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
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-dimensio
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 exercis
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 Exerc
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 , induce
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 6
Date Due: 10:00 AM, Thursday, the 26th of June 2014
Exercise 1. Consider the function g : R2 R,
cfw_
1
(x2 + x2 ) sin(x2 + x2 )
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-p
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(
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.
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 R
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
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