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, R), the set f (A) = ran f does not
have to be closed.

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 or unitary vector space V we
dene the adjoint A End(V )

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 Exercise 3 of Assignment 7). A spring
is characterized by t

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 exercise we use s = s(p) = (p) to denote
the length of the cur

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 R,
g : R3 R,
x 2y
3x + y
g(x, y, z) = cos(x + y + z)
f

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 exercises.
Exercise 1. In electrostatics, the potential at a

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(A, R), the set f (A) = ran f does not
have to be close

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, y, z) R : 2 + 2 + 2 1
a
b
c
where a, b, c > 0.
ii) the

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 to 10% of the total score may
be deducted solely due t

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 , . . . , en a basis of V . For an
endomorphism A L(V,

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 to 10% of the total score may
be deducted solely due t

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(A, R), the set f (A) = ran f does not
have to be closed

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 lecture, wehave already discussed
the general linear grou

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 JI)
Functions of Multiple Variables
Summer 2014
1 / 685

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 or unitary vector space V we
dene the adjoint A End(V )

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 : x1 = x4 .
i) Find dim U , dim V and dim U + V . Is the

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