Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 4
Date Due: 10:00 AM, Tuesday, the 23rd of June 2014
Exercise 1.
i) Give an example to show that if a set A R is closed and f C(A
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 8
Date Due: 10:00 AM, Thursday, the 16th of July 2015
Exercise 1. Consider again the problem of compression of a spring (see Exer
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 3
Date Due: 10:00 AM, Thursday, the 11th of June 2014
Exercise 1. For an endomorphism A End(V ) of a nite-dimensional euclidean o
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 9
Date Due: 12:10 PM, Monday, the 1st of August 2016
Exercise 9.1. Consider the vector eld
( )
1
y
F (x, y) = 2
.
2
x +y
x
F : R
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 7
Date Due: 12:10 PM, Monday, the 18th of July 2016
Exercise 7.1. Let C be a smooth, oriented, simple, open curve. In this exerci
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 8
Date Due: 12:10 PM, Monday, the 25th of July 2016
Exercise 8.1. Consider again the problem of compression of a spring (see Exer
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 6
Date Due: 12:10 PM, Monday, the 11th of July 2016
Exercise 6.1.
i) Let f, g : R R, F : R2 R. Show that
d
F (f (t), g(t) = f (t)
Vv285 Honors Mathematics III
Functions of a Multiple Variables
Term Project
Date Due: 4:00 PM, Monday, the 8th of August 2016
General Information
For this term project you will form groups of four or
Vv285 Assignment 6
Dong Jing
515370910182
July 10, 2016
1
1
Ex 6.1
i)
Consider a map G : R R2 , G(t) = (f (t), g(t).
d
d
F (f (t), g(t) = F (G(t) = DF |G(t) DG|t
dt
dt
0
f (t)
DG|t =
0
g (t)
DF |G(t)
Vv285 Assignment 4
Dong Jing
515370910182
June 20, 2016
1
1
Ex4.1
i)
We need to show that SL(n, R) is a subgroup of GL(n, R).
Thus, the group operation of SL(n, R) is also the matrix multiplication.
A
Vv285 Assignment 5
Dong Jing
515370910182
July 9, 2016
1
1
Ex 5.1
i)
(
0
x = 0 or x = 1
0<x<1
Because R \ A = cfw_x R : x < 0 or x > 1, for every x in R \ A, assume that
x = 0 or x = 1 + ( > 0).
There
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 6
Date Due: 10:00 AM, Thrusday, the 2nd of July 2015
Exercise 1. Let C be a smooth, oriented, simple, open curve. In this exercis
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 5
Date Due: 10:00 AM, Tuesday, the 30th of June 2014
Exercise 1. Consider the function g : R2 R,
cfw_
1
(x21 + x22 ) sin(x21 + x2
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 2
Date Due: 4:00 PM, Friday, the 5th of June 2015
Exercise 1. Let
U = cfw_x R4 : x1 + x2 + x3 = 0, x1 + 3x2 = x4 ,
V = cfw_x R4 :
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 4
Date Due: 10:00 AM, Thursday, the 11th of June 2014
Exercise 1. For an endomorphism A End(V ) of a nite-dimensional euclidean o
Honors Mathematics
Linear Algebra and Functions of Multiple Variables
Dr. Horst Hohberger
University of Michigan - Shanghai Jiaotong University
Joint Institute
Summer Term 2014
Dr. Hohberger (UM-SJTU
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 4
Date Due: 12:10 PM, Monday, the 20th of June 2016
Exercise 4.1. This exercise introduces the classical matrix groups. In the le
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 5
Date Due: 12:10 PM, Monday, the 27th of June 2016
Exercise 5.1.
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 2
Date Due: 12:10 PM, Monday, the 6th of June 2016
You are required to compose your solutions in neat and legible handwriting. Up
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 3
Date Due: 12:10 PM, Monday, the 13th of June 2016
Exercise 3.1. Let V be a nite-dimensional inner product space and B = cfw_e1
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 1
Date Due: 12:10 PM, Friday, the 27th of May 2016
You are required to compose your solutions in neat and legible handwriting. Up
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 10
Date Due: 10:00 AM, Thursday, the 30th of July 2015
Exercise 1. Find the volume of
i) the ellipsoid
cfw_
2
y2
z2
3 x
E = (x,
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 4
Date Due: 10:00 AM, Tuesday, the 23rd of June 2014
Exercise 4.1.
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 11
Date Due: Not graded
This assignment will not be graded; it is for your reference only in roder to provide some practice exerc
Vv285 Honors Mathematics III
Functions of Several Variables
Assignment 7
Date Due: 10:00 AM, Thursday, the 9th of July 2015
Exercise 1. Calculate the following directional derivatives:
f : R2 \ cfw_0
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.