section28 - Chapter 2 MAT188H1F Lec03 Burbulla Chapter 2...

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Unformatted text preview: Chapter 2 MAT188H1F Lec03 Burbulla Chapter 2 Lecture Notes Fall 2007 Chapter 2 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 2 Chapter 2 2.8 Systems of Differential Equations Chapter 2 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 2 2.8 Systems of Differential Equations Exponential Growth and Decay Hopefully, you’ve seen the following in high school, or in MAT186H1F. If y is a function of x and y = ky , then y = y e kx , where y = y , when x = 0 . If you haven’t, the result is easy to check: y = y e kx ⇒ dy dx = d y e kx dx ⇒ dy dx = y d e kx dx ⇒ dy dx = y k e kx ⇒ dy dx = k y e kx ⇒ dy dx = k y Chapter 2 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 2 2.8 Systems of Differential Equations Systems of Linear Equations What we will do is extend the previous result to a linear system of differential equations, which we will be able to solve if the coefficient matrix is diagonalizable. Here’s an example: y 1 = 3 y 1 + y 2 y 2 = 3 y 1 + 5 y 2 What we are solving for are two functions of...
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This note was uploaded on 06/22/2008 for the course ENGINEERIN MAT188 taught by Professor Burbula during the Fall '07 term at University of Toronto.

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section28 - Chapter 2 MAT188H1F Lec03 Burbulla Chapter 2...

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