Lectures29and30

Lectures29and30 - F ig e : F ig e : E a a i fD b e eg a i a...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: F ig e : F ig e : E a a i fD b e eg a i a C d i a e e e ih ea a ea i eg a R f ( x, y ) dA ad h ed a i R i ch ha ica c e ie b ee eed i a c d ia e ac ic e ce eeda h e ig i f ea e e i igh e i eg ad iea egh ; e i e x = r cos ad y = r sin ad h e f ( x, y ) = f ( r cos , r sin ) ha hghd ed ih h ea ea e e e dA ? f ea i i age fa e f r i eg e fea eg h dr ad age fa e f i a ea ag e d h e h eeec i bd i id e R i a a ec ag e h icha e ea ec ag ea a eeF ig ee eed k ha h ea ea fa ica a ec ag e i ;c id eF ig eeca ha f ac ic e fad i r a ec fag e ha a ea 1 2 r 2 igh i ecaca c a eh ea ea fh ehad ed a ec ag e a h ed iee ceb e ee h ea ea fh e f ec fad i r + dr ad h e a e e ie had ed ec fad i r : dA = 1 2 ( r + dr ) 2 d- 1 2 r 2 d = rdrd + 1 2 dr 2 d. i ce eeg ig b e ig h i ia i eg a i h ich dr ad d a e i ie i a a ecad ica d h eecd e : dA = d bracketleftbig rdr + O ( dr ) 2 bracketrightbig b e e fec c ec eh db e i ig r ad a h iagead ak ig i i a h eea ache a a eh ik fh ec e d ic ia a i e fh e f fh ee f F ig e : ad h eecd e i i ie a eha h e h ee f e R xy f ( x, y ) dxdy = R r f ( r cos , r sin ) rdrd h ee e e ie R xy ad R r d e eh ea ed a id ec ib ed i h e a ia ec d ia e e C e : ha eha eh ee h ee iaecd e i i i e a d ead iA dr ad d a ach e ica a ec ag e b ec e ead eec ag a e id e fiha eg h r h ieh e h e id eha a c eg h rd fc e e ha e dA = rdrd A iceha h eec ag ea e a fh ea e ie ;h e i...
View Full Document

This note was uploaded on 04/05/2010 for the course MATH 119 taught by Professor Harmsworth during the Spring '08 term at Waterloo.

Page1 / 8

Lectures29and30 - F ig e : F ig e : E a a i fD b e eg a i a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online