M 427L Second Exam
Put your answers to all the questions on the scan-tron sheet. Be sure you put
your eid on the scan-tron, and check to be sure you have entered it correctly (or
the computer will not give you credit for the exam)
1. Let : R3 R3 be a smoo
M 427L: Advanced Calculus for Applications II
Unique number: 58895
Meeting time and place: T,Th 9:30-11:00 RLM 4.102
Professor: Sean Keel, RLM 9.130, 471-3126
My Oce hours: M, Tu 8:30 - 9:30
TA: Kris Clabes, RLM 12.132, 475-8687, [email protected]
T
M 427L Second Practice Exam
1. Let : R3 R3 be a smooth function. What is the geometric meaning of
| det(D()(p)| (the absolute value of the determinant of the derivative at the
point p)?
(a) This tells you whether or not preserves orientation
(b) This give
M 427L
Each question is
worth 10
points,
the total is
120
No Graphing Calculators.
Put your answers to all the questions on the scan-tron sheet. Be sure to ll out
the top of the scan-tron sheet. I suggest you look at all of the possible answers
before mak
M 427L Practice for the third exam. The actual exam will not be so long
1. Let T (r, ) : R2 R3 be a dierentiable function. Which of the following is the
geometric meaning of
T
T
(
) dr d
r
(a) This is a vector normal to the surface, with length (roughly)
M
427L
Dierential form
Practice
for
the
third
exam
6. Explain why a 2-form on Rn is the same thing as a anti-symmetric n n matrix.
7. Let F = (F1 , F2 , . . . , Fn ) (take the corresponding column vector) be a vector
eld on Rn . Let =
Fi dxi be the corres