleft").Value) + (Range("curright").Value)) / 2

End Sub

Private Sub CommandButton3_Click()

Horda_Kas

End Sub

Private Sub UserForm_Deactivate()

ListBox1.Clear

TextBox1.Value = 0

End Sub

Sub Perenos()

Range("a1").Value = Range("L1").Value

Range("a2").Value = Range("L2").Value

Range("a3").Value = Range("L3").Value

Range("a4").Value = Range("L4").Value

Range("a5").Value = Range("L5").Value

Range("a6").Value = Range("L6").Value

Range("a7").Value = Range("L7").Value

Range("a8").Value = Range("L8").Value

Range("a9").Value = Range("L9").Value

Range("a10").Value = Range("L10").Value

Range("a11").Value = Range("L11").Value

Range("a12").Value = Range("L12").Value

Range("a13").Value = Range("L13").Value

Range("a14").Value = Range("L14").Value

Range("a15").Value = Range("L15").Value

Range("a16").Value = Range("L16").Value

Range("a17").Value = Range("L17").Value

Range("a18").Value = Range("L18").Value

Range("a19").Value = Range("L19").Value

End Sub

FORM_MAIN

Private Sub CommandButton1_Click()

Form_Koeff.Show

End Sub

Private Sub CommandButton2_Click()

Form_Mnogo.Show

End Sub

Private Sub CommandButton3_Click()

Gra

Form_Main.Height = 84

Sheets("D1").Select

Form_WP.Show

Form_Main.Height = 360

Sheets("Ëèñ�E").Select

End Sub

Private Sub CommandButton4_Click()

Form_Korni.Show

End Sub

Private Sub CommandButton5_Click()

Application.Quit

End Sub

Private Sub CommandButton7_Click()

Form_About.Show

End Sub

Private Sub CommandButton8_Click()

ActiveWorkbook.Save

End Sub

Private Sub UserForm_initialize()

Sheets("Ëèñ�E").Select

Form_Main.Height = 360

End Sub

FORM_MNOGO

Dim mn As String

Private Sub CommandButton1_Click()

Form_Mnogo.Hide

End Sub

Private Sub UserForm_activate()

mn = "F(x)="

If Range("a20") > 0 Then mn = mn + Range("a20").Text + "X^20"

If Range("a20") < 0 Then mn = mn + Range("a20").Text + "X^20"

If Range("a19") > 0 Then mn = mn + " + " + Range("a19").Text + "X^19"

If Range("a19") < 0 Then mn = mn + Range("a19").Text + "X^19"

If Range("a18") > 0 Then mn = mn + " + " + Range("a18").Text + "X^18"

If Range("a18") < 0 Then mn = mn + Range("a18").Text + "X^18"

If Range("a17") > 0 Then mn = mn + " + " + Range("a17").Text + "X^17"

If Range("a17") < 0 Then mn = mn + Range("a17").Text + "X^17"

If Range("a16") > 0 Then mn = mn + " + " + Range("a16").Text + "X^16"

If Range("a16") < 0 Then mn = mn + Range("a16").Text + "X^16"

If Range("a15") > 0 Then mn = mn + " + " + Range("a15").Text + "X^15"

If Range("a15") < 0 Then mn = mn + Range("a15").Text + "X^15"

If Range("a14") > 0 Then mn = mn + " + " + Range("a14").Text + "X^14"

If Range("a14") < 0 Then mn = mn + Range("a14").Text + "X^14"

If Range("a13") > 0 Then mn = mn + " + " + Range("a13").Text + "X^13"

If Range("a13") < 0 Then mn = mn + Range("a13").Text + "X^13"

If Range("a12") > 0 Then mn = mn + " + " + Range("a12").Text + "X^12"

If Range("a12") < 0 Then mn = mn + Range("a12").Text + "X^12"

If Range("a11") > 0 Then mn = mn + " + " + Range("a11").Text + "X^11"

If Range("a11") < 0 Then mn = mn + Range("a11").Text + "X^11"

If Range("a10") > 0 Then mn = mn + " + " + Range("a10").Text + "X^10"

If Range("a10") < 0 Then mn = mn + Range("a10").Text + "X^10"

If Range("a9") > 0 Then mn = mn + " + " + Range("a9").Text + "X^9"

If Range("a9") < 0 Then mn = mn + Range("a9").Text + "X^9"

If Range("a8") > 0 Then mn = mn + " + " + Range("a8").Text + "X^8"

If Range("a8") < 0 Then mn = mn + Range("a8").Text + "X^8"

If Range("a7") > 0 Then mn = mn + " + " + Range("a7").Text + "X^7"

If Range("a7") < 0 Then mn = mn + Range("a7").Text + "X^7"

If Range("a6") > 0 Then mn = mn + " + " + Range("a6").Text + "X^6"

If Range("a6") < 0 Then mn = mn + Range("a6").Text + "X^6"

If Range("a5") > 0 Then mn = mn + " + " + Range("a5").Text + "X^5"

If Range("a5") < 0 Then mn = mn + Range("a5").Text + "X^5"

If Range("a4") > 0 Then mn = mn + " + " + Range("a4").Text + "X^4"

If Range("a4") < 0 Then mn = mn + Range("a4").Text + "X^4"

If Range("a3") > 0 Then mn = mn + " + " + Range("a3").Text + "X^3"

If Range("a3") < 0 Then mn = mn + Range("a3").Text + "X^3"

If Range("a2") > 0 Then mn = mn + " + " + Range("a2").Text + "X^2"

If Range("a2") < 0 Then mn = mn + Range("a2").Text + "X^2"

If Range("a1") > 0 Then mn = mn + " + " + Range("a1").Text + "X"

If Range("a1") < 0 Then mn = mn + Range("a8").Text + "X"

If Range("a21") > 0 Then mn = mn + " + " + Range("a21").Text

If Range("a21") < 0 Then mn = mn + Range("a21").Text

TextBox1.Value = mn

End Sub

FORM_WP

Private Sub Label1_Click()

Call Gra

End Sub

Private Sub CommandButton1_Click()

Sheets("D1").Print

End Sub

Private Sub CommandButton2_Click()

Form_WP.Hide

Call Gra

End Sub

Private Sub UserForm_Click()

Form_WP.Hide

End Sub

____________________________

VoID InVaSiON HG ©

VI Function 2.0 beta

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