PHYSICS II (Fall 2012)
PROBLEM SET 9
Due: 13 December 2012, 4 p.m.
Problem 1. Electromagnetic radiation is emitted by accelerating charges. As we briey mentioned
in the class the rate at which energy E is emitted due to an accelerating charge q is
given b
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 10
Date Due: 10:00 AM, Thursday, the 24th of July 2014
Exercise 1. Consider the following velocity elds v : R2 R2 of two-dimensional uid ow (here c R xed
is a xed parameter):
( )
i) la
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 7
Date Due: 10:00 AM, Thursday, the 3rd of July 2014
Exercise 1. Let C be a smooth, oriented, simple, open curve. In this exercise we use s = s(p) = (p) to denote
the length of the cur
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 8
Date Due: 10:00 AM, Tuesday, the 15th of July 2014
Exercise 1. Consider again the problem of compression of a spring (see Exercise 3 of Assignment 7). A spring
is characterized by th
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 9
Date Due: 10:00 AM, Tuesday, the 22nd of July 2014
Exercise 1. In electrostatics, an electrostatic potential V : R, R3 , induces an electric eld, whose
electric eld intensity at p is
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 4
Date Due: 10:00 AM, Thursday, the 12th of June 2014
Exercise 1. The sketch at right shows a linear electric quadripole or
two-port network in pi () conguration. The relationship betw
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 5
Date Due: 10:00 AM, Thursday, the 19th of June 2014
Exercise 1.
i) Give an example to show that if a set A R is closed and f C(A, R), the set f (A) = ran f does not
have to be closed
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 1
Date Due: 10:00 AM, Thursday, the 22nd of May 2014
You are required to compose your solutions in neat and legible handwriting. Up to 10% of the total score may
be deducted solely due
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 2
Date Due: 10:00 AM, Thursday, the 29th of May 2014
Exercise 1. Let
U = cfw_x R4 : x1 + x2 + x3 = 0, x1 + 3x2 = x4 ,
V = cfw_x R4 : x1 = x4 .
i) Find dim U , dim V and dim U + V . Is
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 3
Date Due: 10:00 AM, Thursday, the 5th of June 2014
Exercise 1. The transpose of a matrix A = (aij ) Mat(m n, C) is dened as AT
For example,
a11
a11 a12 a13 a14
a12
T
A = a21 a22 a23
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 11
Date Due: 10:00 AM, Thursday, the 31st of July 2014
Exercise 1. Find the volume of
i) the ellipsoid
E=
cfw_
x2
y2
z2
(x, y, z) R3 : 2 + 2 + 2 1
a
b
c
where a, b, c > 0.
ii) the fou