hw_4_14_09

hw_4_14_09 - x and y , then 1 T ′ T X ′′ Y XY ′′...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MA 221 Homework Solutions Due date : April 14 , 2009 Section 10.2, #2 ̄ 7 ̄ ̄ 9 ̄ (Underlined Problems are to be handed in) 2 ̄ 7 ̄ .) 2 u r 2 1 r u r 1 r 2 2 u 2 0 with u r , R r T . Subsituting into the PDE we get R ′′ T 1 r R T 1 r 2 RT ′′ or r 2 R ′′ rR R T ′′ T since the left hand side is purely a function of r , and the right hand side is purely a function of . Thus we have the two ODEs r 2 R ′′ rR R 0 T ′′ T 0 2 ̄ 9 ̄ .) u t u xx u yy with u x , y , t X x Y y T t . Substituting into the PDE we get XYT X ′′ YT XY ′′ T or 1 T T X ′′ Y XY ′′ XY Since the left hand side depends only on t , whereas the right hand side depends only on
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x and y , then 1 T ′ T X ′′ Y XY ′′ XY K where K is a constant. Therefore the equation for T t is T ′ − KT Now we also have from the above euqation that X ′′ Y XY ′′ KXY or 1 X ′′ X − Y ′′ Y K Since the left hand side depends only on x , whereas the right hand side depends only on y , we have X ′′ X − Y ′′ Y K J where J is a constant. Therefore, we get the equations X ′′ − KX Y ′′ J − K Y 2...
View Full Document

This note was uploaded on 09/22/2009 for the course MA MA221 taught by Professor Levine during the Spring '09 term at Stevens.

Page1 / 2

hw_4_14_09 - x and y , then 1 T ′ T X ′′ Y XY ′′...

This preview shows document pages 1 - 2. Sign up to view the full document.

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