2010 Exam 2.pdf - Mathematics 3363 Review for Examination II Summer 2010 1 Derive the solution to ∂u(x t ∂t u(0 t u(L t u(x 0 ∂2u(x t for t ≥ 0

# 2010 Exam 2.pdf - Mathematics 3363 Review for Examination...

• 4

This preview shows page 1 - 3 out of 4 pages.

Mathematics3363 ReviewforExaminationII Summer2010 1. Derivethesolutionto ∂u ∂t ( x,t ) = κ 2 u ∂x 2 ( x,t ) for t 0 and 0 x L , u (0 ,t ) = 0 for t 0 , u ( L,t ) = 0 for t 0 , and u ( x, 0) = f ( x ) for 0 x L whereeachof κ and L isapositivenumber. 2. Derivethesolutionto ∂u ∂t ( x,t ) = κ 2 u ∂x 2 ( x,t ) for t 0 and 0 x L , ∂u ∂x (0 ,t ) = 0 for t 0 , u ( L,t ) = 0 for t 0 , and u ( x, 0) = f ( x ) for 0 x L whereeachof κ and L isapositivenumber. 3. Findthesolutionto ∂u ∂t ( x,t ) = κ 2 u ∂x 2 ( x,t ) for t 0 and 0 x 1 , u (0 ,t ) = u (1 ,t )=0 for t 0 ,and u ( x, 0) = sin πx for 0 x 1 . 4. Sketch the graphs where y = x 2 with x> 0 and where y =tan x with x> 0 on the same set of axes and find numerical approximations to the first two numbers x such that 2sin x x cos x =0 . 5. Derivethesolutionto ∂u ∂t ( x,t ) = κ 2 u ∂x 2 ( x,t ) for t 0 and L x L , u ( L,t ) = u ( L,t ) for t 0 , ∂u ∂x ( L,t ) = ∂u ∂x ( L,t ) for t 0 , and u ( x, 0) = f ( x ) for L x L whereeachof κ and L isapositivenumber.
Summer2010page2 6. Sketchthegraphswhere

#### You've reached the end of your free preview.

Want to read all 4 pages?

• Spring '19

### 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