MATLAB Notes IV -

!"$#%&'(
)+*(,-*/.10324,5768*/9;:/<;0=,80328.?>8@BADCE@"68<EFGA9EH8<JIKFL:/*M9NAO03CE>QP4RTSOUVRNWNXZY[S\>8*
:/@1]^]"FL28689`_-acbdeFL26gf_hacbdeFL<;*iH89E*M6^[email protected]<kFml8>!I[H828:nCk0=@L289Z@LI-@128*oqpmFL<;0rFL,8s3*LX
)t*ZAO03s=s28@LC`68039E:MH89E9VCk>0=9/XvujS\>8*w:/@1]^]?Fm286NCk@O68<EFGAxF\9EH<;IKFL:M*T0=9yBz|{cfw}J~wwJhcX
*M<E*\~w(FL<E*\]"FmCk<;0=:M*/9@mI-CE>8*\9kFm]"*i9;0=M*LXTwFL:>gCk<;0=l8s3*@LI-2cH8]!,-*/<;9ZCFLm*/2
I[<E@1]CE>8*?:M@1<E<;*/9;l@12680=28.l@19;03CE0=@1289'032+Ck>*?]"FmCk<;0=:/*M9039@L28*?l-@10=2C@12tCE>8*
9EH8<JIKFL:/*mX
H8ll@19;*Ck>FmC(A*AFL2C^CE@.1<kFml8>ZY[`E8ugmcn;cE!@Bp1*M<eCE>8*9EcHFm<E*
¡£ X¢S\>8*§¦<E9JC"CE>80=2.¨CE@+68@+0=9gI[@1<;]©]?FCk<E03:/*M9
~w J¢¨¡ AO>8 @19;¡£
¥

N
¤
N

¡
**/2Ck<;0=*/9eFm<E*l-@10=2CE9!0=2xCE>80=9!9;cHFL<E*mX+)+*,*M.10=2t,c5+I[@1<E]^0=2.F
p1*M:MCk@L<"AO03CE>¢*M¥H8FLs=sª5«9ElFm:/*/6¬*Ms=*M]"*M2cCE9"032CE>8*78oq680=<;*/:nCk0=@L2®X&S\>8*I[@Ls=s=@BAio
0=28.g:M@1]^]?FL267l0=:c9O@1HC¯l@L0=2Ck9\9;lFL:/*M6Q°± H82803CE9OFLlFL<JC¯,*nC²A*M*/2 N FL286
0=:MCEs35«2*/:/*M9E9EFL<;5LX½u
¾|³ *¿|~¥C ~¥´68µ@¶c·CE>8¸¹w*!º9k·wFm]"¸J·1*(»w¼I[@L<Y$CkCk>8>*7*!9E4cH6Fm0=<E<E*7*M:M,8CE0=<k@1FL2 :m*MFLCE2896FL]^<E*§*/<;28.1@m*C"CE9J>8Ck*/<;]À
[email protected]*nCk>8*M<NAO03CE>
¤
¤
B
y
|
Ã
c
Ä
h
{
Å
h
Æ
X
ÁÂ
ÇcÇ ~cc~¥¥´¥´~¥¶¥~w·w¼¸¹wº·¸·Z¼
ÇcÇ µq~w¥»¥´ y%Ã|Äc{hÅ%Æw}J~c~w¥h`¼
ÇcÇ
ÁÂ
\S >8*@L28s35xCE>80=2.ts=*nI$C^0=9eCk@+I[@L<E]©Ck>*4]"FmCk<;0ª¿ÈxAO0ªCk>*/2Ck<;0=*/9"*/cHFLsOCk@x
FLl8l8s30=*M6Ck@gCk>8*'*M2cCE<E03*/9O@LIZ~?FL2867hX
ÇcÇ ¥´ Â ~_}E¶1~ºÉ·c¶1ºÉ·8`¼
¾@LCE0=:M*NCk>FCiA*j60=6§¾ Ê SËAO<E0ªCk*¶1~-Ém·c¶1-É·Xw)+*j]!H89;Cil8HC\Ck>*j68@LC\,-*MI[@1<;*
Ck>8*7É?9;@4P4RTSOUVR WÌc28@BAO9'A*eAFL2CCE@79;cHFL<E*eCk>*"wU`Pw¾S @mICE>8*
]?FCk<E0Í¿ <EFmCk>*/<VCk>Fm29;¥H8FL<E*wCk>8*w]"FmCk<;0ª¿ 03Ck9;*/sªI®YKFL9`0=2]?FCk<E0Í¿ ](H8s3CE0=l803:GFmCE0=@12huX
S\>8*9kFL]^*<;H8s=*wA@1<Ec9ÎI[@L<](H8s3CE0=l8s30=:GFCk0=@L2®XÏ~Ð'0=9`6803Ñ*/<;*/2CI[<E@1]D~ºEÐ-XÎS\>8*
¦<E9JCN@L28*(]^*GFL29]!Hs3Ck03l8s35"Ck>8*]"FmCk<;0=:/*M9/ÒCk>*(9E*M:/@126Q@128*]"*/FL289¯]!H8s3CE0=l8sª5
Ck>8*':M@1<E<;*/9El-@12860=28.e*/s3*/]^*/2Ck9O@LICk>*]"FmCE<E0=:M*/9MX
Ó032FLs=sª5 A*H89;*'CE>8*gyBz{cf:M@1]"]"FL286ÏX)t*FLs39E@esrFm,*MsÏCk>8*jQFL2867F¿|*/9
.103pL*^CE>8*^.1¤ <kFLl>xF7CE03CEs=* ¤ FL26xl8<E032C0ªCGXŸ[S\>80=9l8<E032C(:M@1]"]"FL286AO<E0ªCk*M9CE>8* ¤
¦.1H8<;*FL9!FL2x*/2:GFLl89;H8srFCk*/6«l-@19JCk9E:M0=lC¦s=*^Ck>FC!:GFm2«,*"9E*/2CgCE@QFl8<;0=2Ck*M<
H89E0328.§Ck>8*eH8280Í¿¨:/@1]^]"FL286xa%_{hX§Ê 2¨]?Fm2c5Q]?FL:>0=28*M95L@1Ht68@L2®ÔÕC28*M*/6tCE@
68@gCk>8039Ö5L@1H7:GFL27l8<E032COH89E0328.^FelH8s=sÍo²68@BAO2§]"*M2cH®X½u
ÇcÇ ~8yBz|a1{c×mØfw}J~wa}¥wÙ~JhÙ
ÇcÇ 8a1×mØ Â a}¥ÙÙ
ÇcÇ d-ÅBda Â }¥Ù²dÃÏÅyÚÅy¢fT}J~w-´ ~1_}E¶1~ºÉm·c¶1ºÉm·8`Ùn
ÇcÇ _|{hÅGÛ|dÂ ¶Æ _-ycÜ¬fhÅÄ|¶ a8Ý Â Þ
ÇcÇ
Â
Á
ß
this is f(x,y)=exp(−x.2−y.2)
1
0.8
0.6
0.4
0.2
0
2
1
2
1
0
0
−1
−1
−2
y
−2
\S >8*P4RTSOUVR W:/@L]"]"FL286NI[@L<®68<kFGAO0328.Os=*MpL*/s1:MH8<;pL*/90=9Üb%Û¥dbz|{T}J~wJwhcX
*M<E*(~wwFL<;*Oà;H89JC'FL9¯I[@1<yBz|{cfhXN)Ë03CE>4Ck>*pmFLs=H*/9I[<;@1]á,*nI[@1<E* ¤ A*!.1*nC
s=*np1*/sV:MH8<;pL*/9OI[@1<¯ZY$`k8uTâmc c ,5C²5¥l80=2.
ÇcÇ d-Üb%ÅBÛ¥ddha b%z|}¥{TÙã }J~waæhåLz{ y¬f8bm{ fT};~wh´ ~1_}E¶~ºÉ·c¶ºÉ·8Ù
ÇcÇ Â Â1äÂ äÂ
Â
x
Level Curves for f(x,y)=exp(−x.2−y.2)
2
1.5
1
0.5
0
−0.5
−1
−1.5
Ü b%Û|db%z|{t>Fm9!FL2+@1lCk03@12FLsTI[@1H<;Ck>tFL<E.LH8]"*M2CCE>FmC!:M@12Ck<;@1s=9>8@BAç]?Fm2c5
s=*np1*/s|:/H8<Jp1*M9Fm<E*i68<EFGAO2®XTÓ@1<*¿FL]"ls=* ¤ Ücb%Û¥db%z{T}J~ww;·c¹jI[@1<;:/*M9P4RTSo
UVR W&Ck@^68<kFGAæs=*MpL*/sV:MH8<;pL*/9¯:/@1<;<E*/9;l@L28680=2.^CE@ °e"pLFms=H8*M9/X
UV*MC/Ôè9¯68<kFGAæs=*MpL*/sV:MH8<;pL*/9I[@L<¯ZY[`kuZâ9;0=2®Y[é®êmëu:/@19GY[éVêmëcuX
ÇcÇ zcz´8´¥y¥¶ÅBÛì}²¸_¹wÅº·Ð%zh¸qìwîmìh¼ ÎäcºkäÐcÜ´Lzcb¥zy`}¼_ÅµÐz îmä ìh»¥`´ Á¼ Â yBÃ|Äc{hÅÆT}²zcz äcä `¼
ÇcÇ¬íÜb%Û¥dhb%z|{T}²z E·c¹8 ä
ÇcÇ
ä í
y¥ÅGÛ¬FL26ïÜcb¥ytFL<E*,8H80=sªC;oq0=2«I[H828:nCk0=@L289?Ck>8FmC@1l-*/<EFmCk*@12¢Ck>*Q*/2Ck<;0=*M9@LI
F]?FmCE<E0Í¿ÏX«Rs=9;@ ¤ A*§H89E*M6ºEÐ,-*MC²A*/*/2C²A@¨]?FCk<E03:/*M9g,8HC à;H89;C§ÐFm286Ëî
−2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
AO>8*/2]!H8s3CE0=l8sª5¥0=28.g,57é«FL2866803p¥0=60=28.e,57ëY$_Åg0=9F?:M@1289;CkFL2C ,8H0=s3CJo²032§CE@
P4RTSOUVR W\uX
ð
Level Curves at 20 Levels
4
3
2
1
0
−1
−2
−3
−4
−4
−3
−2
−1
0
1
2
3
4
S@68<EFGAp1*M:MCE@1<7¦8*/s=69§AO0ªCk>æP4RTSOUVR W H9E*Ck>8*:/@L]"]"FL286òñLzÅ {hX
S\>80=9¯:/@L]"]"FL286§CFLm*/9¯I[@1H8<¯]?FmCE<E03:/*/9¯FL9NFL<E.L¤ H8*/]^2Ck9 ¤ FLs3sV@LICE>8*(9EFL]"*ä9E03Â /*mX
ñLzÏÅ äÂ {T};~wwqz ä g68<EFBAO9ipL*/:nCk@1<;9¯6*MCk*M<E]^0=28*M6,5"z ä FCiCk>8*Nl@1032Ck9i~whX
Ó@1<*¿8Fm]"l8s3* ¤ 9EH8l8l-@19;* A* AO039E>Ck@!9;L*nCk:>4CE>8*NpL*/:MCE@1<i¦*Ms=67ZY$`k8uTÌYJó
` 8u@12CE>8*'9EcHFL<;* ô^¡ ¡Ëô¤Vô^¡ ¡Ëô X
ÇcÇ ~cñLz~¥´¥Å ¶cõ{T¸¹w}J~wº²õJw¸²õTMÝ%¼¶1~c|;¶1´h~c~w ¼µq~wJc»¥´ ÁÂ yBÃ|Äc{hÅÆT}J~c~wJch`¼
ÇcÇ ä8Â
¾@LCE0=:M*Ck>FCTAO>8*/2Â*\AO<E0ªCk*Ý%¶1~ ¤ P7RTSOU`RNWFm9E9EH]"*M9wCE>FmCwA*¯]^*GFm2eCE@j68@
Ck>8*9EH8,|Ck<kFm:MCk03@12@12?*GFL:>§*/2CE<;51XTRs=9;@!28@LCE0=:/*¯Ck>FCi@1H8<]"*M9E>8.L<E0=6"0=99ElFL:M*/6
°± ô >8*M<E*mX7öqC0=9'.1*M28*/<EFLs=sª5,*M9;CCk@4H89E*?F4:/@1FL<E9;*/<.1<E036ÄO0ªCk>xñLzÅ äÂ {CE>FL2
AO03CE>yBz|{cf@1<jÜb%Û|db%z|{hX
f(x,y)=(1−x,−y)
3
2
1
0
−1
−2
Lñ zÅ äÂ {!>Fm9TFL2g@1lCE0=@128FLs¦8I$Ck>eFL<;.1H8]^*/2CZCE>FmCT9;:GFLs3*/9Z*/FL:>e@LICk>8*OFm<E<E@BAO9MX
Ó@1< *n¿FL]^l8s3* ¤ ñLzÅ äÂ {T}J~wqz ä ;·8]"FLL*M9'*GFL:>+FL<E<;@BA÷C²AO0=:M*eFL9's=@12.§FL9
ñLzÏÅ äÂ {T};~wwqz ä cX'@BA*Mp1*M< ¤ ]"FLc0=2.^CE>8*!FL<;<E@[email protected]*M<H9EHFLs3s35§]"FLL*M9
Ck>8*M]ø@Bp1*M<EsrFml7AO>803:>4s3@|@L¥9OFgs303CECEs=*9;Ck<EFL28.1*mX
−3
−3
−2
−1
0
1
2
3
ù
quiver(x,y,1−x,−y,2)
3
2
1
0
−1
−2
VU *MC/Ôè968@¬@L28*x¦2FLs*n¿FL]^l8s=*t@LI^68<kFGAO0=2.&p1*/:nCk@1<Q¦8*/s=69/XúU`*nCGÔÕ968<kFGA
ZY[È8u^ Y$hû u(@12ÈCk>8*§9EcHFm<E* ó1±vü ó1±vü óL±½ü óL±½ü|X
)t*']^0=.1>C\,-* Ck*M]" l|Ck*/6§Ck@gCE<;5 ¡ ¡ ¤¯ ¡ ¡
ÇcÇ ~cñLz~¥´¥Å ¶-Ý`{Tºýw}J~w¸¹Jwº·c~ýw¸ºÉmÝ·wºýZºEÐ¼¨w¥E·8¥´~c~w¼µq~c»¥´ ÁhÂ yBÃ|Äc{-Å%ÆT}J~c~ch`¼
ÇcÇ {¥ä8{8Âbm{òz-y¥ÅGÛ|ÄDć´ ñLzÏÅ {
þcþ¥þ¢ÿ
×1d¥{hÅ%~ïå Á z-y%dâØ Â dcÃÇ Â y1× ÁäÂÂ y¥Å% Â ×ywº
S\>8*Ol8<E@L,8s=*M]÷>8*M<E*O0=9CE>FmCP4RTSOUVRNW68@¥*/9;2®Ô CH2868*/<;9;CkFL286"CE>8* Ö!ñ1zÅ äÂ {
FL:/:M*/lCE9Z@128sª5]?FmCE<E03:/*/9MXZÊ 28*jYK>FL:|uAFG5CE@jFGp1@1036(Ck>0=9l<E@1,8s3*/]0=9Ck@NAO<;03CE*
ñLzÏÅ {T};~ww~ºÉ·wºEÐmw;·~¶1~hcXR ]^@1<E*e*Ms=*/.1FL2C(9;@1s=HCE0=@12039'CE@H89;*"CE>8*
:/@1]^ä]"Â FL286+b%Û Â y|XgS\>0=9':/@1]^]"FL286Q:M<E*GFCk*/9F]"FmCk<;0ª¿@LIwAO>FmCk*np1*M<9;0=/*!A*
AiFm2cC(¦s=s3*/6t*M2Ck0=<;*/sª5AO03Ck>¢ó1Ôè[email protected]*MCCk>8*":/@1<;<E*M:MCg9;0=/* ¤ A*:GFL2«H9E*?CE>8*
:/@1]^]"FL286Qy¥Å% Â X
ÇcÇ ~cñLz~¥´¥Å ¶-Ý`{Tºýw}J~w¸¹Jwº·c~ýw¸ºÉmÝ·wºýZºEÐ¼¨w¥E·¥Ð´b%~cÛ ~w¼y`}µqy~Å%c»¥´ }E~hÁhcÂ cyBÃ| Äc{-Å%ÆT}J~c~ch`¼
ÇcÇ ä8Â
Â Â
−3
−3
−2
−1
0
1
2
3
f(x,y)=(x2y,2)
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2

Download Report

MATLAB Notes IV -

Paperzz.com

Your Paperzz