II e II ?O
IAOO
?aoa?ao ii eioi?iaoeea ia oaio «Iaeao MathCAD»
oaeoeueoao: AAO
a?oiia: A – 514
nooaeaio: Eiaaeaiei N.A.
i?aiiaeaaaoaeue: Iaiiiiaa A.A.
Iiaineae?ne – 1997
Niaea?aeaiea :
Aaaaeaiea________________________________________________3
Aiciiaeiinoe nenoaiu____________________________________4
2.2 Aeieoiaio 1______________________________________________5
2.3 A?aoe/aneea aiciiaeiinoe _______________________________6
Aeieoiaio 2______________________________________________7
Aeieoiaio 3______________________________________________8
Aeieoiaio 4______________________________________________9
Aeieoiaio 5______________________________________________10
?aaioa nenoaiu n oaeeaie_______________________________11
Iauaiea n aiaoieie ono?ienoaaie_______________________11
Nenoaia MathCAD noaiiaeony aieaa aeaeie
Nenoaia MathCAD aa?nee 3.0______________________________11
MathCAD PLUS 6.0
?aoaiea aeaaa?ae/aneeo nenoai_________________________12
Aaeeeieaiiay nai??ea MathCAD_________________________15
Ni?oe?iaea___________________________________________16
Eeiaeiay aii?ieneiaoeey ______________________________16
Aeeooa?aioeeaeueiua o?aaiaiey_________________________17
I?ia?aiie?iaaiea____________________________________17
4. MathCAD eee i?ia?aiie?iaaiea ia ycueao aunieiai o?iaiy _18
1. Aaaaeaiea
I
aoaiaoe/aneea e iao/ii – oaoie/aneea ?an/aou yaeythony aaaeiie noa?ie
i?eiaiaiey ia?niiaeueiuo eiiiuethoa?ia . *anoi iie auiieiythony n
iiiiuueth i?ia?aii , iaienaiiuo ia ycuea aunieiai o?iaiy, iai?eia?
Aaeneea eee Ianeaea. Naaiaeiy yoo ?aaioo ia?aaeei auiieiyao iau/iue
iieueciaaoaeue IE. Aeey yoiai ii auioaeaeai eco/aoue ycuee
i?ia?aiie?iaaiey e iiiai/eneaiiua, iiae/an aanueia oiieea eai?eciua
/eneaiiua iaoiaeu iaoaiaoe/aneeo ?an/aoia. Ia?aaeei i?e yoii ec iiae
?oee niiniaiiai oeceea, oeieea eee eiaeaia?a auoiaeyo aeae?eea io
niaa?oainoaa i?ia?aiiu.
Yoi ia aiieia ii?iaeueiia iieiaeaiea iiaeao eciaieoue e eo/oaio
i?eiaiaiea eioaa?e?iaaiiuo i?ia?aiiiuo nenoai aaoiiaoecaoeee
iaoaiaoe/aneeo ?an/aoia (Eureka, MathCAD, MatLab e ae?.). Caeanue
?anniao?eaathony aiciiaeiinoe e yaiethoeey iaeiie ec oaeeo nenoai –
MathCAD.
Oe?ia MathSoft Inc.(NOA) auionoeea ia?aoth aa?neth nenoaiu a 1986 a.
Aeaaiay ioee/eoaeueiay iniaaiiinoue nenoaiu MathCAD caeeth/aaony a a?
aoiaeiii ycuea, eioi?ue iaeneiaeueii i?eaeeae?i e anoanoaaiiiio
iaoaiaoe/aneiio ycueo, eniieuecoaiiio eae a o?aeoaoao ii iaoaiaoeea, oae
e aiiaua a iao/iie eeoa?aoo?a. A oiaea ?aaiou n nenoaiie iieueciaaoaeue
aioiaeo oae iacuaaaiua aeieoiaiou. Iie iaeiia?aiaiii aeeth/atho iienaiey
aeai?eoiia au/eneaiee, i?ia?aiiu oi?aaeythuea ?aaioie nenoai, e
?acoeueoao au/eneaiee. Ii aiaoiaio aeaeo oaenou iaei iaiiieiatho iau/iie
i?ia?aiiu .
2. Aiciiaeiinoe nenoaiu
MathCAD iauaaeeiyao a naaa i?inoie oaenoiaue ?aaeaeoi?, iaoaiaoe/aneee
eioa?i?aoaoi? e a?aoe/aneee i?ioeanni?. Nenoaia i?eaioe?iaaia ia IBM –
niaianoeiua eiiiuethoa?u. Oiiiyiooua auoa aeieoiaiou niaea?aeao
oaenoiaua, oi?ioeueiua e a?aoe/aneea aeiee. Ia ye?aia aeenieay iie
caieiatho i?yiioaieueiua iaeanoe, a?aieoeu eioi?uo iau/ii ia aeaeiu (ii
i?e aaaaeaiee a aeie eo?ni?a i?ioeaieaaeauea oaeu i?yiioaieueiuo
iaeanoae ioia/athony i?yiioaieueieeaie). Aeiee auiieiythony neaaa
iai?aai e naa?oo aiec.
Iiaeaioiaea e eniieiaiea aeieoiaioia MathCAD iiaeao inouanoaeyaony n
iiiiuueth: aeaaiiai iaith e nioneathueony iiaeiaith (aeey eo iiyaeaiey
iaiaoiaeeii iaaeaoue eeaaeoo
iaaeaoeai eeaaeoe
eiiaeiaoeee iau/iuo eeaaeo, a oae aea n iiiiuueth oi?aaeythueo eeaaeo. A
iineaaeiai neo/aa, iai?eia?, iaaeaoea eeaaeoe
nenoaiu iiaeneacie,
Ec ?aaeeiia ?aaiou iaiaoiaeeii iniai ioiaoeoue ?aaeeiu auto e manual.
?aaeei auto iaania/eaaao aaoiiaoe/aneea au/eneaiey n?aco iinea caa?ocee
aeieoiaioa ii ia?a aai i?ie?ooee (ne?ieeeiaa) ia ye?aia aeenieay. A yoii
?aaeeia ne?ieeeia iuooeii caiaaeeai, iniaaiii i?e eniieueciaaiee nenoaiu
ia IE eeanna IBM PC XT aac iaoaiaoe/aneiai nii?ioeanni?a. ?aaeei manual
(?o/iie) iicaieyao inouanoaeyoue auno?ue ne?ieeeia aac auiieiaiey
aeieoiaioa. Aeey i?iaaaeaiey au/eneaiee io ia/aea aeieoiaioa e aei
eiioea aeaeeiie ia ye?aia aeenieay aai /anoe ioaeii iaaeaoue eeaaeoo
Oaenoiaua aeiee yaeythony ia aieaa /ai eiiiaioa?eyie. Eo iacia/aiea –
iiynieoue nooia e eaeiie/iia iaoaiaoe/aneia iienaiea, i?aaenoaaeaiiia ia
aoiaeiii ycuea nenoaiu. Oaenoiaua aeiee iiaoo auoue iieiioi?iaoiuie (ia
anth aeeeio no?iee) e a aeaea i?yiioaieueieeia ia?aie/aiiuo ?acia?ia.
Anee aaanoe ciae «eaau/ee», oi ia ye?aia aeenieay iiyaeony ia?a
eaau/ae, iaaeaeo eioi?uie aaiaeeoue e ?aaeaeoe?iaaoue oaeno a iau/iii
ii?yaeea.
Oaenoiaue ?aaeaeoi? nenoaiu ia iaeaaeaao anaie aiciiaeiinoyie
niaoeeaeece?iaaiiuo ?aaeaeoi?ia oaenoa, iaeiaei iicaieyao
ei??aeoe?iaaoue oaenou, au?aaieaaoue eo ii e?ath, ia?aiauaoue oaenoiaua
aeiee a ethaia ianoi aeieoiaioa e o.ae. Aanueia oaeiaiu n?aaenoaa
?aaeaeoe?iaaiey aeieoiaioia, iicaieythuea, a /anoiinoe, noe?aoue
oeacaiiue eo?ni?ii aeie (eeaaeoa
(eeaaeoa
nenoaiu, ia?aiiny aeiee ec iaeiiai ieia a ae?oaia.
Iaoaiaoe/aneee eioa?i?aoaoi? nenoaiu – iaeaieaa eioa?aniay a? /anoue.
Iaoaiaoe/aneea oi?ioeu, iiaeeaaeauea eioa?i?aoaoeee, caienuaathony a
iauai?eiyoii aeaea. Iai?eia?, au/eneaiea eaaae?aoiiai ei?iy ec aeaoo a
nenoaia MathCAD caaea?ony eae (2 =, a ia a aeaea PRINT SQR (2) , eae
yoi aeaeaaony, neaaeai, ia Aaeneea. Aeey aaiaea oi?ioe eniieuecothony
oaaeiiu, aaiaeeiua ii?aaeae?iiuie eiiaeiaoeeyie eeaaeo. Eiaaony
aiciiaeiinoue eciaiaiey oi?iaoa i?aaenoaaeaiey /enae, iai?eia? /enea
ciaeia iinea ?acaeaeeoaeueiie oi/ee, iia?aoiinoe au/eneaiee e
iaicia/aiey iieiie aaeeieoeu (i ia j e iaiai?io) i?e iia?aoeeyo n
eiiieaeniuie /eneaie.
*oiau auaanoe ia ye?ai aeenieay a?aoe/aneee aeie, iaiaoiaeeii
onoaiiaeoue eo?ni? ia ianoi eaaiai aa?oiaai aoaeouaai a?aoeea e aaanoe
ciae @. Ia ye?aia aeenieay iiyaeony i?yiioaieueiee – oaaeii aoaeouaai
a?aoeea. Ia/eiay n aa?nee 2.0, ianooaa iiaeii e ia oeacuaaoue – ii
au/eneyaony aaoiiaoe/anee.
Aiciiaeiinoe nenoaiu iiyniytho neaaeothuea eiie?aoiua i?eia?u.
Iacaaiea iia?aoeee Caaeaiea iia?aoeee
*eneaiiue i?eia?
2
Aicaaaeaiea a noaiaiue X(Y
3 = 9
Au/eneaiea oaeoi?eaea X!
4! = 24
Au/eneaiea eaaae?aoiiai ei?iy \X
(9 = 3
Au/eneaiea aaniethoiiai cia/aiey (X
(-5( = 5
Neiaeaiea
X+Y 2 + 3 = 5
Oiiiaeaiea
X*Y 2(3 = 6
12
Aeaeaiea
X/Y (3 =
4
I?enaaeaaiea cia/aiee ia?aiaiiie X:Y
X : = 8
Auaiae cia/aiey ia?aiaiiie X =
X = 8
Caaeaiea oeeeee/aneie ia?aiaiiie i : = N1..N2
i : = 1,…,5
Noiie?iaaiea /eaiia ?yaea i \ X
(X = 2i
i i
3
Ia?aiiiaeaiea /eaiia ?yaea i # X
( X = 3.84(10
i
i
1
Au/eneaiea ii?aaeae?iiiai eioaa?aea x&f(x)
( (2xdx = 0.93
(
0
Caaeaiea ooieoeee iieueciaaoaey f(X) : …
f(x): = sin x
Eieoeeaeecaoeey ia?aiaiiie o : …
x : = 1, f (x) = 0.841
df(x) = 0.54
Au/eneaiea i?iecaiaeiie x ? f (x)
( dx
Caaeaiea e i?iaa?ea ia?aaainoaa X > Y
5 > 4 = 1, 4 > 5 = 0
Au/eneaiea niaoeeaeueiuo ooieoeee Jn(x) =
Jn(1,.5) = 0. 242
Aannaey e eioaa?aea aa?iyoiinoe J1(x) =
J1(.5) = 0.242
erf(x) = erf(1) = 0.843
Aeieoiaio 1. I?eia?u auiieiaiey iaoaiaoe/aneeo iia?aoeee .
Aeieoiaio 1 eeethno?e?oao caaeaiea e eniieiaiea a nenoaia
MathCAD ?yaea iaoaiaoe/aneeo aeaenoaee. N?aaee ieo au/eneaiea
aeaaa?ae/aneeo, o?eaiiiiao?e/aneeo e aeia?aiee/aneeo ooieoeee, noii e
i?iecaaaeaiee ?yaeia, ii?aaeae?iiiai eioaa?aea e i?iecaiaeiie.
A MathCAD i?aaeoniio?aiu n?aaenoaa aeey ?aoaiey iaeeiaeiuo o?aaiaiee,
ia eiathueo aiaeeoe/aneeo ?aoaiee. Oae , ooieoeey root (f(x,y,z,),x)
euao cia/aiea ia?aiaiiie x, i?e eioi?ii f(x,y,z) = 0. Aieaa neiaeiua
au/eneaiey (?aoaiea nenoai iaeeiaeiuo o?aaiaiee, ieieiecaoeey ooieoeee
ianeieueeeo ia?aiaiiuo e ae?.) iaania/eaathony i?aaiecaoeeae
au/eneeoaeueiiai aeiea, ioe?uaaaiiai neiaii Given.
Aeieoiaio 2 iieacuaaao ?aoaiea aeooaeueiie aeey naaeiaiaea eee ethaeoaey
aaiueee caaea/e: eae, naeaay aeaeaciue eeno, iieo/eoue yuee caaeaiiiai
iau?ia. Ieacuaaaony, anoue o?e ?aoaiey. ssuee iiaeao auoue iaaeoaieei,
ii n aeiii aieueoie ieiuaaee eee aeoaieei, ii n aeiii iaeie ieiuaaee.
O?aouea ?aoaiea oece/anee ia?aaeueii. Ai aoi?ie /anoe aeieoiaioa
iieacaii ?aoaiea caaea/e i eiino?oe?iaaiee yueea iaeneiaeueiiai iau?ia,
au? aieaa aeooaeueiie i?e iaoai aeaoeoeeoa no?ieoaeueiuo iaoa?eaeia.
Niaoeeaeenoia a yeaeo?ioaoieea e ?aaeeioaoieea iaaa?iyea i?eaea/?o
niiniaiinoue nenoaiu MathCAD auiieiyoue ana i?aaeoniio?aiiua a iae
au/eneaiey eae n aeaenoaeoaeueiuie, oae e n eiiieaeniuie /eneaie. A
aeieoiaioa 3 i?eaaaeaiu i?eia?u iia?aoeee n eiiieaeniuie /eneaie,
ia/eiay io i?inouo e eii/ay neiaeiuie. E iineaaeiei ioiineony
au/eneaiea eiiieaeniiai e?oaiaiai eioaa?aea, a oiaea eioi?iai
auiieiyaony /eneaiiia eioaa?e?iaaiea e aeeooa?aioee?iaaiea n
eiiieaeniuie a?aoiaioaie.
Ia/eiay n aa?nee 2.0 a MathCAD aaaae?i ooieoeeiiaeueii iieiue iaai?
aaeoi?iuo e iao?e/iuo iia?aoeee. Yoi nouanoaaiii iaeaa/aao ?aoaiea
caaea/ eeiaeiie aeaaa?u. A ea/anoaa i?eia?a a aeieoiaioa 3 aea?ony
?aoaiea nenoaiu eeiaeiuo o?aaiaiee n eiiieaeniuie eiyooeoeeaioaie, a
oiaea eioi?iai i?iecaiaeeony ia?auaiea eiiieaeniie iao?eoeu. E oaeei
o?aaiaieyi i?eaiaeeo aiaeec yeaeo?e/aneeo e yeaeo?iiiuo oeaiae ia
ia?aiaiiii oiea.
Aanueia i?eaeaeaoaeueiu n?aaenoaa eeiaeiie e nieaei-eioa?iieyoeee e
yeno?aiieyoeee aeaiiuo. Eeiaeiay eioa?iieyoeey a?aoe/anee icia/aao
i?inoi niaaeeiaiea oceiauo oi/ae a?aoeea io?aceaie i?yiuo. A ioee/ee io
ia? nieaei-eioa?iieyoeey iaiiieiaao niaaeeiaiea yoeo oi/ae n iiiiuueth
aeaeie eeiaeee. No?iai iaoaiaoe/anee yoi icia/aao i?iaaaeaiea /a?ac
eaaeaeua o?e oi/ee eeiee, iienuaaaiie eoae/aneei iieeiiiii. I?e yoii ai
anao noueoaiuo oi/eao iaania/eaaaony iai?a?uaiinoue eae ia?aie , oae e
aoi?ie i?iecaiaeiie eaaeaeiai ec iieeiiiia. Nieaei-eioa?iieyoeey – yoi
iiuiia n?aaenoai i?aaenoaaeaiey aeaiiuo, caaeaiiuo iaaieueoei /eneii
oceiauo oi/ae.
Aeieoiaio 4 aeaiiino?e?oao caaeaiea a aeaea aaeoi?ia iai?yaeaiee e oieia
N – ia?aciie aieueo – aiia?iie oa?aeoa?enoeee ooiiaeueiiai aeeiaea.
Caoai i?iaiaeeoueny eioa?iieyoeey-yeno?aiieyoeey yoie oa?aeoa?enoeee
iienaiiuie a aeieoiaioa niiniaaie . Iiaeii caiaoeoue ,/oi nieaei-
eioa?iieyoeey a aeaiiii neo/aa i?aaeii/oeoaeueiaa eeiaeiie .
MathCAD eiaao iaoe?iue iaai? noaoe/aneeo iia?aoi?ia e ooieoeee
,iaania/eaathueo aaia?aoeeth neo/aeiuo /enae ,a oaeaea au/eneaiea
n?aaeiaai ,aeenia?nee e aa?eaoeee ,eiyooeoeeaioia eeiaeiie ?aa?annee,
?yaea niaoeeaeueiuo iaoaiaoe/aneeo ooieoeee .Aeieoiaio 5 i?aaiecoao
aaia?aoeeth 200 neo/aeiuo /enae ,eo i?aaenoaaeaiea ia ieineinoe
,au/eneaiea ?yaea noaoenoe/aneeo ia?aiao?ia e iino?iaiea aenoia?aiiu
?ani?aaeaeaiey .
A?aoe/aneea aiciiaeiinoe nenoaiu.
Iu oaea ioia/aee a?aoe/aneea aiciiaeiinoe nenoaiu. MathCAD iicaieyao
no?ieoue naiua ?aciiia?aciua a?aoeee: a aeaea?oiaie e a iiey?iie nenoaia
eii?aeeiao, n ianooaaiie naoeie e aac ia?, n eeiaeiui e eiaa?eoie/aneei
ianooaaii, n ioiaoeie eeiee i?yiioaieueieeaie, e?anoaie, ?iiaaie e o.ae.
Caaeaiea aeaea e ?acia?a a?aoeea inouanoaeyaony aaiaeii
niioaaonoaothuaai oi?iaoa. Aeey caaeaiey oi?iaoa iiaeii aaanoe aioo?ue
oaaeiia a?aoeea eo?ni? e iaaeaoue eeaaeoo
aeaiiua i oi?iaoa caaeaiiiai a?aoeea, iai?eia?:
logs = 0,0 subdivs = 1,1 size
= 5,15 type = 1
Anee ia?aiao?u logs – ioee, a?aoee no?ieony n eeiaeiui ianooaaii, eia/a-
n eiaa?eoie/aneei (a yoii neo/aa ia?aiao?u oeacuaatho /enei aeaeaiee
oeaeu a i?aaeaeao aeaeaaeu) . Ia?aiao?u subdivs caaeatho /enei aeaeaiee
oeaeu, a ia?aiao?u size – ?acia?u a?aoeea, au?aaeaiiua a ciaeiianoao.
Ai anao yoeo neo/ayo ia?aue ia?aiao? ioiineony e ine Y a?aoeea, aoi?ie
– e ine O. Ia?aiao? type iienuaaao oeacaiea i oeia a?aoeea a aeaea iaeie
eee aieueoie eaoeineie aoeau. Iai?eia?, oeacaiea L caaea?o nieioiie
a?aoee, d «no?ieo» oi/ee a oceao e o.ae. Aiciiaeia eiiaeiaoeey oaeeo
oeacaiee.
Eiino?oe?iaaiea aeaeaciiai yueea caaeaiiiai
iau?ia
VO : = 7.5
Caaeaiiue iau?i yueea
W : = 4
Oe?eia eenoa
L : = 8
Aeeeia eenoa
X : = 0,0.2 .. 5
?annoiyiea io eeiee
ioaeaa eenoa
V(X) : = (L – 2X)((W – 2X)(X
Iau?i yueea
F(X) : = V(X) -VO
Iniiaiia o?aaiaiea
A?aoe/aneia ?aoaiea
caaea/e
60
F(X), 0
20
0 X
5
?aoaiea caaea/e /eneaiiui iaoiaeii
Eieoeeaeecaoeey ?aoaiea
Eiiiaioa?ee
X : = 0 root(V(X) – VO, X) = 0.297
Ieineee yuee
X : = 1 root(V(X) – VO, X) = 1.5
Aeoaieee yuee
X : = 4 root(V(X) – VO, X) = 4.203
?aoaiea oece/anee
ia?aaeueii (X > W/2)
Eiino?oe?iaaiea aeaeaciiai yueea iaeneiaeueiiai iau?ia
X : = 1
Eieoeeaeecaoeey
Given Ia/aei aeiea
?aoaiey
V(X) : = (L – 2X)((W – 2X)(X Iniiaiia o?aaiaiea
V(X) ( 100 Iau?i, caaaaeiii
i?aauoathuee
o?aaoaiue
X M : = minerr ( X ) Iiene iioeiaeueiiai
cia/aiey O
X M = 0.848 Iaeaeaiiia
iioeiaeueiia cia/aiea O
V(X M ) = 12.317 Iaeneiaeueii
aiciiaeiue iau?i yueea
Aeieoiaio 2. Caaea/a i eiino?oe?iaaiea aeaeaciiai yueea caaeaiiiai e
iaeneiaeueiiai
iau?ia
Caaeaiea iieiie aaeeieoeu
i : = (-1
A?eoiaoe/aneea iia?aoeee
Z1 : = 2 + 3i Z2 : = 4 + 5i
Z : = Z1 + Z2 Z = 6 + 8i
Re ( Z ) = 6 Im ( Z ) = 8
sin ( Z1 ) = 9.154 – 4. 169i
Au/eneaiea eiiieaeniuo ei?iae eaaae?aoiiai o?aaiaiey
o : = 0 + 3i ( Eieoeeaeecaoeey
ia?aiai ei?iy )
2
root(x + 2x +15, x) = – 1 + 3.742i ( Ia?aue ei?aiue )
x : = 0 – 3i ( Eieoeeaeecaoeey
aoi?iai ei?iy )
2
root(x + 2x +15, x) = – 1 + 3.742i ( Aoi?ie ei?aiue )
?aoaiea nenoai eeiaeiuo o?aaiaiee n eiiieaeniuie eiyooeoeeaioaie
(10 + 200i 0 – 200i ( (5 + 0i(
A : =( ( B : = ( (
(0 – 200i 0 + 170i( (0 + 0i(
-1
X : = A B (?aoaiea n iiiiuueth
iao?e/iuo iia?aoi?ia)
(0.037 + 0.131i (
O : =( ( (Aaeoi? ?aoaiey)
(0.044 + 0.154i (
Au/eneaiea eiiieaeniiai e?oaiaiai eioaa?aea
1
f(x) : = ( z(t) : = cos(t) +
sin(t)
x
-4
te : = 6.2832 TOL : = 10
(Iia?aoiinoue)
te
( (d (
(f(z(t))( ( z(t)( dt = 6.283
(dt (
0
Aeieoiaio 3. I?eia?u iia?aoeee n eiiieaeniuie /eneaie.
Caaeaiea AAO ooiiaeueiiai aeeiaea
0
0
.2
50 ( Aaeoi?u enoiaeiuo aeaiiuo,
.4
20 niaea?aeauea eii?aeeiaou
U: = .6 I : = 3
naie oceiauo oi/ae AAO )
.8
4
1.0
14
1.2
55
Eeiaeiay eioa?iieyoeey AAO
linterp(U, I, 0.15 ) = 37.5
(I?eia?u eioa?iieyoeee AAO)
linterp(U , I, 0.5) = 11.5
J(V) : = linterp(U, I, V)
(Caaeaiea ooieoeee J(V) AAO )
V : = -0.05, – 0.025 .. 1.2
40
Ia a?aoeea AAO i?e eeiaeiie
eioa?iieyoeee io/?oeeai aeaeiu
io?acee i?yiuo, e e?eaay A AO
J(V),0
iaanoanoaaiii
-40
-0.05 V 1.2
Eioa?iieyoeey eoae/aneeie nieaeiaie
IS : = cspline(U ,I) (Aaeoi?u aoi?uo i?iecaiaeiuo)
interp (IS, U, I, 0.15) = 49.493 (I?eia?u nieaei – eioa?iieyoeee)
interp (IS, U, I, 0.5) = 8.191
J(V) : = interp (IS, U, I, V ) (Caaeaiea ooieoeee J(V) AAO)
V : = -0.05, – 0.025 .. 1.2
40
E?eaay AAO i?e nieaei –
eioa?iieyoeee ioee/aaony
ieaaiinoueth e iioiaea ia
J(V),0
?aaeueioth e?eaoth AAO
-40
-0.05 V 1.2
Aeieoiaio 4. Eeiaeiay e nieaei – eioa?iieyoeey N –
ia?aciie aieueoaiia?iie oa?aeoa?enoeee (AAO) ooiiaeueiiai aeeiaea .
Aaia?aoeey 200 neo/aeiuo /enae n ?aaiiia?iui ?ani?aaeaeaieai
i : = 1..200 x : = rnd ( 10
)
i
A?aoe/aneia i?aaenoaaeaiea neo/aeiuo /enae
10
o
A?aoee iaaeyaeii iieacuaaao
i
?aaiiia?iinoue ?ani?aaeaeaiey
neo/aeiuo /enae
0
1 i
200
Au/eneaiea iniiaiuo noaoenoe/aneeo ia?aiao?ia ianneaa o
mean(x) = 4.619 var(x) = 8.869
max (x) = 9.95 min (x) = 0
stdev (x) = 2.978
Iiaeaioiaea aeaiiuo e iino?iaieth aenoia?aiiu
N : = 10 j : = 0..N k : = 0..N – 1
10
intervals : = 1 + j ( P : = hist (intervals, x
)
j N
Aenoia?aiia ?ani?aaeaeaiey /enae a ianneaa o
30
P
k
0
0 intervals
10
k
Aeieoiaio 5. Aaia?aoeey neo/aeiuo /enae e oa?aeoa?enoeee eo
?ani?aaeaeaiey.
A?aoeee iiaeii ia?aiauaoue a ethaia ianoi aeieoiaioa, oeacaiiia
iieiaeaieai eo?ni?a, iie iiaoo eiaoue ethaua ?acia?u. Ia iaeiii a?aoeea
iiaeii no?ieoue ianeieueei e?eauo; aeey yoiai a oi?iaoa iinea neiaa type
ioaeii ia?a/eneeoue ia?aiao?u e?eauo, ?acaeaeyy eo caiyouie.
Aa?ney 2.50 nenoaiu iaania/eaaao aiciiaeiinoue iino?iaiey iiaa?oiinoae e
oeao?. I?e yoii iaiaoiaeeii caaeaoue ooieoeeth aeaoo ia?aiaiiuo e
noi?ie?iaaoue iao?eoeo n oneiaiui eiaiai I – iannea oceiauo oi/ae.
?aaioa n oaeeaie
?aaeeciaai e eiii?o oaeeia, niaea?aeaueo neiaeiua a?aoe/aneea iino?iaiey
ec ae?oaeo nenoai, oaeeo, eae AutoCAD e TurboCAD. Aeey yoiai n iiiiuueth
niaoeeaeueiie i?ia?aiiu mostrans, aoiaeyuae a nenoaio, ioaeii
i?aia?aciaaoue eiii?oe?oaiue oaee n ?anoe?aieai mcd. Oaeie oaee iinea
caa?ocee eiiaiaeie Load aucuaaao iino?iaiea a?aoeea, aa?oiee eaaue oaie
eioi?iai caaea?ony iieiaeaieai eo?ni?a.
Iauaiea n aiaoieie ono?ienoaaie
Nenoaia MathCAD iaeaaeaao iaoe?iuie aiciiaeiinoyie aeey iauaiey n
aiaoieie ono?ienoaaie. Iiieii caiene e n/eouaaiey aeieoiaioia
i?aaeoniio?aia caienue e n/eouaaiea oaeeia , o?aiyueo ?acee/iua
aeaiiua, – aieioue aei aaeoi?ia e iao?eoe n eiiieaeniuie
eiyooeoeeaioaie. Yoi iicaieyao eniieueciaaoue nenoaio aeey ia?aaioee
aeaiiuo, iinooiathueo io aiaoieo ono?ienoa. Iiaeaea?aeeaathony ana
iniiaiua oeiu aeenieaaa: iiiio?iiiue Hercules, CGA, EGA, VGA e ae?.
Iineaaeiea aa?nee nenoaiu (ia/eiay n 2.50 ) iiaeaea?aeeaatho ?aaioo
ii/oe n 40 oeiaie i?eioa?ia e ieiooa?ia, aeeth/ay 9 e 24 –
eaieue/aoua i?eioa?u n aeaoooeaaoiie e iiiaioeaaoiie ia/aoueth e
eaca?iua i?eioa?u. Aaoiiaoe/anee iaania/eaaaony ?aaioa n
nii?ioeanni?aie iaoaiaoe/aneeo iia?aoeee.
Nenoaia MathCAD noaiiaeony aieaa aeaeie
Nenoaia MathCAD aa?nee 3.0
A nenoaio MathCAD aa?nee 3.0 (oe?ia Mathsoft ), i?aaeiacia/aiioth aeey
auiieiaiey iao/ii – oaoie/aneeo au/eneaiee, aaaae?i ?yae iiauo iaeia ec
eioi?uo iicaieyao ?aaioaoue a n?aaea Windows. Ii – aeaeeiiio, eo
iiyaeaiea ia?aaeoao anao oa6o, eoi eiaao aeaei n ia?aaioeie /enae.
Nenoaia MathCAD – yoi e?aeia a inaiaiee e iaeiia?aiaiii iiuiia n?aaenoai
aeey auiieiaiey enneaaeiaaiee. N oi/ee c?aiey ooieoeee, eioi?ua iia
auiieiyao, MathCAD iiaeii n?aaieoue n ?aai/ei aeieiioii eiaeaia?a eee
o/?iiai. Ia naieo eenoeao – eaae?ao ye?aia – iia iicaieyao
eiiaeie?iaaoue o?aaiaiey, caiaoee e a?aoeee. ?aaioay iaae caaea/ae ,
iau/ii eniieuecoaony «aeiaa?ao» ec caienae ia eenoeao aoiaae e
?ania/aoie, iieo/aiiuo n iiiiuueth yeaeo?iiiuo oaaeeoe. I?iaee?aynue
/a?ac au/eneaiey n iiiiuueth nenoaiu MathCAD, ia ioaeii i?eaaaaoue ie e
eaeei ae?oaei n?aaenoaai. *oiau iieueciaaoueny nenoaiie, aai ia ioaeii
aea?aeaoue a oia iiiaeanoai niaoeeaeueiuo iaicia/aiee, eae yoi o?aaoaony
a neo/aa yeaeo?iiiuo oaaeeoe. I?aaeony e oi, /oi iiaeii o?aaiaiey a oii
aeaea, a eaeii iie iau/ii ecia?aaeathony a eieaao e ia eeanniuo aeineao
.
A yoo aa?neth nenoaiu aaaaeaiu neiaieueiua au/eneaiey, aac eioi?uo ia
iaoiaeeony ie iaeei na?ue?ciue iaoaiaoe/aneee iaeao. Neiaieueiue
i?ioeanni? aace?oaony ia iaeaoa Mapple oe?iu Waterloo Mapple Software.
MathCAD i?aaeeaaaao aeiaieueii iieiue iaai? ano?iaiiuo ooieoeee. I?e
iiaeaioiaea aeaiiie aa?nee auee aeiaaaeaiu aeaa iiaua iieaciua ooieoeee,
iaania/eaathuea iaoiaeaeaiea nianoaaiiuo /enae e nianoaaiiuo aaeoi?ia
aeey aauanoaaiiuo iao?eoe. Nenoaia aeeth/aao oaia?ue ano?iaiioth
i?ia?aiio, eioi?ay eiio?iee?oao aaeeieoeu ecia?aiey, e ?aaeaeoi? oi?ioe.
*oiau oaa?a/ue aan io iaiaoiaeeiinoe aueneeaaoue oi?ioeu, eioi?ua
i?eaiaeyony oieueei a ni?aai/iuo ecaeaieyo, a aeaiioth aa?neth nenoaiu
aeeth/ai yeaeo?iiiue ni?aai/iee. Ii iaania/eaaao ye?aiiua iiaeneacee
eioi?ua i/aiue i?eaiaeyony iiae/eai.
Eiathony, iaeiaei, aeaa iiiaioa, eioi?ua iaaa?iyea ia iii?aayony a?
iieueciaaoaeyi. Ai – ia?auo, i?e eniieueciaaiee 35 – ni ye?aia,
i?eoiaeeony iai?yaaoue aeaca, /oiau ?acaeyaeaoue i/aiue iaeaiueeea
oeaaoiua ieeoia?aiiu. E ai – aoi?uo, ea/anoai ecia?aaeaiey a?aoeeia
inoaaeyao aeaeaoue eo/oaai.
MathCAD PLUS 6.0
?aoaiea aeaaa?ae/aneeo nenoai
Eo/oa iaeei ?ac oaeaeaoue[noaio caaea/e],/ai noi ?ac oneuoaoue [a?
oneiaea] – oaeia ?anoe?aiea iineiaeoeu iiaeii ioianoe ei anai
i?eeeaaeiui i?ia?aiiai, ?aaioathuei iiae oi?aaeaieai iia?aoeeiiiie
nenoaiu Windows, eioi?oth ia c?y iacuaatho a?aoe/aneie iaiei/eie. Iaeao
MathCAD a yoii niunea – ia eneeth/aiea. ?aaioay a n?aaea Windows, iiaeii
n iiiiuueth a?aoe/aneiai ?aaeaeoi?a PaintBrush (eee eaeiai – oi )
ae?oaiai ia?eniaaoue noaio caaea/e, a iioii /a?ac Aooa? Iaiaiia
ClipBoard ia?aianoe ?enoiie a aeieoiaio MathCAD. Anee oaia?ue a n?aaea
MathCAD iiaeaanoe e ?enoieo eo?ni? iuoe e aeaa ?aca uaeeiooue ii a?
eaaie eiiiea, oi ia?aieaiea ?enoiea n?aco eciaieony – ?enoiie
ia?aian?ony a n?aaeo PaintBrush, aaea aai iiaeii aei?aaioaoue, a iioii
iiyoue aa?iooue a MathCAD.
Neiaaniia iienaiea caaea/e iiaeii aaanoe a MathCAD – aeieoiaio ?aia?eaie
(eiiiaioa?eyie). Iaeao MathCAD iai?oaeiaai oaenoiaui i?ioeanni?ii,
iicaieythuei ioi?ieoue, iai?eia?, iao/ioth noaoueth, ia i?eaaaay e
niaoeeaeece?iaaiiui n?aaenoaai. N ae?oaie noi?iiu, Aooa? Iaiaiia
ClipBoard iiiiaeao ia?aianoe o?aaiaiou MathCAD – aeieoiaioa a Word –
aeieoiaio e oai aeiioi?ieoue eo. A oanoie aa?nee – MathCAD a iaith FILE
(Oaee) iiyaeeny ioieo Export Worksheet (Yenii?o), nouanoaaiii
iaeaa/athuee yoo ?aaioo.
?aoaiea ethaie caaea/e a ethaie i?ia?aiiiie n?aaea, eae i?aaeei,
ia/eiaaony n aaiaea enoiaeiuo aeaiiuo. ?aaioay n ycueii BASIK (eee n
eaeei – oi ae?oaei ), aaiaey ia?aiaiiua e caaeaaay ei ii?aaeae?iiue oei,
i?ia?aiieno caaioeony ia i oeceea ?aoaaiie caaea/e, a i… iaiyoe
iaoeiu. Oei /eneiaie ia?aiaiiie n oi/ee c?aiey i?ia?aiienoa –
i?eeeaaeieea – yoi aoaaeci oao a?ai?i, eiaaea iaiyoue iaoeiu auea iaeiei
ec eeieoe?othueo oaeoi?ia i?e ?aoaiee caaea/e. Iaeao MathCAD a yoii
niunea ?anoi/eoaeai – ii i?enaaeaaao anai /eneiaui ia?aiaiiui aeaieioth
oi/iinoue n 15 ciaeaie a iaioenna. Yoe ia?aiaiiua i?aaenoatho ia?aae
aeacaie iieueciaaoaey eeai a oeaei/eneaiiii (17, iai?eia? ), eeai a
aauanoaaiiii (3.14), eeai a eiiieaeniii aeaea. Ii /a?ac ciae «: =» a
n?aaea MathCAD iiaeii i?enaieoue ia?aiaiiie ia oieueei eiie?aoioth
aaee/eio (20, 1,10, 30 – iaoaiaoeea caaea/e), ii e ?acia?iinoue
(iuethoii, iao?, oaeiaie a?aaeon – oeceea caaea/e ). Aeey i?enaaeaaiey
aaee/eia ?acia?iinoe ca iae noaaeony ciae «iiiiiaeeoue» e aaiaeeony
iacaaiea niioaaonoaothuae ?acia?iinoe. A iiaeii iinooieoue ii ae?oaiio –
iaaeaoue ia iaiaee eino?oiaioia ia eiiieo n ecia?aaeaieai ia?iie
e?oaeee. Iinea yoiai ia aeenieaa iiyaeony ieii ni nieneaie oece/aneeo
aaee/ei (aeeeia, a?aiy, nei?inoue e o.ae.) n niioaaonoaothuei ei
?acia?iinoyi (iao?, naeoiaea, iao? a naeoiaeo e o.ae.),iaeio ec eioi?uo
iiaeii anoaaeoue a MathCAD – aeieoiaio.
MathCAD ia iacuaaeny au iaoaiaoe/aneei iaeaoii, anee au ii ia iia
?aoaoue nenoaiu aeaaa?ae/aneeo o?aaiaiee. Eiino?oeoeey Given … Find
(Aeaii … Iaeoe) eniieuecoao ?an/?oioth iaoiaeeeo, iniiaaiioth ia
iienea ei?iy aaeece oi/ee ia/aeueiiai i?eaeeaeaiey, caaeaiiie
iieueciaaoaeai.
Iiaeii iaienaoue o?aaoaioth nenoaio o?aaiaiee, caaeaa a? iaaeaeo
eeth/aaui neiaii Given e ooieoeeae Find. Ooieoeey Find aica?auaao
cia/aiey ia?aiaiiuo, i?aa?auathueo auoaia?a/eneaiiua (aei neiaa Given )
o?aaiaiey a oiaeaeanoaa. Anee o?aaiaiee aieaa iaeiiai, oi aica?auaaiua
cia/aiey ?aciauathony a aaeoi?a – a a?oiia ia?aiaiiuo, «caaeaouo a
eoeae», ii yoio «eoeae», eae iu oaea ioia/aee, eaaei ?acaeaoue, auaiaey
ia aeenieae iaeaeaiiua cia/aiey n «ia?ai?iaeiie» ?acia?iinoueth iannu
(kg), aeeeiu (m) e a?aiaie (sec): iaeao MathCAD «?acaeeiaao» e nai
aaeoi?, i ninoaaiua ?acia?iinoe, i?eienuaay e /eneai eiiaeiaoeee
iniiaiuo oece/aneeo aaeeieoe. Ii ia oieueei yoei oi?ioa ?acia?iinoue a
caaea/ao. Aeaaiia oi , /oi iia aaoiiaoe/anee iicaieyao ioneaaeeaaoue
«oece/aneea» ioeaee. Anee, e i?eia?o, iieueciaaoaeue neiaeeo naeoiaeu n
iao?aie, oi MathCAD «ca?oaaaony» e auaeano i?ioanoothuaa niiauaiea
incompatible units (ianiaianoeiua aaeeieoeu).
Yeaaaioiinoue ?aoaiey nenoaiu o?aaiaiee a n?aaea MathCAD, ia o?aaothuay
eiaee?iaaiey aeai?eoia eee iienea niioaaonoaothuae aiaoiae i?ioeaaeo?u,
eiaao e ia?aoioth noi?iio : o iieueciaaoaey aicieeatho anoanoaaiiua a
i?aaeeueiinoe ?aoaiey. I?ioanoe?iaaoue ioaeii ia oieueei eiiiuethoa?, ii
e iieueciaaoaey : i?aaeeueii ee ii ninoaaee enoiaeioth noaio ?
N?aaieaay oei ia?aiaiiie n ?acia?iinoueth oece/aneie aaee/eiu, iu oai
naiui i?iaaee aiaeiaeth iaaeaeo iaeaoii MathCAD e ycueii BASIK.
I?iaeieaeei a?. Iiaoi?yai : ciae «: =» a n?aaea MathCAD niioaaonoaoao
iia?aoi?ai Input e Let ia ycuea BASIK, a ciae «=» – iia?aoi?o Print. A
n?aaea MathCAD neaaa io ciaea «:=» iieueciaaoaeue iiaeao iaienaoue
ia?aiaiioth ( i?inooth, n eiaeaenii, iao?eoeo, aaeoi?), a ni?aaa –
au?aaeaiea n ia?aiaiiuie e ooieoeeyie , ii?aaeae?iiuie auoa e eaaaa eee
ano?iaiiuie a iaeao MathCAD. Neaaa io ciaea «=» ?ac?aoaii ienaoue
ia?aiaiioth eee au?aaeaiea, i?aaay aea /anoue – yoi iaeanoue, anaoeaei
i?eiaaeeaaeauay n?aaea MathCAD, eoaea auaiaeyony ?ann/eoaiiua cia/aiey.
Yoi naienoai aeaei iaeaoo MathCAD aoi?ia iacaaiea – noia?eaeueeoeyoi? :
iieueciaaoaeue iaa?ae neiaeiaeooth oi?ioeo, iaaeae ia eeaaeoo «?aaii» –
e ioaao aioia. A aio aee?iiai ciaea «?aaii», ?acaeaeythuaai eaaoth e
i?aaoth /anoe MathCAD – au?aaeaiee, ia ycuea BASIK, e niaeaeaieth, iao
a ii/aio!?
A ycueao QBASIK, Quick BASIK e Visual BASIK io oe?iu Microsoft anoue
eiino?oeoeee, iaeaaeathuea naienoaii, eioi?ia n iaeioi?ie aeieae
oneiaiinoe iiaeii iacaaoue iieeii?oeciii. Iaeii e oi aea eeth/aaia neiai
iaiyao naie niune a ?acee/iuo i?ia?aiiiuo nthaeaoao. Oae, oiiieiaaoeeny
ciae «=» – yoi e neiaie a iia?aoi?a i?enaiaiey ( aaea Let aeaaii oaea ia
ieooo ), e neiaie a aoeaaii au?aaeaiee. Ae?oaie i?eia? – eeth/aaua neiaa
Mid$ e Time$, eioi?ua niaeanii aeieoiaioaoeee ii ycueo ioia/atho e
ano?iaiioth ooieoeeth, e iia?aoi? ycuea:
A$ = Mid$((COMPUTER(, 3, 3) (Caeanue Mid$ – ooieoeey
Mid$(A$, 2,1) =($$$( ( Caeanue Mid$ – iia?aoi?
StartTime$ = Time$ ( Caeanue Time$ – ooieoeey
Time$ = (12:30( ( Caeanue Time$ – iia?aoi?
Eiaaea eeth/aaia neiai Mid$ noieo a i?aaie /anoe iia?aoi?a i?enaiaiey,
iii icia/aao ano?iaiioth ooieoeeth. Ia?aiin aea Mid$ a eaaoth /anoue
i?aa?auaao aai a iia?aoi?.
Aoi?ie i?eia? ia nianai i?aaiia?ai : Time$ i?aaeeueiaa iacaaoue ia
ooieoeeae e ia iia?aoi?ii, a nenoaiiie ia?aiaiiie. Nenoaiiua ia?aiaiiua
anoue e a n?aaea MathCAD.
Iaeaoo MathCAD ia a?ao ia?aiyoue ec ycuea BASIC iaeioi?ua iieaciua aaue.
Aio a /anoiinoe, i/aiue ia oaaoaao oeeeea Do…Loop, a oaei eioi?iai
anoaaeyaony oneiaea i?a?uaaiey If…Then Exit Do. A n?aaea MathCAD
iaeuecy, iai?eia?, a aaoiiaoe/aneii ?aaeeia ?aaeeciauaaoue iaoiae
iineaaeiaaoaeueiuo i?eaeeaeaiee. Aac oeeeea yoio iaoiae aeiionoei
oieueei a iieoaaoiiaoe/aneii ?aaeeia: iieueciaaoaeue caaea?o ia?aia
i?eaeeaeaiea eneiiie ia?aiaiiie, a caoai oeaii/eie oi?ioe, aaea
oeao?e?oao aeaiiay ia?aiaiiay, iieo/aao a? iiaia cia/aiea. ?an/?o
iiaoi?yaony a oeeeea n ?o/iui ia?aiinii aei oao ii?, iiea iiaay ia?a
cia/aiee ia oaeiaeaoai?eo iieueciaaoaey. Iiaeii iinooieoue au? i?iua –
ia ia?aiineoue iiaia cia/aiea ia?aiaiiie a aieiaeo aeiea au?aaeaiee, a
i?iaeoaee?iaaoue aeie ioaeiia /enei ?ac. Anee a oaeii aeai?eoia
noiaeeiinoe iao, oi aai an? ?aaii eniieuecotho, iacuaay i?e yoii
iaoiaeii iao/iiai ouea. Eiaiii aio aae?aniaai iieoaaoiiaoe/aneee oeeee.
E?iia oiai, ioaeii iiiieoue, /oi aieaa – iaiaa neiaeiay nenoaia
iaeeiaeiuo o?aaiaiee ieaaeaony ia ii coaai ia oieueei iaeaoo MathCAD, ii
e ae?oaei iiuiui iaeaoai – Mathemateca, Maple, Gauss e ae?. MathCAD a
oaeie neooaoeee auaeano niiauaiea Did not find solution (?aoaiea ia
iaeaeaii), canoaaeyy iieueciaaoaey ia?aoiaeeoue e iieoaaoiiaoe/aneiio
?aaeeio – iaiyoue cia/aiey ia/aeueiiai i?eaeeaeaiey e (eee) aaee/eio
oi/iinoe TOL (TOLerance – oi/iinoue, iia?aoiinoue). Ooieoeey Find ?aoaao
nenoaio oae, /oiau eaaua e i?aaua /anoe aoiaeyueo a ia? o?aaiaiee
ioee/aeenue ia aaee/eio, ia i?aauoathuoth cia/aiey TOL. Yoi au? iaeia
i?aaeii?aaeae?iiay (nenoaiiay) ia?aiaiiay n?aaeu MathCAD, o?aiyuay ii
oiie/aieth cia/aiea 0.001, eioi?ia iiaeii eciaieoue, caienaa a MathCAD –
aeieoiaioa au?aaeaiea TOL : = 0.00000001, iai?eia?. Ii e yoi /anoi ia
iiiiaaao. Oieueei i?e no?iai ii?aaeae?iiuo ia/aeueiuo oneiaeyo iaeao
MathCAD iaoiaeeo i?aaeeueiia ?aoaiea. Oaa aeaai, oaa ai?aai – ?anno?ae!
Iaeaeoee iooiae io ia/aeueiuo oneiaee – e ec neiaa Find «au?uaaaony
ieaiy»: e?aniia niiauaiea Did not find solution a oie aea e?aniie ?aiea.
Ii yoa aea caaea/a n iaia?aie/aiiui aeeaiaciiii enoiaeiuo aeaiiuo
i?ae?anii ?aoaaony iineaaeiaaoaeueiuie i?eaeeaeaieyie n iieneii a oeeeea
ei?iy iaeiiai – aaeeinoaaiiiai o?aaiaiey. Iooiae io eiaiaie aoaee (io
eniieueciaaiey aeiea Given…Find) aiciiaeai eeoue a oii neo/aa, anee
nenoaia o?aaiaiee ia aano?aeoiay, eaeea iau/ii i?eaiaeyony a caaea/ieeao
ii iaoaiaoeea, a ?aaeueiay, ioia?aaeathuay eiie?aoioth (oece/aneoth,
oeie/aneoth, aeieiae/aneoth e o.ae.) caaea/o. E?iia oiai i?eeeaaeiee
(oecee, oeiee, aeieia e o.ae.), ?aoay caaea/o iiaeao naeaeaoue ?acoiiua
aeiiouaiey, eeiaa?ece?othuea, iai?eia?, iaeioi?ua au?aaeaiey eee
oiaiueoathuea eo /enei. Ae?oaia aaaeiia i?aeiouanoai iaoiaea
iineaaeiaaoaeueiuo i?eaeeaeaiee ninoieo a oii, i?eeeaaeiee, ciay oeceea
caaea/e, iiaeao iaiyoue oi/iinoue ?an/?oia i?e ia?aaioea au?aaeaiee,
aoiaeyueo a nenoaio. A aeiea Given…Find, eae auei oaea ioia/aii, yoi
ia aeiionoeii. A i?i iiaeii eeoue niya/eoue yoo i?iaeaio n ae?oaiai
eiioea – aaanoe a au?aaeaiey aaeeanoiua (ii?ie?othuea ) eiyooeoeeaiou,
o?aaieaathuea eo ii ioiioaieth ae?oa e ae?oao e iicaieythuea ei
?aoaoueny n iaeiie oi/iinoueth. A yoi iiyoue aea iioa?y oeceee a oaiaeo
iaoaiaoeee. Ii oai ia iaiaa ana ia?a/eneaiiua ooeu?aiey /anoi inoathony
ouaoiuie ec – ca oiai, /oi nenoaia i?inoi … ia eiaao ?aoaiey, aea e
any caaea/a i?eaioe?iaaiia ia ia iiene ei?iae, a ia ieieiecaoeeth
iaeioi?uo aaee/ei. A yoii neo/aa ooieoeey Find caiaiyaony ia ooieoeeth
Minerr (MINimal ERRor). N iiiiuueth aeiea Given…Minner iiaeii ?aoaoue
oe?ieee eeann iioeiecaoeeiiiuo caaea/.
Aeey ?aoaiey eeiaeiuo aeaaa?ae/aneeo o?aaiaiee a iaeaoa MathCAD anoue
iniaua eino?oiaiou – iia?aoi?u e ooieoeee ?aaiou n iao?eoeaie e
aaeoi?aie. Yeaiaiou iao?eoe e aaeoi?ia a n?aaea MathCAD aeieaeiu eeai
eiaoue iaeeiaeiaoth ?acia?iinoue, eeai auoue aac?acia?iuie. A yoi ia
i?inoi ioeaea iaeaoa, a iauay iaoiaeieiae/aneay ioeaea: yeaiaiou
iao?eoeu iiaoo auoue n ?acii?iaeiuie ?acia?iinoyie.
Iao?eoea e aaeoi? iaeaoa MathCAD eiatho «?iaenoaaiieeia» ia ycuea BASIC
– aeaoia?iue e iaeiiia?iue ianneau. Iannea aea – yoi iauaaeeiaiea noaoai
iaeiioeiiuo aaee/ei. ?aciioeiiua ia?aiaiiua iauaaeeiythony a caiene. *oi
au i?eie?eoue oeceeo n iaoaiaoeeie, aeinoaoi/ii ?ac?aoeoue a noieaoeao
iao?eoeu iiiauaoue aaee/eiu n ?acii?iaeiuie aaeeieoeaie ecia?aiee,
n/eoay iao?eoeo ia oieueei aeaooia?iui ianneaii i?inouo ia?aiaiiuo, ii e
iaeiiia?iui ianneaii aaeoi?ia. A caiene (a aaeoi?a) iiaoo, eiia/ii
o?aieoueny e iaeiioeiiua ia?aiaiiua – ia?aiaiiua n iaeiie ?acia?iinoueth
eee aiiaua eeoaiiua a?. Aiaeia iaeiiia?iiai ianneaa a MathCAD – yoi
iao?eoea n iaeiei noieaoeii. Ii oaeay «ai?eciioaeueiay» iao?eoea ia
au?aaeaaony /a?ac ia?aiaiioth n eiaeaenii. Ia?aiaiiay n eiaeaenii – yoi
ii?iaeueiue, «aa?oeeaeueiue», aaeoi?. Anee aeiionoeoue, /oi iao?eoea –
nia?aiea (iiiaeanoai) aaee/ei n ?acee/iie ?acia?iinoueth, oi oiaaea
i?eae?ony ana iao?e/iua iia?aoi?u e ooieoeee ?acaeaeeoue ia a?oiiu ii
ioiioaieth e aaeeieoeai ecia?aiee. Oae ooieoeee min (iiene
ieieiaeueiiai yeaiaioa a ianneaa ) e max (iiene iaeneiaeueiiai yeaiaioa
a ianneaa ) ia iiaoo aeiionoeoue iaiaeeiaeiauo ?acia?iinoae a yeaiaioao
iao?eoeu – a?aoiaioa. Iia?aoi? aea ii?aaeaeaiey aeaoa?ieiaioa aeieaeai
i?aia?aciauaaoue iao?eoeo eae iannea aaeoi?ia. Aaee/eiu a no?ieao
caeanue aeieaeiu auoue iaeiie ?acia?iinoe.
N oi/ee c?aiey iaoaiaoeea (ianiio?y ia ionoonoaea ?acia?iinoe, /oi
aaae?o ca niaie niuneiaoth iioa?th oeceee caaea/e) ?aoaiea a n?aaea
MathCAD nenoaiu eeiaeiuo aeaaa?ae/aneeo o?aaiaiee /a?ac iao?eoeu aieaa
iioeiaeueii, /ai /a?ac aeie Given…Find: ioiaaeaao iaiaoiaeeiinoue a
ia/aeueiii i?eaeeaeaiee (o eeiaeiie nenoaiu ia aieaa iaeiiai ei?iy –
aaeoi?a). E?iia oiai, iao?e/iia ?aoaiea caaea/e – oi/iaa.
Anoue e ae?oaea i?e/eiu ii eioi?ui i?eoiaeeony ioeacuaaoueny io
?acia?iinoae. Iaaeaeoia?iaeiay nenoaia oece/aneeo aaee/ei ( NE )
aace?oaony ia naie iniiaiuo aaeeieoeao (aeeeia – iao?, ianna –
eeeia?aii, a?aiy – naeoiaea, neea oiea – aiia?, aaniethoiay oaiia?aoo?a
– eaeueaei, neea naaoa – eaiaeaea e eiee/anoai aauanoaa – iieue). Ii a
n?aaea MathCAD eo oieueei iyoue: aeeeia, ianna, a?aiy, ca?yae e
aaniethoiay oaiia?aoo?a.
Aea, eae yoi ie ia/aeueii, ii n aaeeieoeaie ecia?aiee i?e ?aaioa a
n?aaea MathCAD /anoi i?eoiaeeony ?annoaaaoueny. Aeia caeanue ia oieueei
oe?iu MathSoft, ii e anae oai?ee ?acia?iinoae. Aeaei a oii, /oi yoa
oai?ey eaeay – oi iacaeii/aiiay. Iaaea?ii a? ecaaaatho inaauaoue a
iaoaiaoe/aneeo ni?aai/ieeao. A oece/aneeo aea ni?aai/ieeao, eiaaea aeaei
aeioiaeeo aei ?acia?iinoae, oa?yaony anyeay eiaeea. Ec – ca yoiai iiiaea
iao/iua aeenoeeieeiu noa?athony ecaaaeoueny io ioo ?acia?iinoae, aaiaey
aac?acia?iua aaee/eiu (e?eoa?ee): /enei ?aeiieueaeoea, iai?eia?, anee
aniiiieoue ay?iaeeiaieeo. Inaiaiaeaeaiea io ?acia?iinoae iiaee?aieaii
oeaeie oai?eae – oai?eae iiaeiaey. An? yoi ia iiaei io?aceony ia
?acaeoee iaeaoa MathCAD: oai oiiiyiooay iyo??ea ?acia?iinoae (aeeeia,
ianna, a?aiy, ca?yae e aaniethoiay oaiia?aoo?a) iaoaeiaiaa?eia a
ineoieiae/aneii e aeaaea a ia?aineoieiae/aneii niuneao. Oeieee ieeae ia
iiaoo iiiyoue, eae eiioeaio?aoeeth ?anoai?a iiaeii ecia?youe oieueei
iieyie, eioi?uo , enoaoe, a iaeaoa MathCAD iao. Naia ii naaa
?acia?iinoue – iiiyoea neieueceia, iie?athuaany ia oieueei ia iaoeo, ii
e ia i?eau/ee ethaeae, caeiiu eneonnoaa e aeaaea ia iinooeaou ?aeeaee.
Noieo oieueei aniiiieoue iiiuoee caiaieoue a iaoainaiaeeao ieeeeiao?u
?oooiiai noieaa ia aaeoiianeaee. Ia?aineoieiae/aneee, anee iiaeii oae
au?aceony, aniaeo i?iaeaiu ?acia?iinoae a n?aaea MathCAD au?aaeai a oii,
/oi iyo??ea – /enei iae?aneaia, a cia/eo, e iai?aaeeueiia. Oai aeieaeia
auoue nai??ea, ii ia oa, eioi?ay caeiaeaia a Iaaeaeoia?iaeioth nenoaio,
a iaeay ae?oaay.
Naiue ( /enei niaa?oaiiia a iaoea, a eneonnoaa e a ?aeeaee: noieo
oieueei ia?a/eneeoue oeaaoa ?aaeoae, iiou iocueaeueiie aaiiu, aeie
iaaeaee, /oaeana naaoa, iaeaieaa i?iiuoeaiii ?acaeoua no?aiu ie?a,
aioe/iuo ioae?aoeia, nia?oiua a?aoe… A eeanne/aneii aa?eaioa ycuea
BASIC naiue no?oeoo?iuo oi?aaeythueo eiino?oeoeee aeai?eoia (oeeee n
i?aaei?iaa?eie, oeeee n iinoi?iaa?eie, oeeee n auoiaeii ec na?aaeeiu,
aeueoa?iaoeaa, ooieoeey, i?ioeaaeo?a e iiiaeanoaaiiia aaoaeaiea ) e
naiue oeiia ia?aiaiiuo (Integer, Long Integer, Single – precision
Floating Point, Double – precision Floating Point, Currency, String e
Type – oei, caaeaiiue iieueciaaoaeai). Aea e naia oeeo?iaay
au/eneeoaeueiay oaoieea aace?oaony ia ia /enea 8 (aaeo), eae i?eiyoi
n/eoaoue, a ia /enea 7. Aeaa (aeoa) a noaiaie ainaiue (256) – yoi /enei
neiaieia a ASC(( – oaaeeoea. Ii ASC(( – oaaeeoea ie iaoeiie, ie
/aeiaaeii ieeiaaea ia aini?eieiaaony eae aaeeiia oeaeia, a anaaaea
?acaeaaaony ia aeaa iieiaeiu – aa?oithth e ieaeithth ii 128 ciaeia a
eaaeaeie. A yoi aeaa a noaiaie naiue, a ia ainaiue.
Au? iaeia aaciaay ?acia?iinoue eaaeeo ia iiaa?oiinoe, ii ii/aio – oi
iai?i/ue ioaa?aaaony o/aiuie. Yoi aaeeieoea ecia?aiey noieiinoe – ?oaee,
aeieea?u, ia?ee e o.ae. Ec -ca yoiai a n?aaea MathCAD yeiiiie/aneea
?an/?ou eeoaiu ?acia?iinoe. Enoaoe, a ycue BASIC ?acia?iinoue aaethou
aaaaeaia einaaiii /a?ac iiaue oei /eneiauo ia?aiaiiuo – Currency.
Aaeeeieaiiay nai??ea MathCAD.
?ac iu oae caeacee a ienoeeo (a iienaiea iaae/aneeo naienoa /enea
naiue), oi iiaeioea ii?a ?anneaca i aaeeeieaiiie nai??ea MathCAD – i
naie aeaeao a?aoeeia, eniieuecoaiuo aeey aecoaeueiiai ioia?aaeaiey
?acee/iuo caaeneiinoae. Oeiia a?aoeeia a MathCAD, eiia/ii, iaiiiai
aieueoa, ii ia iaiaee eino?oiaioia eiaaony ?iaii naiue eiiiie aeey
nicaeaiey naie oeiia a?aoeeia. Ienoeea aea e oieueei.
Naiue ?ani?ino?aiaiiue a?aoee: aeaooia?iue aeaea?oia a?aoee (X-Y Plot),
eeethno?e?othuee nayce iaaeaeo aeaoiy eee ianeieueeeie aaeoi?aie.
Aeaea?oia a?aoee no?ieony, eae i?aaeei, a o?e oaaa:
(oaa 1: caaeaiea aeaea ooieoeee iaeiie ia?aiaiiie;
( oaa 2: oi?ie?iaaiea aaeoi?a cia/aiee a?aoiaioa;
(oaa 3: iino?iaiea a?aoeea.
O?aoee oaa a naith i/a?aaeue aeaeeony iiyoue aea ia o?e oaaa
(oaa 1: ?eniaaiea ia ye?aia aeenieay caaioiaee a?aoeea – i?yiioaieueieea
n /??iuie eaaae?aoeeaie o eaaie e i?aaie noi?ii; caaioiaea a?aoeea
iiyaeyaony a ioia/aiiii eo?ni?ii ianoa iinea oiai, eae iieueciaaoaeue
iaaei?o iaeio ec naie eiiiie iaiaee eino?oiaioia «A?aoeee»;
(oaa 2: caiieiaiea iieueciaaoaeai aeaoo /??iuo eaaae?aoeeia caaioiaee
a?aoeea («aaeaioiuo iano) eiaiai ooieoeee e eiaiai a?aoiaioa. Anee
ooieoeee aieueoa iaeiie, oi eo eiaia aaiaeyony /a?ac caiyooth. A
caaioiaea anoue e ae?oaea /??iua eaaae?aoeee, eioi?ua iiaeii ia
caiieiyoue. N?aaea MathCAD caiieieo eo naia. A?aoee iiyaeyaony ia
aeenieaa iinea auaiaea eo?ni?a ec ciiu a?aoeea (aaoiiaoe/aneee ?aaeei
?an/?oia ) eee iinea iaaeaoey eeaaeoe F9 (?o/iie eee aaoiiaoe/aneee
?aaeei ?an/?oia). Ia?aiao?u a?aoeea caaeathony noaiaea?oaie ii
oiie/aieth;
(oaa 3 iaiaoiaeei, anee ia?aiao?u a?aoeea, onoaiiaeaiiua ii oiie/aieth
ia ono?aeaatho iieueciaaoaey e ii oi/ao eo eciaieoue, aucaaa
niioaaonoaothuaa iaith.
Anee a?aoiaio i?aaenoaaeyao niaie oaie, eciaiythueeny io 0 aei 360
a?aaeonia, oi inue a?aoiaioia aeaea?oiaa a?aoeea oeaeaniia?acii
«naa?iooue a e?oa» e iieo/eoue iiey?iue a?aoee ( Polar Plot).
A?aoe/anee ioia?aceoue ooieoeeth aeaoo a?aoiaioia iiaeii n iiiiuueth
a?aoeea iiaa?oiinoe (Surface Plot), eioi?ue no?ieony, eae i?aaeei, ia a
o?e, a a naiue oaaia:
(oaa 1: caaeaiea aeaea ooieoeee aeaoo ia?aiaiiuo;
(oaa 2: ioia?aoeey oceia naoee – iiaa?oiinoe ii ia?aiio a?aoiaioo;
(oaa 3: oi?ie?iaaiea aaeoi?a ia?aiai a?aoiaioa;
(oaa 4: ioia?aoeey oceia naoee-iiaa?oiinoe ii aoi?iio a?aoiaioo;
(oaa 5: oi?ie?iaaiea aaeoi?a aoi?iai a?aoiaioa;
(oaa 6: caiieiaiea iao?eoeu cia/aieyie ooieoeee a oceao naoee;
(oaa 7: iino?iaiea e oi?iaoe?iaaiea a?aoeea iiaa?oiinoe.
I/aiue /anoi, iniaaiii i?e iienea iioeioiia ooieoeee aeaoo ia?aiaiiuo,
iieaciaa i?iniio?aoue ia a?aoee iiaa?oiinoe, a ea?oo eeiee o?iaiy,
eioi?ua iiaeiaiu eeieyi ia oece/aneie aaia?aoe/aneie ea?oa,
ioaaouaathuei ai?u e aiaaeeiu (ieieioiu e iaeneioiu).
Ia ianoi eeiee a?aoeea iiaeii iinoaaeoue iaeaiueeea no?aei/ee,
ioia/athuea iai?aaeaiea eciaiaiey ooieoeee aeaoo ia?aiaiiuo. Oiaaea
iieo/eony aaeoi?iia iiea (Vector Field Plot).
Aea?eaeii aeaea?oiaa a?aoeea e a?aoeea iiaa?oiinoe yaeyaony oae
iacuaaaiue o??oia?iue oi/a/iue a?aoee (3D Scatter Plot). Aai aeaaiia
ioee/ea io a?aoeeia, ioia?aaeathueo i?yiioaieueiua iao?eoeu, a oii, /oi
n aai iiiiuueth iiaeii ecia?aceoue acaeiinaycue o??o aaeoi?ia.
A?aoeee iiaeii ?anoeaaoeoue oae, /oiau aieaa aunieea ciiu eiaee o?ieua
oeaaoa, a aieaa ieceea – oieiaeiua. Iaeao MathCAD iiaeao ?ane?aneoue
iau?iiua eiino?oeoeee (neaaeai oi/iaa, ae?ooaeueiua iau?iiua
eiino?oeoeee) oae, /oiau iieueciaaoaeue niia oaeaeaoue an?, /oi aio
ioaeii.
A oanooth aa?neth MathCAD ano?iaiu n?aaenoaa aieiaoeee, iicaieythuea
iaeeaeoue MathCAD – aeieoiaiou. N aieiaoeeae naycaia nenoaiiay
ia?aiaiiay FRAME, eioi?ie /a?ac eiiaiaeu Windows-Animation-Create… a
ieia Create-Animation iiaeii i?eeacaoue iaiyoueny, iai?eia? io 1 aei 10.
I?e ioe?uoii ieia Create-Animation ioaeii auaeaeeoue iaeanoue,
aecoaeueiia eciaiaiea eioi?ie aeaeaoaeueii i?iaiaeece?iaaoue e iaaeaoue
eiiieo Animate.iinea yoiai iiyaeony ieii Playback, aaea n?aaenoaaie
Microsoft Video aoaeao iieacaii eciaiaiea e?eaie ia a?aoeea a
caaeneiinoe io eciaiaiey cia/aiey ia?aiaiiie FRAME.
Iniiaiie iaaeinoaoie o??oia?iie a?aoeee MathCAD e ae?oaeo iiaeiaiuo
iaeaoia – a oii, /oi iaeanoue eciaiaiey a?aoiaioia aeieaeia auoue
i?yiioaieueiie.
Ni?oe?iaea.
Yenia?eiaioaeueiua aeaiiua ia?aae aeaeueiaeoae ia?aaioeie aeaeaoaeueii
ioni?oe?iaaoue. Yoi iiaeii naeaeaoue a?o/ioth, ia?anoaaea ianoaie aeaa
ia?auo yeaiaioa eee (i?e iau?iiuo ianneaao aeaiiuo) aaoiiaoe/anee /a?ac
ooieoeeth csort, aica?auathuoth oii?yaei/aiioth iao?eoeo ii ioia/aiiiio
iiia?o noieaoea. Aeey yoiai aaeoi?a iauaaeeiythony a iao?eoeo, eioi?ay
iinea ni?oe?iaee ?an/eaiyaony ia oa aea, ii oaea oii?yaei/aiiua aaeoi?u.
Yoi i?eoiaeeony aeaeaoue ec-ca oiai, /oi iaeioi?ua ooieoeee MathCAD
ioeacuaathony eiaoue aeaei n ia ioni?oe?iaaiiuie aaeoi?aie.
Eeiaeiay aii?ieneiaoeey.
Ano?iaiiua ooieoeee intercept (to intercept ii-aiaeeenee – ioeiaeeoue
io?acie ia eeiee) e slope (iaeeii) ?aoatho naioth i?inooth e naioth
?ani?ino?ai?iioth caaea/o ?aa?anneiiiiai aiaeeca – iaoiaeaeaiea i?yiie,
i?iiecuaathuae oi/ee iaoiaeii iaeiaiueoeo eaaae?aoia.
Iaeaeaiiua cia/aiey eiyooeoeeaioia a e b aii?ieneie?othuaai o?aaiaiey
y(x) = a + b(x iicaieytho iino?ieoue ia a?aoeea i?yioth n ?iyueieny
aie?oa ia? oi/eaie. Iiaeiaiui a?aoeeii ia i?aeoeea, eae i?aaeei,
caaa?oatho ?aa?anneiiiue aiaeec: a?aoee, ai-ia?auo, aeano iaaeyaeiia
i?aaenoaaeaiea i ea/anoaa aiaeeca, a ai-aoi?uo, iiiiaeao a neo/aa /aai
ioeiaeoue aeiiouaiiua ioeaee aaiaea enoiaeiuo aeaiiuo (i?iione
aeanyoe/iie oi/ee, iai?eia?). Yoie oeaee iiaeao neoaeeoue e
i?aaeaa?eoaeueiay ni?oe?iaea aaeoi?ia: ioeai/iua cia/aiey /anoi
anieuaatho ia eiioeao oii?yaei/aiiiai aaeoi?a. A-o?aoueeo, a?aoee nai ii
naaa oeaiai. A?aoeeii, o.a. n ae?oaiai eiioea, iiaeii aeiaieueii auno?i
?aoeoue eeiaeioth aii?ieneiaoeeiiioth caaea/o.
Aeiiieieoue ?acoeueoaou ?aa?anneiiiiai aiaeeca iaieioi oeacaieai oi/ee,
iaeneiaeueii ioeeiieaoaeny io i?yiie. Naii cia/aiea oaeiai aua?ina iaeoe
ianeiaeii /a?ac ooieoeeth max. A aio n ii?aaeaeaieai eii?aeeiao yoie
oi/ee i?eae?ony iiaiceoueny: i?eaea/ue aiia?ao aoeaauo au?aaeaiee,
i?eieiathueo aeaa cia/aiey – True (a n?aaea MathCAD – aaeeieoea) e
False (ioeue), oiiiaeaiea eioi?uo ia oaeouee eiaeaen oeene?oao eneiioth
eii?aeeiaoo.
A iaeaoa MathCAD PLUS 6.0 ii/oe 300 ano?iaiiuo ooieoeee. I?e an?i
aiaaonoaa ano?iaiiuo ooieoeee iaeaoo MathCAD ia oaaoaao ooieoeee
ii?aaeaeaiey a aaeoi?a eee a iao?eoea eii?aeeiao ieieiaeueiiai
(iaeneiaeueiiai) yeaiaioa. Auoiae ec iieiaeaiey – yoi noiia (aeey
aaeoi?a) eee aeaieiay noiia (aeey iao?eoeu) i?iecaaaeaiee iiia?a
oaeouaai yeaiaioa ia aoeaai au?aaeaiea. Yoo eiino?oeoeeth oae e oi/aony
ioi?ieoue a aeaea iiaie ooieoeee n eiaiai imax, iai?eia? e aieueoa n
oaeie caaea/ae ia aiceoueny. Ii a iiaoth ooieoeeth ia?aei/oao e aoaeao
caianee?iaaia ioeaea – ia ynii, /oi aoaeao aica?auaoue iiai?iaeae?iiay
ooieoeey imax, anee a a?aoiaioa-aaeoi?a (a ianneaa) aeaa eee aieaa
iaeneiaeueiuo yeaiaioia. Ec i?ic?a/iie oi?ioeu n noiiie yoi iiiyoii, a
ec «caoai?iiie» ooieoeee imax – iao. Ana yoe caia/aiey iiaeii ioianoe e
e ano?iaiiui ooieoeeyi intercept e slope,aica?auathuei cia/aiey
eiyooeoeeaioia eeiaeiie ?aa?annee. Anaaaea inoathony niiiaiey, a iao ee
a yoeo ooieoeeyo oaeoe/aneie eee iaoiaeieiae/aneie ioeaee. Iineaaeithth
iiaeii iaia?oaeeoue, anee iiaenoaaeoue a ooieoeee intercept e slope
a?aoiaiou – aaeoi?u n aeaoiy eee aeaaea iaeiei iaoiaeii. *a?ac aeaa
oi/ee iiaeii anaaaea i?iaanoe oieueei iaeio i?yioth. *a?ac iaeio oi/eo
i?yiuo iiaeii i?iaanoe aan/eneaiiia iiiaeanoai. E a oii, e a ae?oaii
neo/aa noiia eaaae?aoia ioeeiiaiee aeaoo oi/ae (iaeiie oi/ee) aoaeao
ioeaaie e o?aaiaaiey iaoiaea iaeiaiueoeo eaaae?aoia aoaeoo auiieiyoueny
aaniethoii. Ii a ia?aii neo/aa ooieoeee iiaeii intercept e slope aoaeoo
?aoaoue i?inooth eioa?iieyoeeiiioth caaea/o, aeey eioi?ie a n?aaea
MathCAD anoue iniaue iaoaiaoe/aneee aiia?ao. Ai aoi?ii neo/aa (X e Y –
ia aaeoi?u, a neaey?u) ooieoeee intercept e slope aeieaeiu auaeaaaoue
aan/eneaiiia iiiaeanoai cia/aiee, naycaiiuo ia?aie/aieai Y = a + b(X.
A ieaia auiieieiinoe e?eoa?ey iaeiaiueoeo eaaae?aoia caeanue an?
aacoi?a/ii, ii iaoiaeieiaey, caeiaeaiiay a ooieoeee intercept e slope,
i?eaiaeeo e oiio, /oi i?e /enea yeaiaioia a aaeoi?ao X e Y, iaiueoa
aeaoo, auaea?ony niiauaiea ia ioeaea. An? yoi neaaay caueoa, eioi?oth
iieueciaaoaeue iiaeao eaaei iaieoe, iiaenoioa ooieoeeyi intercept e
slope aieaa iaeiie oi/ee, ii n iiaoi?ythueieny cia/aieyie a?aoiaioia.
?acthia: ea?aoue iiaeii ia oieueei n ea?iauie i?ia?aiiaie. Ia yoo ?ieue
iiaeoiaeyo e na?ue?ciua iaoaiaoe/aneea iaeaou – auei au aeaeaiea o
iieueciaaoaey.
Aeeooa?aioeeaeueiua o?aaiaiey.
A n?aaea MathCAD aei aa?nee PLUS 5.0 aeeooa?aioeeaeueiua o?aaiaiey aac
iniauo ooeu?aiee iiaeii auei ?aoaoue oieueei iaoiaeii Yeea?a, o eioi?iai
ieceea oi/iinoue e i?iecaiaeeoaeueiinoue (ieaoa ca i?inoioo).
Eino?oiaioa?ee aeey ?aoaiey aeeooa?aioeeaeueiuo o?aaiaiee (nenoai)
?acee/iiai ii?yaeea e ?acee/iuie iaoiaeaie a a?naiaea MathCAD iiyaeeny
n?aaieoaeueii iaaeaaii. A iaai aoiaeyo 13 ano?iaiiuo ooieoeee (Bustoer,
bustoer, bvalfit, multigird, relax, Rkadapt, rkadapt, rkfixed, sbval,
Stiffb, stiffb, Stiffr e stiffr). Ooieoeey rkfixed aica?auaao a iao?eoeo
Z n ?+1 noieaoeaie e n no?ieaie (? – eiee/anoai o?aaiaiee eee ii?yaeie
o?aaiaiey) – oaaeeoeo ?aoaiee nenoaiu: ia?aue (aa?iaa, ioeaaie) noieaaoe
– yoi cia/aiey a?aoiaioa t (eo caaea?o iieueciaaoaeue), a iineaaeothuea
noieaoeu – cia/aiey i?aeeiao ?aoaiey. A ooieoeeth rkfixed caeiaeai
oe?iei ?ani?ino?ai?iiue iaoiae ?oiaa – Eoooa. Ianiio?y ia oi /oi yoi ia
naiue auno?ue iaoiae, ooieoeey rkfixed ii/oe anaaaea ni?aaeyaony n
iinoaaeaiiie caaea/ae.
I?ia?aiie?iaaiea.
Iaeaieaa caiaoiay «ecthieiea» oanoie aa?nee MathCAD, eioi?oth n?aco
ioeaieee iieueciaaoaee, – yoi ano?iaiiue ycue i?ia?aiie?iaaiey. A
MathCAD, ii nooe, ia ano?iai ycue i?ia?aiie?iaaiey, a i?inoi niyoi
ia?aie/aiea ia eniieueciaaiea ninoaaiuo iia?aoi?ia a oaea
aeai?eoie/aneeo oi?aaeythueo eiino?oeoeee auai? e iiaoi?aiea. E?iia
oiai, aeiaaaeaiu oeeee n ia?aiao?ii e iia?aoi? aein?i/iiai auoiaea
break. Aeai?eoie/aneea eiino?oeoeee e ninoaaiua iia?aoi?u a n?aaea
MathCAD aaiaeyony iaaeeiii iaeiie ec naie eiiiie iaiaee oi?aaeaiey:
Add line (
if while
for break
otherwise
Add line – aeiaaaeoue no?ieo i?ia?aiiu, oaea oeeeea, iea/a aeueoa?iaoeau
e o.ae.
( – ciae i?enaiaiey.
While – i?e iaaeaoee ia yoo eiiieo ia ye?aia iiyaeyaony caaioiaea oeeeea
n i?aaei?iaa?eie: neiai while n aeaoiy ionouie eaaae?aoeeaie. A
eaaae?aoee i?aaaa while ioaeii caienaoue aoeaai au?aaeaiea
(ia?aiaiioth), oi?aaeythuaa oeeeeii, a ai aoi?ie eaaae?aoee (ieaea while
) – oaei oeeeea.
If – iicaieyao aaiaeeoue a i?ia?aiio aeueoa?iaoeao n iaeiei iea/ii.
Otherwise – iicaieyao i?aa?aoeoue iaiieioth aeueoa?iaoeao a iieioth:
C ( D if A > B
E ( F otherwise
for – eiiiea aeey aaiaea a i?ia?aiiu oeeeea n ia?aiao?ii.
Break – eiiiea aein?i/iiai auoiaea ec i?ia?aiiu eee oeeeea.
MathCAD eee i?ia?aiiu ia ycueao aunieiai o?iaiy?
Eoae nenoaia MathCAD iicaieyao aaoiiaoece?iaaoue iiiaeanoai
iaoaiaoe/aneeo, eiaeaia?iuo e o/aaiuo ?an/?oia. N a? iiiiuueth iiaeii
ninoaaeyoue aeaeeioaee e iaeaou ec aeieoiaioia, ?aaeecothueo oaeea
?an/?ou.
Oeaeaniia?acia ee, i?e iaee/ee MathCAD, iiaeaioiaea i?ia?aii
iaoaiaoe/aneeo ?an/?oia ia ycueao aunieiai o?iaiy? Iaeiicia/iiai
io?eoeaoaeueiiai ioaaoa aeaoue iaeuecy. Nenoaia iniiaaoaeueii caa?oaeaao
IE. Eioa?i?aoaoeey oi?ioe e ?aaioa nenoaiu anaaaea a a?aoe/aneii ?aaeeia
aaae?o e iioa?a nei?inoe au/eneaiee. Aeey IE aac nii?ioeanni?ia ( eeanna
IBM PC XT ) iaaeeeoaeueiinoue nenoaiu aiieia iuooeia.
Niaoeeaeece?iaaiiua i?ia?aiiu ia Ianeaea e aeaaea ia Aaeneea
iaania/eaatho iaiiiai aieaa aunieoth nei?inoue au/eneaiee iaeiaei e
o?aaotho aieueoa a?aiaie aeey iiaeaioiaee i?ia?aii.
*oi aai aaaeiaa : iio?aoeoue ianeieueei aeiae (a oi e iaaeaeue) ia
?ac?aaioeo e ioeaaeeo i?ia?aiiu, ?aoathuae ioaeioth caaea/o ca aeanyoua
aeiee naeoiaeu, eee cao?aoeoue anaai aeanyoie ieioo ia ninoaaeaiea
aeieoiaioa, ?aoathuaai oo aea caaea/o n iiiiuueth nenoaiu MathCAD ca
ianeieueei naeoiae? Anee iineaaeiee aa?eaio i?aaeii/oeoaeueiaa – aai
iiaeoiaeeo MathCAD! Ianiiiaiii aaaeiu e oaeea aeinoieinoaa nenoaiu, eae
aunieay aeinoiaa?iinoue e iaae?aeiinoue ?acoeueoaoia au/eneaiee,
iaaeyaeiinoue aeieoiaioia e oaeiaiua a?aoe/aneea n?aaenoaa auaiaea
?acoeueoaoia au/eneaiee.
Eeoa?aoo?a :
«Ie? IE» ?8’91 no?43
2.«Ie? IE» ?8’91 no?48
3.I/eia A.O MathCAD PLUS 6.0 aeey nooaeaioia e eiaeaia?ia. – I.: OII
oe?ia «Eiiiuethoa? I?ann»,1996.
Yoi ia nianai oae: iieueciaaoaeue MathCAD iiaeao i?aaaa /enea, noiyuaai
ca ciaeii «=», aaanoe ae?oaoth ?acia?iinoue, iai?eia? iao?u.
Ae?oaia iacaaiea – a?aoee ?annayiey.
No?aeea a a?aoiaioa ooieoeee max oeacuaaao ia oi, /oi ii – aaeoi?.
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