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LastName, FirstName
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Student #
Econ 351, Spring 2014
Homework 2
Due at the beginning of the lecture on January 30, 2014.
This homework covers materials from chapters 19 and 20 in the textbook.
Email submissions and late assignments will NOT be conside
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Linear, First Order Difference Equations
Hoy et al. Chapter 18
1 / 41
Outline
Linear, Autonomous, First Order Difference Equations
Form
What we mean by Solving a difference equation
Solution Method 1: by Conjecture
Provin
Economics 351
Math Econ II: Introduction to Dynamic Methods
MidTerm Examination
Spring 2012
The standards and reputation of a University and its Departments are the shared responsibility of its
faculty and students. Students are expected to observe the s
ECON 351
ASSIGNMENT 3
Due no later than 4:00 on Monday January 30th. Late assignments will not be graded.
Hand in your completed assignment by dropping it in the return box marked ECON 351 outside of
the Department of Economics main office (BEC 360).
Only
ECON 351
Assignment 2
Due by 4:00 pm on January 23 in the assignment box for econ 351 outside of BEC 363
Late assignments will not be graded and will get a score of zero.
NOTE: Only two randomly selected problems will be graded.
Solve the following proble
ECON 351
Assignment 1
Due by 4:00 pm on January 16 in the assignment box for econ 351 outside of BEC 363
Late assignments will not be graded and will get a score of zero.
For each of the following equations, indicate whether it is a differential or differ
Economics 351
Math Econ II: Introduction to Dynamic Methods
MidTerm Examination
Spring 2010
The standards and reputation of a University and its Departments are the shared responsibility of its
faculty and students. Students are expected to observe the s
Econ 351 Mathematical Economics II: Introduction to Dynamic Methods
Page 50
ASSIGNED READING FOR THIS SECTION: Chapter 24.1 and 24.2: Hoy et al. 2nd Edition
.
10 Systems of Differential Equations
10.1 System of n Linear, Autonomous Difference Equations
Th
Econ 251 Practice Questions (Spring 2005)
Find the general solution of the given system of linear difference equations and describe
the behaviour of the solution as t for questions 1 through 8
3 2
1. x' =
2 2x
2 1
2. x' =
3 2x
2 1
3. x' =
1 2x
1
Price Adjustment with Entry and Exit (Hoy Ch.23)
1. Proof of general solutionsolution
We are trying to show that the generic
solution for the case with imaginary roots :
[email protected]_D = [email protected] * tD * HA1 * [email protected] * tD + A2 * [email protected] * tDL + c
.
solves the differenti
ECON 351
ASSIGNMENT 5
DUE NO LATER THAN 4:30 ON MONDAY MARCH 5.
Only a random selection of these exercises will be graded.
Exercises 16.1 (p. 707708)
 Question 2 (a), (c), (e)
 Question 4 (b), (c), (d)
Exercises 16.5 (p. 747748)
 Question 2 (a), (c),
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Nonlinear Autonomous First Order Differential Equations
Hoy et al. Chapter 22
March 12, 2015
1 / 19
Outline
Nonlinear Autonomous First Order Differential Equations
Form
Analyzing Nonlinear Differential equations
The phase
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Nonlinear Autonomous First Order Difference Equations
Hoy et al. Chapter 19
January 29, 2015
1 / 39
Outline
Nonlinear Autonomous First Order Difference Equations
Form
Solving nonlinear difference equations
The phase diagr
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Linear Autonomous Second Order Difference Equations
Hoy et al. Chapter 20 and Complex Number Appendix
February 22, 2015
1 / 40
Outline
General Form
Solving linear second order difference equations
Homogenous and Particula
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Preliminaries  Hoy et al. Chapter 17
1 / 21
Outline
Time and the Measurement of Variables
Discrete vs. Continuous Time
Difference Equations
The Classification of Difference Equations
Order
Autonomous vs. Nonautonomous
L
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamical Methods
Course Overview
Dr. Daniel Rondeau
Spring 2016
1 / 16
Overview
The Basics
Defining Mathematical Dynamics
Course Objectives
Material Covered
Grading
Should you really take this course?
On Studying this material
So
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
First Order Linear Autonomous Differential Equations
Hoy et al. Chapter 21
March 9, 2015
1 / 23
Outline
Continuous time
A key result: e
Discounting  Generalizing Bernoullis Result!
The Linear Autonomous First Order Ordin
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Systems of Differential Equations
Hoy et al. Chapter 24
April 2, 2015
1 / 57
Outline
Systems of Autonomous First Order Linear Equations
General Form
Solving linear systems
The Homogenous part
Solving the homogenous part b
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Linear Autonomous Second Order Differential Equations
Hoy et al. Chapter 23
1 / 40
Outline
General Form
Solving linear second order differential equations
Homogenous and Particular Parts
The Solution to the Homogenous Par
Mathematical Economics II: An Introduction to Dynamic Methods
ECON 351

Spring 2016
ECON 351: Math Econ II  Dynamics
Integration
Hoy et al. Chapter 16
March 2, 2015
1 / 20
Outline
What is an Integral
Integral as AntiDerivative
Sum of a Continuous Variable
Rules of Integration
Power Rule
Integral of a Sum
Integral with a Constant
Expone
ECON 351
ASSIGNMENT 4
Due no later than 4:00 on Monday February 27. Late assignments will not be graded.
Hand in your completed assignment by dropping it in the return box marked ECON 351 outside of
the Department of Economics main office (BEC 360).
Only
FINAL EXAM ECON 351 SPRING 2010
Q1.
(5 points) Here are two facts:
1) If a variable y satisfies y 0.5 y , it diverges away from its steady state for any initial
value of y different from zero.
2) If a variable y satisfies yt 1 0.5 yt , it converges to its
Econ 351 Mathematical Economics II: Introduction to Dynamic Methods
Page 20
ASSIGNED READING FOR THIS SECTION: Chapter 19: Hoy et al. 2nd Edition
3. NonLinear, First Order Difference Equation
3.1 Generic Form
The generic form of a NonLinear First Order
Economics 351  Spring 2012
Math Econ II: Introduction to Dynamic Methods
MidTerm Examination #1 February 2nd.
The standards and reputation of a University and its Departments are the shared responsibility
of its faculty and students. Students are expect
Econ 351 Mathematical Economics II: Introduction to Dynamic Methods
Page 27
ASSIGNED READING FOR THIS SECTION: Appendix on Complex Numbers: Hoy et al.
2nd Edition
.
4. Complex Numbers (Appendix)
A complex number is a number that contains a square root of
ECON 351
ASSIGNMENT 7
WILL NOT BE GRADED
Exercises 23.1 (p. 918)
 Question 2 (a) (b) (c) (d)
Review Exercises (p. 925)
 Question 2 (a)
 Question 3
 Question 4
 Question 5
EXTRA QUESTION
Consider the differential equation y + a1 y + a2 y = b , where t