Spring 2000 Math 550 Exam 1, Exams of Vector Analysis

The spring 2000 exam 1 for math 550, a university-level mathematics course. The exam covers topics from vector calculus, including problem-solving and calculations based on vector notation, equations of planes, and calculus. Students are required to work logically, show their work, and indicate their reasoning. The exam includes instructions, problem inspirations, and examples from class and homework.

Typology: Exams

Pre 2010

Uploaded on 10/01/2009

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Prof. Girardi Math 550 12 February Spring 2000 Exam 1
MARK BOX
problem points
1 10
2 10
3 10
4 10
5 10
6 10
total 60
%100
NAME:
SSN:
INSTRUCTIONS:
1. To receive credit you must:
(a) work in a logical fashion, show all your work,
indicate your reasoning
(b) when applicable put your answer on/in the line/box provided
(c) if no such line/box is provided, then box your answer
(d) if you use your calculator on a particular problem, then indicate so.
2. The mark box indicates the problems along with their points.
Check that your copy of the exam has all of the problems.
3. As indicated on the syballus:
(a) allowed is a calculator (but not a computer)
(b) allowed are the class handouts: table of integrals, calculus for-
mula sheet, and Spring 2000 informal summary (along with your
personal scribbles on them)
(c) not allowed are books and other notes.
4. During this exam, do not leave your seat. If you have a question, raise
your hand. When you finish: turn your exam over, put your pencil
down, and raise your hand.
5. This exam covers (from Vector Calculus by Marsden&Tromba, 4th ed.):
Chs. 1, 2, §3.1, 4.1, 4.2 .
Problem Inspiration:
1. an example from class
2. homework problem ch 1 review # 9 and quiz 2 problem 2
3. homework problem ch 2 review # 7
4. quiz 3 problem 4
5. an example from class , §2.6 # 21
6. 1997 exam 1 # 5 .
1
pf3
pf4
pf5
pf8

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Download Spring 2000 Math 550 Exam 1 and more Exams Vector Analysis in PDF only on Docsity!

Prof. Girardi Math 550 12 February Spring 2000 Exam 1

MARK BOX problem points 1 10 2 10 3 10 4 10 5 10 6 10 total 60 % 100

NAME:

SSN:

INSTRUCTIONS:

  1. To receive credit you must: (a) work in a logical fashion, show all your work, indicate your reasoning (b) when applicable put your answer on/in the line/box provided (c) if no such line/box is provided, then box your answer (d) if you use your calculator on a particular problem, then indicate so.
  2. The mark box indicates the problems along with their points. Check that your copy of the exam has all of the problems.
  3. As indicated on the syballus: (a) allowed is a calculator (but not a computer) (b) allowed are the class handouts: table of integrals, calculus for- mula sheet, and Spring 2000 informal summary (along with your personal scribbles on them) (c) not allowed are books and other notes.
  4. During this exam, do not leave your seat. If you have a question, raise your hand. When you finish: turn your exam over, put your pencil down, and raise your hand.
  5. This exam covers (from Vector Calculus by Marsden&Tromba, 4th^ ed.): Chs. 1, 2, § 3.1, 4.1, 4..

Problem Inspiration:

  1. an example from class
  2. homework problem ch 1 review # 9 and quiz 2 problem 2
  3. homework problem ch 2 review # 7
  4. quiz 3 problem 4
  5. an example from class , § 2.6 # 21
  6. 1997 exam 1 # 5.

1

  1. A parameterization of the line L parallel to the intersection of the two planes

P 1 : 3 x + y + z = 5 P 2 : x − 2 y + 3z = 1

and passing through the point (4, 2 , 1) is:

R^ ~(t) = 〈 , , 〉 + t 〈 , , 〉

where t varies as:.

  1. An equation of the plane tangent to the graph of

f (x, y) = x^2 + y^4 + exy

at the point (1, 0 , f (1, 0) ) is:

Remark: your solution should be of the form ax + by + cz = d.

  1. Captain Ralph is out for a flight in his space ship again, traveling at a

constant speed of e^6 meters per second. The temperature of the ship’s hull when he is at location (x, y, z) will be given by

T (x, y, z) = exp (−x^2 − y^2 − z^2 )

where x, y, and z are measured in meters. He is currently at (1, 2 , 1). De- scribe the set of possible directions in which he may proceed to bring the ship’s hull temperature down at exactly a rate of 3

2 degrees per second. Box your answer.

  1. Houston, we have a problem. The space shuttle Atlantis is traveling along

with position vector ~r(t) =

t^2 , 3 t^2 , 4 t

If the power thrusters are turned off at time t, the Atlantis will coast off, with constant speed along a straight path tangent to the vector ~r(t). The Atlantis is almost out of fuel when astronaut John Grunsfeld notices the Mir space station off ahead of them at the position (220, 660 , 64). John realizes that their only hope is to turn the thrusters off, just at the proper time, so that the Atlantis will safely coast to dock with the Mir; but, John is not sure if his plan will work. So John quickly calls Tom and Ray for advice. Tom claims that John’s plan will work; Ray claims that John’s plan will not work. Who is right: Tom or Ray? Why? be sure to mathematically support your answer, explaining your thought process. If so needed, continue on the next (blank) page.

MORE SPACE FOR PROBLEM 6: