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Math 303 (Engineering Mathematics II)
Exam 2
RED KEY
Part I: Multiple Choice. Mark the correct answer on your scantron. Each question is worth 5
points.
1. The roots of the characteristic equation for y (4) + 16y = 0 are:
a) 2, 2i
d)
1 i, 1 i
g)
b) 2i, re
Math 303 (Engineering Mathematics II)
Exam 2
RED KEY
Part I: Multiple Choice. Mark the correct answer on your scantron. Each question is worth 5
points.
1. Solve yy (y )2 = 0, y (0) = 1, y (0) = 1. Then, y (ln(2) =
a)
1
b)
d)
1
2
e)
g)
c)
2
f)
2
0
None o
Math 303 (Engineering Math II)
Exam 3
RED KEY
Part I: Multiple Choice Mark the correct answer on the bubble sheet provided.
1. What is the radius of convergence for
n=1
a)
0
b)
1
c)
2
d)
3
e)
4
f)
xn
?
n2
none of the above
Solution: The answer is (b).
2.
Math 303 (Engineering Mathematics II)
Exam 1
RED KEY
Part I: Multiple Choice. Mark the correct answer on your scantron. Each question is worth 5
points. In problems 1 to ?, match the dierential equation to its direction eld.
1. y = y (y + 3)
Solution: d)
Math 303 (Engineering Math II)
Exam 1
RED KEY
Part I: Multiple Choice Mark the correct answer on the bubble sheet provided.
1. How many of the ve functions,
y (t) = 0, y (t) = t, y (t) = t3 , y (t) = et , y (t) = cos t,
are solutions of the ordinary diere
Math 303 (Engineering Mathematics II)
Exam 3
RED KEY
Table of Laplace Transforms
f (t) = L1 cfw_F (s)
F (s) = L cfw_f (t) , G (s) = L cfw_g (t)
1
1/s
eat
1/ (s a)
tn , n positive integer
n!
sn+1
(p + 1)
sp+1
a
2 + a2
s
tp , p > 1
sin at
cos at
s2
s
+ a2
Math 303 (Engineering Mathematics II)
Exam 1
RED KEY
Part I: Multiple Choice. Mark the correct answer on your scantron. Each question is worth 5
points.
1. The solution to y =
a)
x2
is
y
3y 2 2x3 = C
d) x2 + y 3 = C
g)
b)
2x2 3y 3 = C
e) y 2 x3 = C
c) x2
Math 303 (Engineering Math II)
Exam 2
RED KEY
Part I: Multiple Choice Mark the correct answer on the bubble sheet provided.
1. The largest interval in which the solution of the initial value problem
(t3 4t2 + 3t)y + ty + (t 1)y = 0, y (2) = 0, y (2) = 1
i
Math303Winter2007Lecture/Homework/ExamSchedule
Lecture
Homework
SupplementalProblemsS#tobefoundinOutcomeStatements
M Jan. 8 Introduction
T Jan. 9 1.1SomeBasicMathematicalModels;DirectionFields
W Jan. 10 1.24SolutionsofSomeD.E.'s;ClassificationofD.E.'s
M J
Math 303 Review Sheet 2 Chapters 3-4
1. A. Solve the following linear dierential equations y y = 0 with y (0) = 3, y (0) = 1.
B. First solve the following linear dierential equations 9y + 3y 2y = 0, with y (0) = 9, y (0) = 3, then describe
the behavior th
Hi,
This is the new schedule(rooms are changed) for the Math 303 review (retake exams):
-Wednesday, February 04, 2009(Ji Li)
4:00 PM - 5:00 PM ,TMCB TMCB 108
-Thursday, February 05, 2009(Ji Li(2-3 p.m) Yu Hu(3-4 p.m.)
2:00 PM - 4:00 PM ,TMCB TMCB 133
-Tue
Math 303
Review Sheet 1
Chapters 1-2
1. For each of the following rst order ODEs, use the given direction eld to determine the behavior
of y as t . If the behavior depends on the initial value of y at t = 0, describe that dependency.
(a) y = 1 + y .
3
2
1
Math 303 (Engineering Mathematics II)
Exam 3
RED KEY
Part I: Multiple Choice. Mark the correct answer on your scantron. Each question is worth 5
points.
1. Given the initial value problem
y+
t2
1
1
y+
y=0
+ 2t + 2
t+1
y (0) = 1, y (0) = 1
what is the radi