Physics 263: Problem Set #10
These problems are due on Monday June 6.
0. Unassigned homework: go over old homework problems and solutions. Key math tech
niques you’ll want: expansion in Taylor series, Fourier series, various integration tech
niques (parts, parameters), complex numbers and functions thereof, matrices (inverses, de
terminants, eigenvectors). Key physics contexts: basic relativity kinematics,
E
2
=
p
2
+
m
2
collision problems, oscillators (whether damped, driven or coupled).
1. Shankar, BTM problem 6.4.6 pg. 138 (parts A and B only)
2. Shankar, BTM problem 9.7.10 pg. 288.
3. Morin 6.3 (Pendulum with an oscillating support) p. 246.
4. Morin 12.31 (Equal angles) p. 617.
5.
(a) Expand the following function about
z
= 0 through order
z
3
(keeping
only
up to
z
3
)
cosh(
z
) sin(
z
)
√
c
2

z
2
(b) Given
f
(
z
) =
u
(
x, y
)+
iv
(
x, y
), where
u
(
x, y
) =
x
2

y
2
+1+2
x
, find a
v
(
x, y
) which
makes
f
(
z
) analytic. What is this
f
(
z
) (i.e. written explicitly as a function of
z
)?
Is this
f
(
z
) unique? Explain.
6.
(a) Express the complex number
√

i
in both polar and in
x
+
iy
format.
Same for
cosh[1 +
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 Spring '10
 Kilcup
 Determinant, Critical Point, Fourier Series, Work, Complex number, hessian matrix

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