Eo?niaa ?iaioa

Iaaeeaeaia ia/eneaiiy aecia/aieo ?ioaa?ae?a, ui ia aa?ooueny /a?ac
aeaiaioa?i? ooieoe??

TOC \o «1-1» Anooi. GOTOBUTTON _Toc416793604 PAGEREF
_Toc416793604 3

Oi?ioee i?yiieooiee?a ? o?aiaoe??. GOTOBUTTON _Toc416793605 PAGEREF
_Toc416793605 4

Ia?aaie?/ia ?ioa?iiethaaiiy. GOTOBUTTON _Toc416793606 PAGEREF
_Toc416793606 6

Ae?iaeaiiy i?ii?aeeo. GOTOBUTTON _Toc416793610 PAGEREF
_Toc416793610 9

Caeeoeiaee /eai oi?ioee i?yiieooiee?a. GOTOBUTTON _Toc416793621
PAGEREF _Toc416793621 11

Caeeoeiaee /eai oi?ioee o?aiaoe??. GOTOBUTTON _Toc416793624 PAGEREF
_Toc416793624 13

Caeeoeiaee /eai oi?ioee N?iiniia. GOTOBUTTON _Toc416793635 PAGEREF
_Toc416793635 14

Aeiaeaoie 1. GOTOBUTTON _Toc416793639 PAGEREF _Toc416793639 17

Aeiaeaoie 2. GOTOBUTTON _Toc416793648 PAGEREF _Toc416793648 20

Aeniiaee. GOTOBUTTON _Toc416793649 PAGEREF _Toc416793649 22

E?oa?aoo?a. GOTOBUTTON _Toc416793650 PAGEREF _Toc416793650 23

?????

Aaaaoi caaea/ iaoee ? oaoi?ee i?eaiaeyoue aei i?iaeaie ia/eneaiiy
?ioaa?ae?a, aea ia an? ?ioaa?aee i?aeaeathoueny ia/eneaiith. A aeai?e
?iaio? ?acaeyaea?oueny ieoaiiy iaaeeaeaiiai ia/eneaiiy aecia/aieo
?ioaa?ae?a, ui ia aa?ooueny /a?ac aeaiaioa?i? ooieoe??. Cie?aia,
aeaiaeyoueny oi?ioee iaaeeaeaiiai ia/eneaiiy i?yiieooiee?a, oi?ioea
o?aiaoe?e a oaeiae oi?ioea N?iiniia.

Oi?ioee i?yiieooiee?a ? o?aiaoe?e.

iaia?a?aia ooieoe?y. ?nio? aaaaoi i?eeeaae?a ia/eneaiiy iiae?aieo
?ioaa?ae?a, aai ca aeiiiiiaith ia?a?noii?, yeui aiia ae?aaea?oueny a
ne?i/aiiiio aeaeyae?, aai ae – ieioy ia?a?noio – ca aeiiiiiaith ??cieo
i?eeii?a, ye i?aaeei, ooo/ieo. Iio??aii a?aei?oeoe, iaeiae, ui an?i oeei
ae/a?io?oueny aocueeee eean eioaa?ae?a; ca eiai iaaeaie cacae/ae
aaeathoueny aei ??cieo iaoiae?a iaaeeaeaiiai ia/eneaiiy.

A aeai?e ?iaio? iiaeii iciaeiieoeny c iniiaieie ?c oeeo iaoiae?a, a yeeo
iaaeeaeai? oi?ioee aeey ?ioaa?ae?a neeaaeathoueny ii aeayeiio /eneo
cia/aiue i?ae?ioaa?aeueii? ooieoe??, ia/eneaieo aeey ?yaeo (cacae/ae
??aiia?aeaeaeaieo) cia/aiue iacaeaaeii? ci?iii?.

, ie ? noaaeii ia?aae niaith caaea/o ciaoiaeaeaiiy oe??? ieiu?.

, a iio?i eiaeio nioao iaaeeaeaii cai?ieoe i?yiieooieeii, ca aenioo
yeiai i?eeiyoa aoaeue-yea ?c eiai i?aeeiao. Oea i?eaiaea ian aei oi?ioee

,

. Ooo ooeaia ieiua e?eaie?i?eii? o?ao?e cai?ith?oueny ieiuath aeayei?
nooiai/aoi? o?ao?e, yea neeaaea?oueny ?c i?yiieooiee?a (aai ae, iiaeii
neacaoe, ui aecia/aiee ?ioaa?ae cai?ith?oueny ?ioaa?aeueiith noiith).
Oey iaaeeaeaia oi?ioea ? iaceaa?oueny oi?ioeith i?yiieooiee?a.

Iae. 1

, oi oi?ioea ia?aieoaoueny o aeaeyae?

. (1)

Iaaeae?, eaaeo/e i?i oi?ioeo i?yiieooiee?a, ie aoaeaii iaoe ia oaac?
ye?ac oeth oi?ioeo.

. Oiae? iaoa e?eaie?i?eia o?ao?a cai?ieoueny ?ioith, yea neeaaea?oueny
?c ?yaeo o?aiaoe?e (?en2.). sseui, ye ? ?ai?o ?aooaaoe, ui

?acaeoee ia ??ai? /anoeie, oi ieiu? oeeo o?aiaoe?e aoaeooue

.

Iae. 2

Aeiaeath/e, i?eeaeaii aei iiai? iaaeeaeaii? oi?ioee

. (2)

Oea oae caaia oi?ioea o?aiaoe?e.

iaeaea? oe? oi?ioee a?aeoai?ththoue ooeaia cia/aiiy c aeia?eueiei
??aiai oi/iino?.

??????????? ??????????????.

(aeecueeei( aei ia? iiiai/eaiii

(3)

? iieeanoe

— ai ii?yaeeo( (3), a ca(yceo c /ei oeai i?ioean io?eiaa iacao
ia?aaie?/iiai eioa?iiethaaiiy.

aecia/a?oueny iaeiicia/ii, ? eiai ae?ac aeaaoueny ?ioa?iieyoe?iiiith
oi?ioeith Eaa?aiaea:

.

. Oiae? iaaeeaeaii

(4)

Aaiiao?e/ii – ieiua e?eaie?i?eii? o?ao?e cai?ith?oueny ooo ieiuaaeueth
i?yiieooieea c aenioith, yea ??aia na?aaei?e ?? i?aeeiao?.

, oi

(5)

?, ye eaaei ia/eneeoe,

Oaeei /eiii, ooo ie iaaeeaeaii aaaaea?ii

Ia oeae ?ac ieiua e?eaie?i?eii? o?ao?e cai?ith?oueny ieiuath o?aiaoe??:
cai?noue e?eai? aa?aoueny oi?aea, yea ciieo/a? ?? e?ioe?.

aoaea iaoe aeaeyae

(7)

Ca aeiiiiiaith eaaeiai ia/eneaiiy ae?aoiao?ii

?, aiaeia?/ii

,

.

Oaeei /eiii, i?eoiaeeii aei iaaeeaeaii? oi?ioee

.

Ooo ieiua o?ao?e i?ae aeaiith e?eaith cai?ith?oueny ieiuath o?ao?e, yea
iaiaaeaia cae/aeiith ia?aaieith (c aa?oeeaeueiith a?nnth), ui
i?ioiaeeoue /a?ac e?aei? ? na?aaeith oi/ee e?eai?.

?ioa?iieyoe?eiiai iiiai/eaia, oiaoi i?iaiaey ia?aaieo (3) /a?ac ana
a?eueoa /enei aeaii? e?eai?, iiaeii ?ic?aoiaoaaoe io?eiaoe a?eueoo
oi/i?noue. Ii a?eueo i?aeoe/iei aeyaey?oueny ?ioee oeyo, ye?e
a?oioo?oueny ia ii?aeiaii? ?aea? ia?aaie?/iiai ?ioa?iiethaaiiy ?c
?aea?th ae?iaeaiiy.

????????? ????????.

, ??aieo i?ii?aee?a

,

a ca(yceo c /ei, ooeaiee ?ioaa?ae iinoaia o aeaeyae? noie

(9)

Oaia? aea aei eiaeiiai ?c oeeo i?ii?aee?a canoino?ii ia?aaie?/ia
?ioa?iiethaaiiy, oiaoi noaiaii ia/enethaaoe ?ioaa?aee (9) ii iaei?e ?c
iaaeeaeaieo oi?ioe – (4), (6), (8).

Eaaei caaaiooe, ui aeoiaey/e ?c oi?ioe (4) aai (6), ie oaeei oeyoii ciia
io?eia?ii aaea a?aeii? iai oi?ioee i?yiieooiee?a ? o?aiaoe?e, (1) e (2).

Canoino?ii oaia? aei ?ioaa?ae?a (9) oi?ioeo (8), i?e oeueiio aeey
noeneino? iieiaeeii, ye ? aeua,

.

Ie io?eia?ii

,

,

. . . . . . . . . . . . . . . . . . . . . . . . . .

.

C?aooith, aeiaeath/e ii/eaiii oe? ?aaainoaa, i?eeaeaii aei oi?ioee

(10)

Aiia iineo iacao oi?ioee N?iiniia (Th. Simpson); oe??th oi?ioeith
ei?enoothoueny aeey iaaeeaeaiiiai ia/eneaiiy ?ioaa?ae?a /ano?o?, ai?ae
oi?ioeaie i?yiieooieeia ? o?aiaoe?e, ai iia – i?e oeo aea cao?aoao –
aea? cacae/ae a?eueo oi/iee ?acoeueoao.

?????????? ???? ??????? ?????????????.

,

.

, oi ae?oaee /eai ci?aaa cieeia, ai

(11)

Oaeei /eiii, io?eia?ii

,

oae, ui caeeoeiaee /eai oi?ioee (4), yeee iiiiaeth? ?? oi/i?noue ia?
aeaeyae

.

? ei?inooth/enue oei, ui ae?oaee iiiaeiee i?ae?ioaa?aeueiiai ae?aco ia
ci?ith? ciaea, ca ocaaaeueiaiith oai?aiith i?i na?aaeia iiaeaii iaienaoe

,

, ? inoaoi/ii

. (12)

aoaeaii iaoe oi/ioth oi?ioeo

.

) ii/eaiii io?eia?ii i?e cae/aeieo nei?i/aieo iicia/aiiyo

,

aea ae?ac

? ? caeeoeiaee /eai oi?ioee i?yiieooiee?a (1). Oae ye ae?ac

.

Oiio inoaoi/ii ia?ii

(13).

.

?????????? ???? ??????? ????????.

. Nei?enoaaoenue ?ioa?iieyoe?eiith oi?ioeith Eaa?aiaea ?c caeeoeiaei
/eaiii iiaeaii iaienaoe

.

, ciaeaeaii

,

oae ui caeeoeiaee /eai oi?ioee (6) aoaea

.

?ici??eiaoth/e, ye ? aeua, ? ei?enooth/enue oei, ui ae?oaee iiiaeiee
i?ae?ioaa?aeueii? ooieoe?? ? ooo ia ci?ith? ciaea, ciaeaeaii

.

??aieo /anoei

(14).

. Ie aa/aii, ui canoinoaaiiy oi?ioee o?aiaoe?e i?eaiaeeoue aei iioeaee
oiai ae ii?yaeeo, ui ? aeey oi?ioee i?yiieooiee?a.

?????????? ???? ??????? ????????.

Caa?iaiiny, ia?aoo? aei oi?ioee (8). Iiaeii aoei a, aiaeia?/ii oiio, ye
oea aoei c?iaeaii o?euee? ui, ciia nei?enoaoenue oi?ioeith Eaa?aiaea c
caeeoeiaei /eaiii ? iieeanoe

(15).

. Oiio ie c?iaeii ?iaeoa.

Ae?ac

,

iio?aeieo aei /aoaa?oiai ii?yaeeo aeeth/ii – io?eia?ii:

.

; ie ciaeaeaii, ui

oae ye

.

iaia?a?aiith, oi, ye ? a iiia?aaei?o aeiaaeeao, caeeoeiaee /eai
oi?ioee (8)

,

ei?enooth/enue oei, ui ae?oaee iiiaeiee a i?ae?ioa?aaeueiiio ae?ac? ia
ci?ith? ciaea, iiaeii i?aenoaaeoe a oaeiio aeaeyae?:

.

??aieo /anoei, oi – aeey oi?ioee N?iiniia (10) – io?eia?ii caeeoeiaee
/eai o aeaeyae?

(16).

; oaeei /eiii, oi?ioea Neiiniia ae?enii a?eueo aea?aeia, i?ae
iiia?aaei? aea? oi?ioee.

??????? 1.

Oaeno i?ia?aiie aeey aaoiiaoe/iiai ia/eneaiiy ?ioaa?ae?a ia iia?
i?ia?aioaaiiy QBASIC:

‘Ooo iienothoueny noae?

e = 2.718281828459045#

pi = 3.141592653589793#

‘Ooo caaea?oueny a?ae i?ae ?ioaa?aeueii? ooieoe??

DEF fny# (x#) = e(x# (2

DEF fncoef# (i#) = (i# MOD 2) * 2 + 2

DEF fnxi# (i#) = a# + i# * h#

DEF fnxis# (i#) = a# + i# * h# / 2

DEF fnxic# (i#) = a# + i# * h# + h# / 2

DEF fnxir# (i#) = a# + i# * h# + h# / 2

CLS

‘Ooo aaiaeyoueny iaae? ?ioaa?oaaiiy oa

‘e?euee?noue i?ii?aee?a

INPUT «Aaaae?oue ieaeith iaaeo ?ioaa?oaaiiy » a#

INPUT «Aaaae?oue aa?oith iaaeo ?ioaa?oaaiiy » b#

INPUT «Aaaae?oue e?euee?noue i?ii?aee?a » n#

‘Ooo ia/eneth?oueny e?ie

h# = (b# — a#) / n#

‘Ooo ia/eneth?oueny iaaeeaeaia cia/aiiy

‘?ioaa?aea ca iaoiaeii N?iiniia

integ# = 0

FOR i# = 1 TO ((2 * n#) — 1)

integ# = integ# + fncoef#(i#) * fny#(fnxis#(i#))

NEXT

integ# = integ# + fny#(a#) + fny#(b#)

integ# = integ# * (h# / 6)

PRINT «Simpson = «; integ#

‘Ooo ia/eneth?oueny iaaeeaeaia cia/aiiy

‘?ioaa?aea ca iaoiaeii o?aiaoe?e

integ# = 0

FOR i# = 1 TO (n# — 1)

integ# = integ# + fny#(fnxi#(i#))

NEXT

integ# = integ# + (fny#(a#) + fny#(b#)) / 2

integ# = integ# * h#

PRINT (Trapeze = (; integ#

‘Ooo ia/eneth?oueny iaaeeaeaia cia/aiiy

‘?ioaa?aea ca iaoiaeii e?aeo i?yiieooiee?a

integ# = 0

FOR i# = 0 TO (n# — 1)

integ# = integ# + fny#(fnxi#(i#))

NEXT

integ# = integ# * h#

PRINT «L Rectangle = «; integ#

‘Ooo ia/eneth?oueny iaaeeaeaia cia/aiiy

‘?ioaa?aea ca iaoiaeii oeaio?aeueieo i?yiieooiee?a

integ# = 0

FOR i# = 0 TO n#

integ# = integ# + fny#(fnxic#(i#))

NEXT

integ# = integ# * h#

PRINT «C Rectangle = «; integ#

‘Ooo ia/eneth?oueny iaaeeaeaia cia/aiiy

‘?ioaa?aea ca iaoiaeii i?aaeo i?yiieooiee?a

integ# = 0

FOR i# = 1 TO n#

integ# = integ# + fny#(fnxir#(i#))

NEXT

integ# = integ# * h#

PRINT «R Rectangle = «; integ#

??????? 2.

Aeae? iiaeai? ?acoeueoaoe ?iaioe i?ia?aie, yea aeeeaaeaia a aeiaeaoeo 1.

n=1000

Iaoiae N?iiniia -8.742278155181581D-08

Iaoiae o?aiaoe?e -8.742270585611512D-08

Iaoiae e?aeo i?yiieooiee?a 3.141505318306509D-03

Iaoiae oeaio?aeueieo i?yiieooiee?a -3.14167628761223D-03

Iaoiae i?aaeo i?yiieooiee?a -6.283265152840917D-03

n=1000

Iaoiae N?iiniia 2.000000000000067

Iaoiae o?aiaoe?e 1.999998355065565

Iaoiae e?aeo i?yiieooiee?a 1.999998355202888

Iaoiae oeaio?aeueieo i?yiieooiee?a 1.999995887392223

Iaoiae i?aaeo i?yiieooiee?a 1.999990952591778

a iaaeao a?ae 0 aei 1

n=1 n=10 n=100 n=1000 n=10000

I-ae N?iiniia ,33333333333 ,3333333333333 ,3333333333333 ,3333333333
,3333333333333

I-ae o?aiaoe?e ,5 ,335 ,33335 ,3333334999999 ,3333333349999

I-ae e?a. i?yiieooiee?a 0 ,2850000000000001 ,32835 ,3328334999999
,3332833349999

I-ae oeaio?. i?yiieooiee?a 2,5 ,44275 ,34342525 ,33433425025
,3334333425002

I-ae i?aaeo i?niieooiee?a 2,25 ,4425000000000001 ,3434249999999
,33433425

,3334333424999

a iaaeao a?ae 0 aei 1

n=1000

Iaoiae N?iiniia .7468241385662959

Iaoiae o?aiaoe?e .7468240772530558

Iaoiae e?aeo i?yiieooiee?a .7471401375268841

Iaoiae oeaio?aeueieo i?yiieooiee?a .7471916808878213

Iaoiae i?aaeo i?yiieooiee?a .7461916811378212

n=1000

Iaoiae N?iiniia .8323745796964475

Iaoiae o?aiaoe?e .8323723082182791

Iaoiae e?aeo i?yiieooiee?a .8325874590746988

Iaoiae oeaio?aeueieo i?yiieooiee?a .8319367429487694

Iaoiae i?aaeo i?yiieooiee?a .8319318081462942

????????.

O aeaii?e ?iaio? aoei ?icaeyiooi iaoiaee iaaeeaeaieo ia/eneaiue
aecia/aieo ?ioaa?ae?a, aoee aeaaaeei? oi?ioee ia/eneaiue, oi?ioee
aeiaeaoeiaeo /eai?a. ?acoeueoaoe, ye? iaaaaeai? a aeiaeaoeo 2 iai/ii
iieacothoue, ui iaea?eueo aea?aeiei ? aeei?enoaiiy oi?ioee N?iiniia.

??????????.

Ieneoiia I. N. Aeeooa?aioeeaeueiia e eioaa?aeueiia en/eneaiea aeey
AOOCia. O. 1 I.: 1968.

Ai?iaueaaa A. I., Aeaieeiaa A. I. I?aeoeeoi ii /eneaiiui iaoiaeai.

I.: 1979.

Iaoaiaoe/aneee i?aeoeeoi. I.: 1960.

. Oea ia?ii iai(yoaoe ? iaaeae?.

. Cia/eoue, aeey oaeiai iiiai/eaia oi?ioea (8) aoaeao oi/iith.

PAGE 10

Похожие записи