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Unformatted text preview: Atsushi Inoue ECG 765: Mathematical Methods for Economics Fall 2009 Lecture Notes 22 The System of FirstOrder Difference and Differential Equations When we want to introduce interactions among variables, we will consider the system of difference and differential equations. First we will show that higherorder difference and differential equations can be written as a system of firstorder difference and differential equations, respectively. Then we will analyze the system of firstorder difference and differential equations. Outline A. SecondOrder Difference Equations as a System of FirstOrder Differ ence Equations B. The System of FirstOrder Difference Equations C. The System of FirstOrder Differential Equations A. SecondOrder Difference Equations as a System of FirstOrder Difference Equations. Consider a secondorder difference equation y t +2 = ay t +1 + by t + c. Let x t = y t +1 . Then we can express the original secondorder equation by means of two firstorder simultaneous equations as follows: x t +1 = ax t + by t + c, y t +1 = x t . B. The System of FirstOrder Difference Equations Consider " x t +1 y t +1 # = " a b c d #" x t y t # + " e f # 1 or z t +1 = Az t + w....
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This note was uploaded on 10/22/2009 for the course ECG 765 taught by Professor Fackler during the Fall '07 term at N.C. State.
 Fall '07
 FACKLER

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