final

# final - x = 0 Page 5 Name Exercise 5 Determine wether the...

This preview shows pages 1–10. Sign up to view the full content.

Final Exam Math 5C, UCSB, Fall ’06 You have 3 hours to complete this exam. Name: Perm #: Signature: Discussion section: Show all your work. Partial credit will be given only if work is relevant and correct. Please make your work as clear and easy to follow as possible. You might want to put scratch work on the back of every sheet, and put neat clean work on the front of every sheet. You don’t need to simplify your answers but you need to justify them. Possible Problem Points Score 1 10 2 10 3 10 4 10 5 10 Extra 10 Total 50 (+10)

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

View Full Document
Name: Exercise 1. Verify Stoke’s theorem for the vector ﬁeld F = ( xy, xz, z + 1) where S is the surface deﬁned by z = x 2 + y 2 and z = 1. Page 2
Name: Exercise 2. Find the Fourier series of the function f ( x ) = ± 2 if 2 x < (2 k + 1) π 0 if (2 k + 1) π x < (2 k + 2) π where k = 0 , ± 1 , ± 2 , . . . . f ( x ) = Page 3

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

View Full Document
Name: Exercise 3. Let S be the upper half surface of the sphere x 2 + y 2 + z 2 = 4. Compute R R S z 2 dS = Page 4
Name: Exercise 4. Expand the function f ( x ) = x 2 e 2 x into a power series around the point

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.

Unformatted text preview: x = 0. Page 5 Name: Exercise 5. Determine wether the following series converge (Justify your answer): 1) ∞ X k =1 (-1) k 2 k + 1 2) ∞ X k =1 e k e 2 k-1 3) ∞ X k =1 1 2 k 2-1 Page 6 Name: Exercise 6. Find the solution for the wave equation: u tt-25 u xx = 0 u (0 , t ) = 0 t ≥ u ( π, t ) = 0 t ≥ u ( x, 0) = 2 sin( x ) ≤ x ≤ π u t ( x, 0) = 3 sin(2 x ) ≤ x ≤ π u ( x, t ) = Page 7 Name: Exercise 7. Determine for which x the following series converges: ∞ X k =1 e kx Compute its value for all the values of x , for which it converges. Page 8 Name: Exercise 8. ( Extra) Let S be the surface deﬁned by z = x 2 + y 2 , z =-x 2-y 2 and x 2 + y 2 = 1 and let F = ( x + y, y + z, x 2 + z ). Compute Z Z S F n dσ = Page 9 Name: Page 10...
View Full Document

{[ snackBarMessage ]}

### Page1 / 10

final - x = 0 Page 5 Name Exercise 5 Determine wether the...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online