CAAM 336
DIFFERENTIAL EQUATIONS IN SCIENCE AND ENGINEERING
Examination 1
Posted 20 February 2008, 10:00 AM.
Due 12 noon on Wednesday, 27 February 2008.
Instructions:
1. Time limit:
4 uninterrupted hours
.
2. There are five questions worth a total of 100 points.
Please do not look at the questions until you begin the exam.
3. You
may not
use any outside resources, such as books, notes, problem sets, friends,
calculators, or MATLAB.
4. Please answer the questions thoroughly and justify all your answers.
If in doubt, provide more detail rather than less.
Show all your work to maximize partial credit.
5. Print your name on the line below:
6. Indicate that this is your own individual effort in compliance with the instructions above and
the honor system by writing out in full and signing the traditional pledge on the lines below.
7. Staple this page to the front of your exam.
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CAAM 336
·
DIFFERENTIAL EQUATIONS
1. [20 points]
Vector spaces
(a) Determine if the following sets are vector spaces or not justify your answer.
(Define
addition and scalar multiplication in the obvious way.)
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 Fall '09
 Tompson
 Linear Algebra, Vector Space, Boundary value problem, Hilbert space

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