Undergraduate Applied Analysis I APPM 4440 Homework 11
Due: Friday, Dec 2, 2011
A copy of the homework is due on Fri, Dec 2. Your graded hw will be due on Mon, Dec 5.
1. Section 7.3, p188 Read problems #1 through 4. Do two of them. Study example 7.14 and

Undergraduate Applied Analysis I APPM 4440 Homework 10
A copy of the homework is due on Fri, Nov 18. Your graded hw will be due on Mon, Nov 28.
1. Section 6.3, p155: #2
2. Section 6.4, p159: #1, 5
3. Section 6.5, p164: #5, 6
4. Section 6.6, p172: #3, 5
5.

Undergraduate Applied Analysis I APPM 4440 Homework 9
Due: Wednesday, Nov 2, 2011
A copy of the homework is due on Wed, Nov 2. Your graded hw will be due on Fri, Nov 4, or Monday, Nov 7
(your choice).
1. Section 6.1, p141: #5, 6
2. Section 6.2, p149: #3,

Homework 8 Solutions APPM 4440 Fall 2016
1. (4.4.3) (a) Using f (t) = t2 and g(t) = t3 , then
f (1) f (0)
f 0 (c)
2c
2
=1= 0
= 2 = c1
g(1) g(0)
g (c)
3c
3
Thus c = 23 .
(b) On the other hand for f (1) f (0) = 1 = f 0 (c)(1 0) = 2c, we have c = 21 uniquely

Homework 4 Solutions APPM 4440 Fall 2014
1. Copy the definitions from the text. There are many possible examples for each definition. (Grading: This problem is worth 5 points. If you have questions about your examples, please ask.)
2. (2.3.1)
(a) FALSE. O

Homework 9 Solutions APPM 4440 Fall 2016
1. Problem 1: Go over the statements of your definitions and theorems one more time. Then assign
yourself 10 points for this problem.
2. (6.1.1c) Since f (x) = x2 is monotone decreasing on [0, 1], the infima occur

Homework 7 Solutions APPM 4440 Fall 2016
1. (4.1.7) We assume f : R R is differentiable at x0 = 1, and the result of problem 4.1.6
(a) Let g(x) = x + 1, and x0 = 0 then
A = lim
h0
(b) Let g(t) =
f (1 + h) f (1)
f (g(h) f (g(0)
= lim
= f 0 (g(0) = f 0 (1).

Homework 1 Solutions APPM 4440 Fall 2016
Directions: Grade your homework and turn in the graded homework in class on Friday, Sept 2.
Each problem is worth 5 points, so this hw is worth 50 points total. Use a different color pen for
your grading and be sur

Homework 5 Solutions APPM 4440 Fall 2016
1. (3.1.1) These problems are very close to 2.1.1.
(a) FALSE. Consider the functions f, g : R R defined by f (x) = 1, x 0, and f (x) = 1, x <
0, and g(x) = f (x). Then f + g = 0, but neither f nor g is continuous.

Homework 6 Solutions APPM 4440 Fall 2016
1. (3.4.7) We are given f : D R and g : D R are uniformly continuous and bounded. We need
to show that the product, f g : d R is also uniformly continuous.
Proof Assume that cfw_un and cfw_vn are sequences in D w

Homework 10 Solutions APPM 4440 Fall 2016
1. Suppose a function E : R R is defined as the solution of the ODE
E 0 (x) = xE(x),
E(0) = 1.
We will assume that this equation has a solution, and that E(x) 6= 0 for all x R. For this
problem, you are to answer

Homework 2 Solutions APPM 4440 Fall 2016
Directions: Grade your homework and turn in the graded homework in class on Friday, Sept 9. (If
you need extra time, thats fine. You can put your graded homework under my office door later
on Friday or sometime on

Homework 3 Solutions APPM 4440 Fall 2016
1. (2.1.1) (Grading: 1 point each for parts a, b, and d. 2 points for part c.)
(a) FALSE. Consider the sequence an = (1)n . Since cfw_a2n = cfw_1 this converges to 1,
but cfw_an does not converge, recall Example

Undergraduate Applied Analysis I APPM 4440 Homework 8 Due: Wednesday, Oct 26
A copy of your solutions is due on Wed, Oct 26. Your graded solutions are due on Friday, Oct 28.
1. Section 4.4: #6, 7, 8
2. Section 5.2: #3, 5, 8, 11, 12 (11 and 12 go together)

Undergraduate Applied Analysis I APPM 4440 Homework 3
Due: September 14, 2011
A copy of the hw is due in lecture on Wed, Sept 14. Your nal, graded copy is due in lecture on Fri, Sept 16.
1. Section 2.1, p32: #1, 3, 4, 10, 14, 16, 18
2. Section 2.2, p37: #

Undergraduate Applied Analysis I APPM 4440 Homework 2
Due: September 7, 2011
A copy of the homework is due in lecture on Sept 7. Your nal, graded hw is due in lecture on Fri, Sept 9.
1. Section 1.1, p11: #17
2. Section 1.2, p16: #1, 4
3. Section 1.3, p19: