MAT 3320 Example of Mid Term Exam
October 4, 2004
Duration: 80 minutes
INSTRUCTIONS: This is a closed book exam. No calculator of any sort is
allowed. Justify all your responses. You do not need to pr
MAT 3320 Assignment 3: Solutions
Note: You HAD to justify all computations.
1. (a) After you get rid of the window dressing, the problem boils down to solving the partial
dierential equation
2
2m
2
2
MAT 3320 Assignment 2: Solutions
Note: You HAD to justify all computations.
1. As seen in class, you either get
f (x) k 2 f (x) = 0
and g (t) k 2 c2 g(t) = 0,
or
f (x) = 0
and g (t) = 0.
In the rst ca
MAT 3320 Assignment 4: Solutions
Note: You HAD to justify all computations.
1. Since xo is an ordinary point, P (x) and Q(x) are analytic at xo . That means that they
can be expanded in a power series
MAT 3320 Assignment 2: Due November 8, 2004
Note: You have to justify all computations.
1. When solving the one-dimensional wave equation for a string of length L with both ends
xed
2y
1 2y
= 2 2
2
x
MAT 3320 Assignment 1: Solutions
Note: You HAD to justify all computations.
1. The only tools allowed are the ones dening a normed vector space. Thus assuming that
there is an inner product is wrong.
MAT 3320 Mid Term Exam
October 21, 2004
Duration: 80 minutes
INSTRUCTIONS: This is a closed book exam. No calculator of any sort is
allowed. Justify all your responses. You do not need to prove theore
MAT 3320 Mid Term Exam: Solutions
1. (a) An inner product space (V ; <, >) is a K-vector space V (K = R or C) equipped
with a mapping
<, >: V V K
such that
i. < v, v > R and 0 for all v V ; moreover <
MAT 3320 Denitions
1. A K-vector space: A vector space V over some scalar (eld) K(= R or C), is a set
equipped with two operations
+:V V V
and : K V V
where the two operations are required to satisfy
MAT 3320 Assignment 1: Due October 14, 2004
Note: You have to justify all computations.
1. Given a normed vector space (V, ), show that
| f g | f g
for all f, g V .
2. Let C[a, b] be the set of comple
MAT 3320 Assignment 3: Due November 25, 2004
Note: You have to justify all computations.
1. A particle is forced to live within a rectangular plate (2-dimensional), i.e., it is under the
inuence of th