1
PHY481 - Midterm II (2009)
Time allowed 50 minutes. Do all questions - to get full credit you must show your working.
Problem 1. a) Write down the integral and dierential forms of Maxwells equations. b) Set the source terms in the
dierential forms to ze
PHY 203: Solutions to Problem Set 3
October 16, 2006
1
Problem 7.7
Assigning coordinates of the double pendulum in the usual way we have
x1 = l sin 1
(1)
y1 = l cos 1
(2)
x2 = l(sin 1 + sin 2 )
(3)
y2 = l(cos 1 + cos 2 ).
(4)
The potential energy is V = m
PHYSICS 140B : STATISTICAL PHYSICS
PRACTICE MIDTERM SOLUTIONS
Consider a four-state ferromagnetic Ising model with the Hamiltonian
H = J1
Si Sj H
Si Sj J 2
i
ij
ij
Si ,
where the rst sum is over all nearest neighbor pairs and the second sum is over all ne
PHY 203: Solutions to Problem Set 4
October 24, 2006
1 Buoy Dropped from an Airplane
From energy conservation the buoy hits the surface of the water with a velocity
120 = x/2gh. The equation of motion that determines its subsequent behaviour
is
F 2 m7)
PHYSICS 140A : STATISTICAL PHYSICS
MIDTERM EXAM : DO ANY TWO PROBLEMS
(1) For each of the following situations, explain clearly and fully why it is or is not thermodynamically possible.
(a) Energy function E(S, V, N ) = a S V N with a constant. [6 points]
PHYSICS 140B : STATISTICAL PHYSICS
MIDTERM EXAM SOLUTIONS
Consider a four-state ferromagnetic Ising model with the Hamiltonian
H = J
Si Sj H
Si ,
i
ij
where the rst sum is over all links of a lattice of coordination number z. The spin variables
Si take va
INTRODUCTION TO DIFFERENTIAL EQUATIONS, FINAL EXAM
Sections 13-16, Fall 2002
Section meeting time Name 8 o \ A ( 0n )
Instructions. You are allowed to use three 8 1/2 X 11 inch sheets of paper of notes. No
calculators, PDAs, computers, books, or cellular
PHY 203: Solutions to Problem Set 1
September 30, 2006
1
Firing Shells at Constant Speed
Here we would like to nd the set of all points that lie on some trajectory of
a shell red with xed speed v0 , but at an arbitrary angle to the horizontal.
In particul
INTRODUCTION TO DIFFERENTIAL EQUATIONS, TEST 3
Sections 13—16, Fall 2002
Section meeting time Name
Instructions. You are allowed to use one 8 1/2 x 11 inch sheet of paper of notes. No
calculators, PDAs, computers, books, or cellular phones are allowed. Do
PHY 203: Solutions to Problem Set 2
October 9, 2006
1
Laser Beam in Refractive Medium
Here we nd the path of a light ray using Fermats principle. The travel time is
T=
n0
ds
=
v
c
1 + (y )2 (1 + ky )dx.
(1)
The rst integral (second form of the Euler-Lagra
PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #2 SOLUTIONS
(1) Consider a d-dimensional ideal gas with dispersion (p) = A|p| , with > 0. Find the
density of states D(E), the statistical entropy S(E), the equation of state p = p(N, V, T ), the
heat capa
INTRODUCTION TO DIFFERENTIAL EQUATIONS, TEST 2
Sections 13—16, Fall 2002
Section meeting time _ Name _——
Instructions. You are allowed to use one 8 1/2 X 11 inch sheet of paper of notes. No
calculators, PDAs, computers, books, or cellular phones are allow
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'f\.o+\.,~n~& con1ri bVl+~
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Math 38
Spring 2011
Midterm Exam 2 with Solutions
1. (15 points): Use the method of undetermined coecients to nd a particular solution
of the equation
x + x 2x = 18te2t .
Solution: The characteristic equation corresponding to the homogeneous equation is
2
INTRODUCTION TO DIFFERENTIAL EQUATIONS, TEST 1
Sections 13-16, Fall 2002
Section meeting time _-_ Name
Instructions. You are allowed to use one 8 1/2 x 11 inch sheet of paper of notes. No
calculators, PDAs, computers, books, or cellular phones are allowe