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Math background answers for Physics 316, Modern Physics I (HoFstaetter/Hinderer/Thibault)
Date: Wednesday, 01/28/04
0)
Have you taken the prerequisite math courses?
These are: coregistration in at least MATH 294 (linear algebra) or equivalent. MATH 294 has the
prerequisit MATH 192, covering polar coordinates, in±nite series, and power series, vectors and
calculus of functions of several variables, double and triple integrals.
Result:
85% yes, 12% don’t know, 3% no.
1)
Use complex numbers to derive the following equation: sin(2
α
) = 2 sin(
α
) cos(
α
).
Solution:
sin(2
α
) =
e
i
2
α

e
i
2
α
2
i
=
(
e
iα

e
iα
)(
e
iα
+
e
iα
)
2
i
= 2
e
i
2
α

e
i
2
α
2
i
e
i
2
α
+
e
i
2
α
2
= 2 sin(
α
) cos(
α
).
Result:
42% correct, 58% wrong.
2)
What is the general solution of the following ODE:
x
00
=
kx
for
k <
0 and for
k >
0?
Solution:
²or
k <
0 it is
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.
 Spring '05
 HOFFSTAETTER
 Physics

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