AMS 510.01 Fall 2008, Final Exam
Name:
Student ID:
Score:
/200
The exam is in three parts:
•
The first section consists of problems involving the fundamental concepts of single and
multiple variable calculus. Do
all
questions from this portion. (100 points)
•
The second section consists of comprehensive problems in Linear Algebra. Choose
two
out of the three problems to do. (50 points)
•
The third section consists of comprehensive problems in Advanced Calculus. Choose
two
out of the three problems to do. (50 points)
Attention:
•
Write all solutions on this paper; extra sheets are available if needed.
•
Explain your answers and show all work. Correct answers with incomplete work will
not be given full points.
•
Calculators may
not
be used.
•
All cellular phones must be
turned off
. Anyone with a phone that rings during the
exam will be asked to turn in their exam and leave immediately. This includes text
message alerts and phones in vibrate mode.
Possibly useful trignometric relations
sin(
x
)
=
2 sin(
x
2
) cos(
x
2
)
cos(
x
)
=
cos
2
(
x
2
)

sin
2
(
x
2
)
d
d
x
(sin

1
(
x
))
=
1
√
1

x
2
;

x
 ≤
1
d
d
x
(cos

1
(
x
))
=

1
√
1

x
2
;

x
 ≤
1
d
d
x
(tan

1
(
x
))
=
1
1+
x
2
;
x
∈
R
Generalized curvilinear coordinate subsitutions
Elliptical
x
=
aρ
cos(
φ
)
y
=
bρ
sin(
φ
)
Elliptic

cylindrical
x
=
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 Fall '08
 Feinberg,E
 Calculus, Applied Mathematics, Derivative, Cos, Coordinate system

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