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MATH 241 MAKEUP FINAL JANUARY 12, 2012 (LU, SHATZ)
The examination consists of 15 problems, the ﬁrst ten are worth 10 points
each, the second ﬁve are worth 20 points each. Answer all of them. The ﬁrst
10 are multiple choice, NO PARTIAL CREDIT given, but NO PENALTY
FOR GUESSING. To answer,
CIRCLE THE ENTIRE STATEMENT
YOU DEEM CORRECT
in the problem concerned. No work is required
to be shown for these 10 problems, use your bluebooks for computations and
scratch work. The next 5 are long answer questions, PARTIAL CREDIT
GIVEN–YOU MUST SHOW YOUR WORK. SHOW THE WORK FOR
THESE IN THE SPACE PROVIDED ON THE EXAM SHEETS. DO NOT
USE BLUE BOOKS FOR THESE 5 QUESTIONS; DO NOT HAND IN
YOUR BLUE BOOKS. No books, tables, notes, calculators, computers,
phones or electronic equipment allowed; one 8 and 1/2 inch by 11 inch pa
per allowed,
handwritten on both sides, in your own handwriting
;
no substitutions of this aid allowed.
NB. In what follows, we write
u
x
for
∂u
∂x
and
u
xx
for
∂
2
u
∂x
2
, etc. in those
problems concerning PDE.
YOUR NAME (print please):
YOUR PENN ID NUMBER:
YOUR SIGNATURE:
INSTRUCTOR’S NAME (CIRCLE ONE):
LU
SHATZ
SCORE:
Do not write below–for grading purposes only.
——————————————————————————————–
I
VI
XI
II
VII
XII
III
VIII
XIII
IV
IX
XIV
V
X
XV
——————————————————————————————
TOTAL:
——————————————————————————————
1
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This note was uploaded on 04/01/2012 for the course HIST 241 taught by Professor Zhu during the Spring '12 term at UPenn.
 Spring '12
 zhu

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