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
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