23424615-رياضيات-تخصصية
TRANSCRIPT
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XDf =2121 )()( xxxfxf ==1x2xK
EW)()( 2121 xfxfxx ==1x2xKXDf =YRf =
EW)()( 2121 xfxfxx ==1x2xKXDf =2121 )()( xxxfxf ==1x2xKYRf =
KWKWK{K
W
ExFE)(xfy =KE),( yxKEx
KKK
-
JJ
- -
WWRR: fxxf =)(KW
WWx 00.0 25.0 50.0 75.0 00.1 25.1 50.1 75.1 50.1 25.2
xy = 00.0 50.0 71.0 87.0 00.1 12.1 22.1 32.1 41.1 50.1
WW
0.5 1 1.5 2
0.20.40.60.81
1.21.41.6
WW
0.5 1 1.5 2
0.20.40.60.81
1.21.41.6
KKK
WWEW)()( xfxf =0)()( =+ xfxffDxfDxK
-
JJ
- -
EW)()( xfxf =0)()( = xfxffDxfDxKWW
ERR: f1)( += xxfW
0211)1(1)()()(0211)()()(
=+=++==+++=+
xxxxxxfxfxxxfxf
RR: g2)( xxg =W0)()()( 2222 === xxxxxgxg
ENN: f1)( += xxfN= fDxfDx
NN: g2)( xxg =KENN: fxxf =)(N= fDxfDxERR: fxxf =)(
FKEK
WFKE
WK
WK{K
WRR: faxfy == )(aKKW
ER=fDKE}{aR f =KE)()( xfxf =K
-
JJ
- -
EKWWRR: f2)( =xfK
W
-4 -2 2 4
-3-2.5-2
-1.5-1
-0.5
0.51
{KWWRR: fxaxfy == )(0aKK
WER=fDKER=fRKKE)()( xfxf =KEKK
WWRR: fxxf 2)( =KW
-3 -2 -1 1 2 3
-3
-2
-1
1
2
3
-
JJ
- -
{KWRR: fbxaxfy +== )(0a0b
KW
ER=fDKER=fRKEKE
KWWRR: f5.12)( += xxfKW{K
WRR: fcxbxaxfy ++== 2)(0abc
KW
ER=fDKERfRKKE0=bKE0== cbK
-2 -1 1 2 3
-3
-2
-1
1
2
3
-
JJ
- -
WWRR: f5.12)( 2 += xxfKW
-2 -1 1 2
-3
-2
-1
1
2
K
WKKFE
FEW =180W
KKWRR: f0>pW)()( pfpxf =+
fDxFpEKWxW
xsinxcosK
{KWsinWRR:sin xy sin=KKKW
ER=fDKE]1,1[=fRW1sin1 xKKKExx sin)sin( =K
-
JJ
- -
Exx sin)2sin( =+ 2KEK
- 2 p - 3 p2- p - p2
p2 p3 p2
2 p
-1
-0.5
0.5
1
{KWcosWRR:cos xy cos=KKK
WER=fDKE]1,1[=fRW1cos1 xKKKExx cos)cos( =KExx cos)2cos( =+ 2KEK
- 2 p - 3 p2- p - p2
p2 p3p2
2p
-1
-0.5
0.5
1
-
JJ
- -
{KWRR: fxbxfy == )(1bKK
WER=fDKE)[0,=fRW0>xbKKEKEWxey =71828.2eK
xKEbKK
WWxey =KW
-1 1 2 3 4
10
20
30
40
50
{K
WblogWRR:log bxy blog=ybx =1bKK
WExbxb =)(logxb xb =logKE),0( =fDKER=fRKKEK
-
JJ
- -
EWxxy elogln ==71828.2eKK
xKEW
bxxb ln
lnlog =KEWbxx eb ln=KEbKK
WWxy ln=KW
5 10 15 20
-1
1
2
3
-
JJ
- -
WW
1)(,RR:)41)(,RR:)3
)(,NN:)2)(,NN:)133
33
=+===
xxffxxff
xxffxxff
WWFWE
11)(,RR:)61)(,RR:)5
1)(,RR:)41)(,RR:)3
)(,NN:)2)(,NN:)1
2
3
2
3
33
33
+=+==+=
==
xxxff
xxxff
xxffxxff
xxffxxff
4W
xxffexffx
xffxxff
x ====
)(,RR:)4)(,RR:)3
1)(,RR:)22sin)(,RR:)1
5W6WW
xxffexffxxff x === )(,RR:)3)(,RR:)22sin)(,RR:)17W
-
JJ
- -
W
W
W K K K K K K K K
W{K
-
JJ
- -
K
sNN
.NnKK)(nsK
1(sW
aE NNW
...),(....,),3(),2(),1( nssss)(nsK
sKn2KW)1(....,2....,8,6,4,2 n
sK12
2+nnKW
)2(....,12
2....,,98,
76,
54,
32
+nn
bE nss{ }nsKsnsFEsW...,....,,,, 321 nssss
)1(W{ }n2n2)2(W
+122nn
122+nn
-
JJ
- -
{ } { } { } ...,,, nnn cba...,,, nnn cbaKcE ssW
{ }= nsns n :),()1(KW{ }nnn :)2,()2(KW
+ nnnn :
122,
K2( W
...,17,13,11,7,5,3,2 K
K3({ } { }nn ba ,W
= nba nnW...,,, 332211 bababa ===W...,25,16,9,4,1
W21 11==s22 24 ==s23 39 ==s
24 416 ==s{KKKKKW2nsn =
{ }2n{W{ }nnn :),( 2W...,36,25,16,9,4,1
W2111 1)1(1 == +s2212 2)1(4 == +s
-
JJ
- -
2313 3)1(9 == +s2414 4)1(16 == +s{KKKKK
W21)1( ns nn +=W{ }21)1( nn+
( ){ } + nnn n :)1(, 21
1(K
2({ } 18,12,6,0,3=na
{ } 23,20,17,14,11,8,5,2,1=nbK{ } { }nn ba
WW{ } ...,1....,,5,4,3,2) += naa n
{ } ...,1
1....,41,
31,
21) += nbb n
{ } ...,1
1)1(....,,61,
51,
41,
31) += ncc
nn
{ } ...,3,....,3,3,3,3) =nddW
{ } { }1+= nanW
-
JJ
- -
{ }
+= 11
nbnW
{ }
+= 11)1(
nc nnW
{ } { }3=ndKW
1 2 3 4 5 6 7 8 9 10
12345678910
1 2 3 4 5 6 7 8 9 10
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
-0.6
-0.4
-0.2
0.2
0.4
-
JJ
- -
1 2 3 4 5 6 7 8 9 10
0.51
1.52
2.53
3.54
{K{ }nsKW +== + ndssas nn 11 , da,KaWdW
KKKW
...,3,2,, dadadaa +++W,1 as =
dadss +=+= 12dadss 223 +=+=dadss 334 +=+=
nsW+= ndnasn :)1(WW
...,.....,,4,3,2,1) na1,11 == ds
31,29,27,25,23,21,19)b2,191 == ds
-
JJ
- -
...,61,
31,
21)c
61,
21
1 == ds...,17,13,9,5)d
4,51 == ds...,7,5,3,1,1) e
2,11 == dsWW
...,11,7,3,1 W
W413,1 12 ==== ssdaW75)4(191)4)(120(1)1(20 =+=+=+= dnasW46,2 153 == ss50sWW4614,22 153 =+==+= dasdas
W44812 == ddW1028 == aa
W186)4(4910)1(50 =+=+= dnasW38KKW
Wdasdasas 2,, 321 +=+==333)2()(321 =+=++++=++ dadadaasss)1(1=+ daW)2(8))((8)2)((321 =+++=++= ddadaadadaasssFEFEW)3(88)1( ==+ adada
-
JJ
- -
FE)4(11 adda ==+)3(W0)4)(2(0828)1( 2 =+=+= aaaaaaa
W4=a2=a4=aW3411 =+== ad2,1,4 2=aW3211 === ad4,1,2
W2,1,4 4,1,2 W10489713W
W897,1041 == nssW)1(13104897)1( +=+= ndnasnW62
138068061310489713 ===+= nn1313104897 = nW62
{{Kba,Ka
bKba,Wbca ,, W
2baccbac +==
W5W245,13W
5K245,137W245,13 7 == saW4361324567 =+=+= dddas
W)43(513),43(413),43(313),43(213,4313 +++++
W202,159,116,73,30
-
JJ
- -
{K{ }nsWNnrssas nn == +11 ,ra,r
KW
12
4
2
3
1
2 ...
=====n
n
ss
ss
ss
ssr
W334 arrss ==,223 arrss ==,12 arrss ==,1 as =
nsW1= nn rasWW
...,24,12,6,3)1 3=a2=r
...,64,16,4,1)21=a4=r
...,271,
91,
31,1)3
1=a31=r
...,271,
91,
31,1)4
1=a31=r
...,81,
21,2,8)5
8=a41=r
W8.124.6W
8.12=a21
8.124.6
1
2 ===ssr
-
JJ
- -
W25.0218.12
99
101 =
=== rasras nn
WW...,21,
41,
81
W
81=a2
48
81
41 ===r
W64281 99
101 ==== rasras nn
W2431W...,3,9,27
W27=a
31
93 ==r
W2431=ns1= nn ras
W181
8
13
5
1
31
31
31
31
313
31
3127
2431
=
=
=
=
nnnn
18 = n
9=n2431K
{{K ba, a b
ba, cWbca ,,0>abWabcabc
cb
ac === 2
WW8
189,7W
48
189,7 4 == Sa
W3
334
1
23
8277
8189
===== rrSras nn
-
JJ
- -
W23=r
W2
23)7(,
23)7(
463,
221
-
JJ
- -
WaE W
{ } { } { } ++ nnnnnn n 1)5)1( 1)4)1()31)212)1 2
bE W..,.1,
21,0,
21)8..,.1,1,1,1)7...,
41,
31,
21,1)6
...,3,2,,)10...,,,,)9 32 dadadaaararara +++cE
+1nnK
WW
ns...,1,0,1 aE ns...,0,4
1,21
bE ns...,12,12,32 + xxxcE 18s...,2,3,8 dE 10s...,45,3,2 yxyxyx +++eE 13s...,,,
32
yx
yx
yx0,0 yx
fE 21S...,51,
51,
51
234W
1(200135014K2(W
aE 32243KbE 73,83 K
-
JJ
- -
cE F25.4,25.2K
dE 20,5K3(18{27K4(20
5(3600{40{
{6(648K7(6
18KK
{ }nanWnaaaa ++++ ...321
nKnaW
=
n
kka
1
WW)15(...1494 ++++ nW15 = kakW
==
= nk
n
kk ka
1115
WW2217127 +++
-
JJ
- -
W22,17,12,75=a5=d
255)1(7)1( +=+=+= kkadkaa kkW
==+= 4
1
4
125
kkk ka
WW
=5
132
k
kW
k5,4,3,2,1W486162544863232323232 54321 ++++=++++
{K
=
n
kka
1{ }na
K151617K
W{{K
=
n
kka
1n{ }naad
=
= nk
kn aS1
FnSEW)(2
1n
nn
kkn aaaS +==
=
=
= nk
kn aS1
KnKana
-
JJ
- -
WW
=
15
1kna10,4 136 == aa
W1012,45 136 =+==+= daadaa
2147104)12(5136 ===++=+ dddadaaa
6aW14410 ==+ aaW( )dadaaaaaS nn
kk 142))115(()( 2
152
152
15
115 +=++=+==
=
( ) 0)2(14)14(221515
115 =+==
=kkaS
W=
n
kna
1W
40,5,131
1 === =
n
knn aaa
WW)513(
240)(
2 11=+=
=naana n
n
kn
W10440 == nn10{{K
=
n
kka
1n{ }naa
r=
= nk
kn aS1
W
1,1
)1(1
==
=r
rraaSnn
kkn
1=rWanSn =1...111 ++++=nSFnE
-
JJ
- -
W
=
==
= 1,
1,1
)1(
1 rna
rrra
aS
nn
kkn
WW=
10
12
k
kW
W=
++++=101
10321 2...2222k
k2=a2=r10=n
1)1(
1 ==
= rraaSnn
kkn1rW
2046)11024(212
)12(2 1010
1==
==k
ka
W61458K
WW6,1458 3489 ==== araara
336
1458 553
8
=== rrarar
W2766)3(6 334 ==== aaara
W92=a
W4374)2187(2)3(2)3(92
10799
10 ===== aaraW
1,1
)1(1
==
=r
rraaSnn
kkn
9
5904813
)13(21
1)1(
101010
110 =
=
=== r
raaSk
k
-
JJ
- -
W321
21{
32255{
W
32255
11)1(
1=
===
= raarS
rraaS
n
n
nn
kkn
W641
21.
3211 ==== rararar nnn
W21
641
32255
121
641
32255
=
=aa
32256
321
3225522
321
32255
6412
32255 =+=+=
= aaa
W4W
=n
k
k
1
339
364W
9
364 W
93643...3333 3012
1
3 =++++= =
nnk
k23=a3=rn
1)1(
1 ==
= rraaSnn
kkn1rW
9
36413
)13(3 2
1=
=
= nnk
ka
W637293728139
36418
13 ==== nnn
W6=n6
-
JJ
- -
W W
1) =
51
)52(k
k 4) =
5
13
k
k 7) =
91
1
5415
n
n
2) =
+301
)13(k
k 5) =
101 2
1n
n
8) =
6
19
k
k
3) =
1001
)12(k
k 6) =
8
1
12k
k 9) ( )=
+81
)122k
k k
WaE
=
19
1kka116,130 193 == aa
bE =
5
1kka9,3
153 == aa
cE =
+nk
k1
)53(
dE W=
=
nk
k
1 16195
23
eE 48 800
fE 21280K
gE 54718K hE 40 430 60 945
K iE 348
K jE 42
512K
-
JJ
- -
kE 144486K
lE W2561...163264 +++++
mE 2520{21 22{K
-
JJ
- -
{K
KaE ab
Wba bE
naaaa ,...,,, 321W naaaa ...321
WKW
{
{ K
W6123 ={Kn
1nnFactorial !nnnnn = )1()2(...321!
nWW
720654321!6,12054321!5,244321!4
6321!3,221!2,1!1======
=====
-
JJ
- -
!nWnnnnn == ])!1[()].1(...3.2.1[!)!1(! = nnn
nW)!22(23!23),!8(9!9 ==
W
)!3)(2)(1(
)!2)(1()!1(!
==
=
nnnnnnn
nnn
W)!4)(3)(2)(1(! = nnnnnn1=nW)!0(1!1 =!01=
W1!0 =1=n
K nr
F{EK PermutationK
rn PKnK{1nK
1nK{2n{K
FE1)1( += rnrnrn Prn
)1.(..).2)(1( += rnnnnPrnWW
12)3(4)14(4
210)14(15)115(15336)6)(7(8)28)(18(8
24
215
38
======
===
PPP
-
JJ
- -
rn PW
)!(!rn
nPrn =
nr =!
!0!
)!(! nnnn
nPnn ===
WW
12
!2!434
210!2!151415
336!3!8678
24
215
38
===
===
===
P
P
P
W
WK
W67204567858 ==PWK
Wdcba ,,,K
2423434 ==PW
dbcdcbcdbcbdbdcbcddcadaccdacadadcacddbadabbdabadadbabdcbacabbcabacacbabc
,,,,,,,,,,,,,,,
,,,,,
-
JJ
- -
abc acbbac K
KKrnK
rn W
=rn
CrnKrn
FrEFrE Krn Pr
nK)(rN
r
nPrn
=
)(rNrK)(rN!rPrr =rrK
W!rrn
=rn P
W.!)!(
!! rrn
nrP
rn rn
==
W
1.2).....1()1).....(1(
+=
rrrnnn
r
nr
K
-
JJ
- -
WW21
1267
1234534567
5
7)56
123678
)23)(13(3)28)(18(8
3
8) =
==
=
==
ba K
K
r
=
=
=
rnn
rn
nnn
.
..1
0
rn)( rn Kr
)( rn )( rn
rn
n
rnF
rnKE
WW
12254925124950
2
50
4850
50
48
50)21
1267
2
7
57
7
5
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=
=
=
=
=
=
ba
114031920123181920
!17!3!17181920
!17)!1720(!20
17
20) ==
===
c
8008123456
111213141516!10!6
!10111213141516!10)!1016(
!1610
16) =
===
d
-
JJ
- -
W425W
425
126501234
2122232425!4!21
!2122232425!4)!425(
!25425 =
===
K
rn W
aE rnKbE
)!(!)1).....(2)(1(rn
nrnnnnPrn =+=
cE .)!(!!rnr
nrn
=
W{K
WW
352525252 ==rnWW510P30240678910
!5!5678910
!5!10
)!510(!10
510 =====P
W7,6,5,4,3,2,1
-
JJ
- -
W
.....231132123 37 P210567
!4!4567
!4!7
)!37(!7
37 =====P
W10K{K
a(FEb(Wa(
10W1000103 =b(
10{98K
K7208910 =W7208910
!7!78910
!7!10
)!310(!10
310 =====P
W8W
28
282
78!2!6
!678!2)!28(
!828 ====
Knba,W
-
JJ
- -
nkknnnnnk
kknn bbarn
ban
ban
abarn
ba ++
++
+
+=
=+ =
......21)( 221104,3,2,1 ==== nnnn
baba +=+ )( 222 2)( bababa ++=+
32233 33)( babbaaba +++=+ 4322344 464)( babbabaaba ++++=+
WaE K bE a{a
K cE b{bKdE a{b{K eE {
KW5)( ba + W
54322314550
55
45
35
25
155
)( babbababaabar
bak
kk +
+
+
+
+=
=+ =
543223145 510105 babbababaa +++++=
W4)21( b+ W
43240
4 )2()2(34
)2(24
214
1)2(4
)21( bbbbbr
bk
k +
+
+
+=
=+ =
432443322
443322
1632248122)4(2)6(2)4(1
2234
224
214
1
bbbbbbbb
bbbb
++++==++++=
+
+
+
+=
-
JJ
- -
W10)03.1(WW03.0103.1 +=W
344.13439101.1...0001701.000324.00405.003.01103...
10310...
103
210
103
110
1
103...
10310...
103
210
103
110
1)03.0(10
)03.01(
20
10
24
2
2
10
22
2
22
10
0
10
+++++=++
++
+
+=
++
++
+
+=
=+ =
k
k
k
k
k
k
kk
{K
W13
2
21
+x
x{0xWW998
99132
21
413
21)(
913
xx
xx
=
19 512715
21
123410111213 =
= xx
-
JJ
- -
1(W
)a 515P )b 1827 P )c 1732P )d 13371537 PP )e 210310 PP )f 512C )g 1827C )h 1732C )i 13371537 CC )j 210310 CC )k 13371537 CP )l 310310 CP
2(a( K
b(K3(WW
a( b( K
4(F52E
a(b(
c(
5(
6({
K7({
300K8(25
-
JJ
- -
9( a(b(
10(
11(K
12(4
13(128414(10ba,{64K
15(( )722xx +K16(
5
1
+yx0y
17(15
31
xx
0x
18(172 8
2
xx0x
19(8x)212( 32 yx
-
J
- -
EJK
EK
3) Gwyn Davies and Gordon Hick, Mathematics for scientific and technical students, Addison Wesley Longman, Harlow, England, 1998.4) Anders Hald, A History of Probability and Statistics and Their Applications before
1750, John Wiley and Sons, New York, 1989.
5) Alexander Schrijver, Theory of Linear and Integer Programming, John Wiley & Sons,
Chichester, England, 1986.
6) Seymour Lipschutz and Marc Lipson, Discrete Mathematics, McGraw-Hill, New York,
1997.7) Peter Tebbutt, Basic Mathematics, John Wiley & Sons, Chichester, England, 1998.
-
JJ
W:
K
K
FE
W
KKN
Z
-
JJ
QK
R
K
KWW
KK
K
cbxax ++2
-
JJ
KW
KKK
K
W
KKKK
-
JJ
WKKK
KKW:
1K
K
WKKKK
-
FEGOTEVOT appreciates the financial support provided by BAE SYSTEMS