Math 432-532
Prof. Dimock
Spring 2015
name.SOLUTIONS.
class (432 or 532?) .
Exam 1
1. Consider the following subsets of R2
A = R2
B = cfw_(x, y) : |x| 1
C = cfw_(x, y) : 0 x 1, 0 < y < 1
D = cfw_(0, 0), (0, 1), (1, 0), (1, 1)
For each set state whethe
Math 432-532
Prof. Dimock
Spring 2015
name.
class (432 or 532?) .
Exam 2
1. (10 points) A polynomial in cos x is a function of the form
n
ck (cos x)k
p(x) =
k=0
Show that every continuous function on [0, ] is a uniform limit of a sequence of polynomials i
Syllabus for Math 432-532
Spring 2015
Prof. Dimock
1. This is a course in analysis in several variables. The textbook is Principles of Mathematical Analysis by Rudin. The prerequisite for the
course is Math 431 (analysis in one variable). The book actuall
Math 432-532
Prof. Dimock
Spring 2015
name.
class (432 or 532?) .
Exam 3
1. (12 points) Let f be a C function (i.e. C k for all k) dened in an open ball in Rn
around the origin. Let x be a point in this ball and for t [1, 1] dene
h(t) = f (tx)
(a) Find ex