Differential Equations, Exercises - Advanced Calculus, Exercises of Advanced Calculus

Differential Equations, Eigenvalues, Exercises, Advanced Calculus, Richard Yamada, Michigan

Typology: Exercises

2010/2011

Uploaded on 11/08/2011

rothmans
rothmans 🇺🇸

4.7

(20)

249 documents

1 / 8

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
 
! #"$&%('*)+-,/.0213.41657859;:<.0.=8+>4+?0A@B9C50A=EDF6.GIHKJLNMO9C50/4)+P9CD7Q>41657
H-R1TS167#RI4)+VUW.0X41TQ?DF6.0Y@25F6D#421657ZK[\C]A^VL_G`\a]A^XHb\C]A^Y@A)5DFTc`de+V402+?.4+fc.@<.g@Ah@X4+?=
59F6167#+.0/+?iKDW.421657#@Bjg1T42)D7kK75ljg7S+fQf4250*HKJXmn'*)KD@fo#45qpW7c4)#+r@25FTD#41T57sZK[#\a]A^>o
57+t@216=uUFvhO@A5FTS+?@*4)1T@g@Ah@A42+?=w9C50*HKJA\C]A^*.7cx167y42+?R02.4+f@I45spW7cxHz\a]A^>m
{|u} ~ ~x} ?~
+I75ljQ?57#@216c#+?0@A5=8+B+>#.=uUF6+f@59FT167+?.0<c#1Tb+?02+f7y413.F+fiD.41T57@&jg1v4)Q?57@A4.7y4
Qf5+>uQ?16+f7y4@
m
Z
J
L rZ
J
L
+?0A+4)+t=8.40A1vO1T@
-

4)+t+?1TR+?7yS.FTD+?@g.0A+sr
oW.7c4)#+`R+?7+f0.F@A5F6D#4216571T@
Z\a]A^VL_¢¡
¤£¥
¦¨§
?¡
£
'*)+tQ?021v41TQ.FbUb51T7y4Pu1T@*Q.FTF6+?c.O©?ªy«y«#¬6>m
'*)+t502d1v4@*7+?.0Ps.02+tc+fU16Q>4+?cx16742)+pWRD0A+`de+?FT5ljtm
m
Z
J
L Z8
J
L Z
§
'*)+t=O.42021®¯16@
`

pf3
pf4
pf5
pf8

Partial preview of the text

Download Differential Equations, Exercises - Advanced Calculus and more Exercises Advanced Calculus in PDF only on Docsity!

! #"$&%('*) +-,/.0213.4 1 657859;:<.0 .=8+>4 +?0A@B9C50A=ED F6.GIHKJLNMO9C50/4 ) +P9CD 7 Q>4 1 65

H-R1TS167#RI4 ) +VUW.0X4 1 TQ?D F6.0Y@25F6D#421657ZK[\C]A^VL_G\a]A^XHb\C]A^Y@A) 5 D FTcde+V4 0 2+?.4 +fc.@<.g@Ah@X4 +?= 5 9F6167#+.0/+?iKDW.421657#@Bjg1T42)D 7 kK7 5 ljg7 S+fQf4250HKJXmn')KD @fo#4 5 qpW7 c4 )#+r@25FTD#4 1 T57sZK[#\a]A^>o 5 7 +t@216=uU FvhO@A5FTS+?@4 ) 1 T@g@Ah@A42+?=w9C50HKJA\C]A^*.7 cx167y42+?R02.4 +f@I4 5 spW7 cxHz\a]A^>m

{ |u} ~ ~€x} ‚„ƒ?~

†‡+I7 5 ljˆQ?57#@216c#+?0‰@A5=8+B+>Š#.=uU F6+f@‰59‹FT167 +?.0<c#1TŒb+?02+f7y4 1 3.F+fiD .4 1 T57 @&jg1v4 )ŽQ?57 @A4 .7y Qf5+>uQ?16+f7y4 @

m

Z J L  r‘Z ’ J L ’

“€+?0A+4 ) +t=8.4 0 A1vŠO”•1T@ –  -‘ — —  ˜š™ 4 ) +t+?1TR+?7yS.FTD +?@g.0A+sr‘ ™ oW.7 c›4 )#+`R+?7 +f0 .Fœ@A5F6D#421657 1 T@

Z‰\a]A^VL_žŸ ¢¡

') +tQ?021v4 1 TQ.FbUb51T7y4P—u1T@Q.FTF6+?c›.O©?ªy«y«#¬6>m ') +t502d 1 v4 @7 +?.0P—s.02+tc +fU 1 6Q>4 +?cx167 4 2) +pWRD 0 A+`de+?FT5ljtm

‘m

Z J L ‘ Z8 (^) ’ ’ J L Z § ’

'*) +t=O.42021®Š”¯16@ – ‘  `  ˜ š™

  X‘

'*) +tQ)W.0 .Qf4 +f021T@A4 1 TQtUb5Fvh7 5 =u13.Fe16@P° ²±y° §

±oW.7 c›4 ) +t+f16R+f7KS.FTD +?@g.02+

° L

‘s³μ´¶

·+>4242167 R8°L¹¸

o j B+q)W.S+t42) +t=O.4 0 21®Š +fiD .4 1 T5

\C”»²°‹¼^

H

H

L

'*) 1 6@qR1TS+?@ \½‘¾°‹^XH

L¿H o<@25À42)W.4.ÁQ?5=8U FT+>Ф+f16R+f7KS.FTD +u16@ \CH

H ^L

\X

‘-Â°e^>m †!+tR+>4P.uQf5=8U#F6+>Š@25FTD#4 1 T57 5 9;4 ) +9C50A=

Z‹Ã>\C]A^ÄL ž ° ¡

rÂ°²˜

L žÅÇÆ È ÊÉ#ËÍÌ ÈÆ¡vÎ

L ž ÅÆÈÉ#Ë Ìȉ¡vÎÆ

Ï

Ð

') +t02+.F.7 cx16=8.R167 .0AhuUW.0X4 @59<4 ) 1 T@g.02+

ÑžrL_ž ÆÈ¡

fÒÓ

]

A^

Ï

Ð

Ó

½Ô

\

]

A^

Ï

Ð

¼KÕwL_ž ÆÈ¡

>ÒÓ

\

]

A^

Ï

Ð

Ó

ÇÔ

\

]

A^

Ï

Ð

Ö +?+4 )#+tp RD 0 2+m

  Ú

Û m

Z J L ±Z §

ÛÜ

’ J L PZO^ ’  Ü

Ü J L ‘Z

Ü

'*) +t=O.42021®Š1T@

_LÞÝßà

 Û

  q ‘ —  áXâã

'*) +tQ)W.0 .Qf4 +f021T@A4 1 TQtUb5Fvh7 5 =u13.Fe16@

ä \½°b^nLå°^ ¸ ²±y°^ § ELæ\ǰ8Â‘^^ \½°^ § ^Êç

èéëê‹ìbí# Wî½ïÀ° LN‘ð ·+>4€ñòL»”»²‘¼‹mn'*) +?7zo

ñ óLõôö÷

 Û

q -±  ‘ — øúùû

üý (^) Ԝþ \½ñš^VLå‘m^

ñ L õôö÷

-‘‘ q — r‘ ` — ‘‘  øúùû

üý (^) Ԝþ \½ñš^^ L¯m '*) +S+?Q>4 5 

H

ŽL Ýßà

q ‘ á â ã

   Û

þ

žü \½ñÀ^>m '*) +S+?Q>4 5 

ÿ

L

Ý

ß à

á â ã

@.4216@Ap +?@Pñ (^) ÿ L¾H‹m †!+tR+>44Új(58F6167#+.0AFThu167 c#+?Ue+?7 c +f7y4-@A5F6D#421657#@ þ

žü \½ñ ^*dyh

ž¢¡ H

ž¢¡ \ÿ § ]Xñ (^) ÿ ^

 Áéëê‹ìbí î½ï„° L¯qm ·+>4€ñòL»” § ¼‹m '*) +?7Yo

ñ óL ôö÷

 Û

q — ` ‘ — ‘ ø úùû

'*) +?7Yo (^) üý (^) Ԝþ

\

ëñš^VLN‘o‹.7 c þ

žü \ëñš^I16@57 +>¢c 1 6=u+?7 @A1657 .FÇm ') +S+?Q>4 5 

H

ŽLÞÝßà

`

¥Ú¥

á Xâã

1 6@167 4 2) +tk+?0A7 +?F59&ñ‡oW@A581T@g.7x+?16R+?7yS+fQf4 5 0g9C50”æ.@2@25Q?16.4 +fc 45 O°Læ`m  9 CD 7 cW.=u+?7y4 .Fœ@2+>4€59&@A5F6D#421657#@?o#42) +?7YoW1T@I4 ) +t@A+f

ž¢¡(Ýßà

`

á â 㠙

ž¢¡ \ë¼ § ]Xñš^ Ýßà

á â 㠙

žŸK¡BÝßà

`

¥Ú¥

á â ã

jg) +?0A+

  gm

n •L \o Ü9p (^) X Ü X _Herq^=sˆ\5t I

kvuhF G

\½°I?^A^

Ö 1 T7 Q?+ (^) ä \Ü ^t1T@tQ?57y4 1 T7KD 5 D @q.7 c‡7 5 7l?+?0A5Á57‡4 )#+uQf5=uUW.Qf4q@2+>4wnuo;42) +?0A+81T@`. Qf57 @X4.7y

K —@2D Q)„4 ) .4 (^) Xä \Ü ^ X K

9 C50r.FTF Üfx n8mzy¢9 (^) c 1 6@-. Ô

Â]AM„c +fR02+f+ Ue5Fvh7#5=816.Fyjg) 5 @A+Q?5+fpWQf16+?7y42@B.02+IQfF65@A+(4 5 r42) 5 @2+59 (^) ä o4 ) +f7 (^) c )W.@‰42) +*U 0 A5Ub+f0A4216+?@ 4 2)W.

m (^) X c \Ü ^ X K Ã 9 C50 Ü`x n

‘m (^) X c \Ü ^ X K

9C50 X Ü X

K e

'*) 1 T@t16=uU F61T+?@€42)W.442) +s02554 @59 (^) c F61T+E167|{ I F G

\½°If^>m`}P5ljto;1v9~¹16@t. =O.4 0 21®Š jg)#5@2+Á+?7y4 0 A16+?@8.0A+ÁQfF65@A+x425¤42) 5 @2+Á59€F8o(4 ) +xQ?5+fp Q?16+f7y4 @u59r4 )#+ÁQ)W.0 .Q>4 +?0A16@X4 1 6Q Ue5Fvh7#5=816.F‹59~ .02+-Q?F65@2+r4 5 Ž42) 5 @2+59‚FOmV“P+?7 Qf+o ~æjg1TF6Fedb+)yhUb+f02de5F61TQrdyh4 )#+ .db5lS+t5d#@2+?0XS.4 1 T57 @?m„ƒ€ /†

] <16RD 0 A+Ž p ]&1TRD 0 2+r9C50h ‰Š#.=uU FT+?@f¢