Econ 431: Homework 4
Due date June 7, 2017
Example 1 Show that if x and y are real numbers, and x 6= 0, then there is a
unique real number r such that xr + y = 0.
We have to show
(1) existence. That i
Econ 431: Homework 5
Due date June 14, 2017
Denition 1 A set X is nite if there exists a bijection g that maps X onto
the set f1; 2; :; ng, n 2 N.
Denition 2 A set is countably innite if there exists
Econ 431: Homework 3
Due date May 31, 2017
Exercise 1 Suppose that A; B; C are sets. If A
C.
C and B
C, then A [ B
Solution 1 Let A C and B C, and let x be arbitrary such that x 2 A [ B.
Then either x
Econ 431: Homework 5 Solutions
Due date June 14, 2017
Denition 1 A set X is nite if there exists a bijection g that maps X onto the set f1; 2; :; ng, n 2 N.
To show that a set if nite, we need to nd s
Econ 431 Assignment 1
Due date: May 17, 2017
Abstract
Based on based on "Lecture01_preparatory" and Chapter 1 in "The
Way of Analysis." The document "Truth_Table" can be used as a quick
reference for
Econ 431: Homework 2
Due date May 24, 2015
Abstract
Attempt exercises 1 to 3 if you wish. They are dealing with binary relations, and are based on the document called Lecture2_Relations_2015.
Efe Ok a
Econ 431: Bang-Bang Optimal Control Example
Example 1 Find the optimal control that will
M ax
R2
V =
0
subject to
(2y 3u) dt
y0 = y + u
y(0) = 4 y(2)
f ree
and
u(t) U = [0, 2]
Since the problem is cha
ECON 431
Linear, First-Order Dierential Equations
1
Autonomous Equations
Definition 1 The general form of a linear, automomous, first-order dierential equation is
dy
+ ay = b
dt
(1)
where a, b are kno
Econ 431: Homework 3
Due date May 31, 2015
Exercise 1 Suppose that A; B; C are sets. If A
B and B
Exercise 2 Suppose that A; B; C are sets. Then An (BnC)
C, then A [ B
C.
(AnB) [ C.
Exercise 3 Show th
Econ 431 Assignment 1
Due date: May 17, 2017
Abstract
Based on based on "Lecture01_preparatory" and Chapter 1 in "The
Way of Analysis." The document "Truth_Table" can be used as a quick
reference for
Econ 431: Mathematical Economics
Assignment 6
From Chapter 20, exercise 20.2 questions 2, 3, 4
Summer 2007
Kevin Wainwright
2 The Hamiltonian is H = 6y + y + u (linear in u). Thus to maximize H, we ha
Econ 431: Mathematical Economics
Assignment 5 ANSWER KEY
Summer 2007
Kevin Wainwright
Denition 1 The particular integral (solution) yp is ANY solution that completes equation ?. In the case of the lin
Econ 431: Homework 2
Due date May 24, 2015
Abstract
Attempt exercises 1 to 3 if you wish. They are dealing with binary relations, and are based on the document called Lecture2_Relations_2015.
Efe Ok a
Econ 431, Homework 9
Due July 26, 2017
Exercise 1 Consider the metric space (R; dD ) where
(
0 if x = y
dD (x; y) =
1 else
Show that the set fag ; a 2 R, is open in (R; dD ). Think about what the open
Econ 431: Homework 4
Due date June 7, 2017
Exercise 1 (a) Show that if x 2 R, then the solution to x2 = 4 is not unique.
(b) Show that if x 2 R+ , then the solution to x2 = 4 is unique. Find this solu
Econ 431: Mathematical Economics
Summer 2007
Assignment 1
Kevin Wainwright
Instructions:The following assignment is a review of material from the second half of ECON 331. These
questions focus on chap