PHZ 3113 Fall 2011 Homework 4
Due at the start of class on Wednesday, September 21. Half credit will be available
for homework submitted after the deadline but no later than the start of class on Friday,
September 23.
Answer all questions. Please write ne

PHZ3113Introduction to Theoretical Physics Fall 2008 Problem Set 3 Solutions Sept 18, 2008 1. Applying the chain rule twice, 2u = f (x - ct) + g (x + ct) = u x2 2u = c2 (f (x - ct) + g (x + ct) = c2 u , t2 (1) (2)
so the equation given follows. As discuss

PHZ3113Introduction to Theoretical Physics Fall 2008 Problem Set 5 Solutions Sept 24, 2008 1. Applying the formula given in notes or Boas, d dx
1/x 1 1/x ext 1 dt = - 2 e1 x + ext dt t x 1 1 e e ex -ex e 1 ey dy = - + - = = - + x x x x x x x
(1) (2)
where

1
Test 1 solutions Phz 3113 Fall 2007 1. Expand x/(ex 1) to order x2 for x 1. x + x3 /3! + 1 (1)
1+x+ To order x2 ,
x2 /2!
1 (1 + x/2! + x2 /3! + . . . )
1 , 1 + (x/2! + x2 /3!)
(2)
which is an alternating geometric series in (x/2! + x2 /3!), so = 1 (x/2!

1
Test 3 solutions (choose 4/6, + extra credit) PHZ 3113 Fall 2007 1. Two blocks of mass m are connected to springs. The equations of motion can be written as m1 = -kx1 + 2k(x2 - x1 ) x m2 = -kx2 - 2k(x2 - x1 ) x (1) (2)
(a) Write the two coupled equatio

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 16
Nov. 19, 2008
Due: Friday, Nov. 21, 2008
Reading: Boas Ch. 14
1. Find residues of
(a)
z2
z 4 + 16
1
(3z + 2)(2 z)
at z0 =
(1)
(2)
2(1 + i).
(b)
at all poles.
Using complex integration met

PHZ 3113 Fall 2011 Homework 11
Due at the start of class on Wednesday, November 30. Half credit will be available
for homework submitted after the deadline but turned no later than the start of class on
Friday, December 2.
Answer all questions. Please wri

PHZ 3113 Fall 2011 Homework 10
Due at the start of class on Friday, November 18. Half credit will be available for
homework submitted after the deadline but turned no later than the start of class on Monday,
November 21.
Answer all questions. Please write

PHZ 3113 Fall 2011 Homework 7
Due at the start of class on Wednesday, October 19. Half credit will be available
for homework submitted after the deadline but no later than the start of class on Friday,
October 21.
Answer all questions. Please write neatly

PHZ 3113 Fall 2011 Homework 3
Due at the start of class on Wednesday, September 14. Half credit will be available
for homework submitted after the deadline but no later than the start of class on Friday,
September 16.
Answer all questions. Please write ne

PHZ 3113 Fall 2011 Homework 1
Due at the start of class on Monday, August 29. Half credit will be available for
homework submitted after the deadline but no later than the start of class on Wednesday,
August 31.
Answer all questions. Please write neatly a

PHZ 3113 Fall 2011 Homework 8
Due at the start of class on Wednesday, October 26. Half credit will be available
for homework submitted after the deadline but no later than the start of class on Friday,
October 28.
Answer all questions. Please write neatly

PHZ 3113 Fall 2011 Homework 9
Due at the start of class on Wednesday, November 9. Half credit will be available
for homework submitted after the deadline but turned in to NPB 2162 no later than noon
on Friday, November 11.
Answer all questions. Please wri

PHZ 3113 Fall 2011 Homework 2
Due at the start of class on Wednesday, September 7. Half credit will be available
for homework submitted after the deadline but no later than the start of class on Friday,
September 9.
Answer all questions. Please write neat

PHZ 3113 Fall 2011 Homework 12
Due at the start of class on Monday, December 5. No credit will be available for
homework submitted after the deadline.
Answer all three questions. Please write neatly and include your name on the front page of
your answers.

PHZ 3113 Fall 2011 Homework 5
Due at the start of class on Wednesday, October 5. Half credit will be available
for homework submitted after the deadline but no later than the start of class on Friday,
October 7.
Answer all questions. Please write neatly a

PHZ3113Introduction to Theoretical Physics Fall 2008 Problem Set 9 Oct. 4, 2008 Due: Wednesday, Oct. 8, 2008 Reading: Boas sec. 5-4,10.8,10.9
1. Calculate (a) sin (b) r2 sin
and
2
if =
in spherical coordinates. 2. Consider the vector field in Cartesian

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 14
Nov. 7, 2008
Due: Friday, Nov. 14, 2008
Reading: Boas Ch. 14
1. (1 pt.) Show whether the function f (z) = Re z is analytic or not.
2. (1 pt.) Find the analytic function w(x, y) = u(x, y)

PHZ3113Introduction to Theoretical Physics Fall 2008 Problem Set 2 Wednesday, Sept. 3, 2008 Due: Wednesday, Sept. 10, 2008 Reading: Boas chapt. 4
1. Show using L'Hospital's rule that (a) xn e-x 0 as x for any n, (b) ln x/xp 0 as x for any p > 0, i.e. an e

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 2 Solutions
Monday Sept. 15, 2008
1. (a) As x , applying LHospital we nd
xn
nxn1
const
. . . . x 0
x
x
e
e
e
(1)
1
ln x
p.
p
x
px
(2)
(b) similarly
If p > 0 this 0.
ax
m sin kx
0e
2. Take

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 5
September 17, 2008
Due: Friday, Sept. 19, 2008
Reading: Boas chapt. 4
1. Find
d
dx
1/x
1
ext
dt
t
(1)
2. The equation of state for a van der Waals gas is
p+
a
(v b) = C.
v2
Calculate dv/dp

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 10
Oct. 8, 2008
Due: Wednesday, Oct. 15, 2008
Reading: Boas sec. 6-11
1. Calculate the electric eld and scalar potential for a conducting sphere of radius
R for all r when a charge Q is dist

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 11
Oct. 15, 2008
Due: Friday, Oct. 17, 2008
Reading: Boas Ch. 3
1. The three Pauli matrices are
1 =
0 1
1 0
;
2 =
0 i
i 0
;
1 0
0 1
3 =
2
Show they have the properties i = 1 for any i, and i

PHZ3113Introduction to Theoretical Physics
Fall 2008
Problem Set 8 Solutions
Oct. 6, 2008
1.
v = 0.
(1)
So we need to show that the surface integral
vanishes. For the faces:
v da over the parallelepiped also
(a) x1 = 0, 0 x2 3, 0 x3 2:
da = dx2 dx3 (x1 )

PHY3113Introduction to Theoretical Physics
Fall 2007
Test 2 SOLUTIONS
Oct. 26, 2007
Useful formulae:
=
A=
1
1
r+
+
.
r
r
r sin
1 2
1 A
1
r Ar +
(sin A ) +
2 r
r
r sin
r sin
x = r sin cos = cos
y = r sin sin = sin
z = r cos = z
E = /
0
B = 0
E =

Phz3113 Fall 08
Test 3 solutions
1. Consider the matrices A =
0 1
1 0
and B =
3
2
1
2
1
2
3
2
.
(a) (3 pts) Specify whether A and B are i) Hermitian (or antiHermitian); ii)
orthogonal; iii) (symmetric (or antisymmetric).
Hermitian means M = M . A = AT

PHY3113Introduction to Theoretical Physics
Fall 2007
Test 1 55 minutes
Sept. 28, 2007
No other materials allowed. If you cant do one part of a problem, solve subsequent
parts in terms of unknown answerdene clearly. Do 5 of rst 6 problems, clearly
indicati