{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Final+and+solutions

# Final+and+solutions - MAE 140 Final Examination Thursday...

This preview shows pages 1–12. Sign up to view the full content.

MAE 140 Final Examination Thursday, December 13, 2007, 8:00am – 10:00am, SSPA 1100 Total Possible Score: 40 Points. No Books/Notes/Calculators/Computers/Phones. Problem 1 (20 Points): Diffusion Partial Differential Equation by Separation of Variables Consider this partial differential equation (PDE) for u x ,t with t 0 and 0 x L : u t = 2 u x 2 with boundary condition u /∂ x = 0 at x = 0 for t 0 , boundary condition u = 0 at x = L for t 0 , and initial condition u = 1 at t = 0 for 0 x L . Using separation of variables and superposition, find the solution u x ,t that satisfies the PDE as well as the boundary/initial conditions. Show all your steps. Express your final answer as a sum, or as the first three nonzero terms, without any integrals. Problem 2 (20 Points): Wave Partial Differential Equation by Separation of Variables Consider this partial differential equation (PDE) for u x ,t with t 0 and 0 x L : 2 u t 2 = 2 u x 2

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

Final+and+solutions - MAE 140 Final Examination Thursday...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online