{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test1_solns

# test1_solns - Test 1 Introduction to PDE MATH...

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

Solutions to Test 1 Test 1 Introduction to PDE MATH 3363-25820 (Fall 2009) This exam has 4 questions, for a total of 20 points. Please answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Upon finishing PLEASE write and sign your pledge below: On my honor I have neither given nor received any aid on this exam. 1 Rules You may only use pencils, pens, erasers, and straight edges. No calculators, notes, books or other aides are permitted. Scrap paper will be provided. Be sure to show a few key intermediate steps when deriving results - answers only will not get full marks. 2 Given You may assume the eigenvalues of the Sturm-Liouville problem X + λX = 0 , 0 < x < 1 X (0) = 0 , X (1) = 0 . are λ n = ( n - 1 2 ) 2 π 2 and X n ( x ) = cos ( ( n - 1 2 ) πx ) , for n = 1 , 2 , . . . , without derivation. You may also assume the following orthogonality conditions for m , n positive integers: 1 0 cos ( ( m - 1 2 ) πx ) cos ( ( n - 1 2 ) πx ) dx = 1 / 2 , m = n, 0 , m = n. Page 1 of 5 Please go to the next page. . .

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

View Full Document
Solutions to Test 1 3 Questions Consider the following heat problem in dimensionless variables u t = u xx + bx 2 , 0 < x < 1 , t > 0 u x (0 , t ) = 0 , u (1 , t ) = 1 , t > 0 u ( x, 0) = u 0 , 0 < x < 1 , where b > 0 and u 0 > 0 are constants. This is the heat equation with a source, where the rod is insulated at x = 0 and kept at 1 degree at x = 1.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern