530_343lecture06 - ME 530.343: Design and Analysis of...

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Unformatted text preview: ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 6 Classification of Differential Equations Friday, February 13, 2009 Todays Objectives Purpose of todays lecture: Introduce classifications of differential equations 1 st order, homogeneous ordinary differential equations Reading: Palm 3.13.2 Why Classify? Different solution techniques exist for certain classes of differential equations. To start: identify independent variable(s) ( usually in time ( t )). Next: identify dependent variables (the unknowns) example: x is a dependent variable if it is governed by a differential equation Note: sometimes symbols such as x , x , and x appear, but x is not a dependent variable be- cause x , x , and x are considered to be known functions of an independent variable (e.g. t ) this is a SPECIFIED or PRESCRIBED variable Assume that x , y , are dependent variables and t is an independent variable. 1. Types of Differential Eqns. Differential vs. Algebraic Eqns. dy dt = 7 diff. equation 3 y = 7 alg. equation d 2 y dt 2 + dy ds = 0 diff. equation 7 y 4 + cos( t )sin( y ) 3 = tan( t ) + 99 alg. equation 1 Ordinary vs. Partial Differential Eqns. If dependent variable ( x ) in a differential equation is a function of only 1 independent variable ( t ), then the derivative dx dt is called the ordinary derivative of x with respect to t If x is a function of 2 or more independent variables, then...
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This note was uploaded on 03/02/2010 for the course MECH 530.343 taught by Professor Sun during the Spring '08 term at Johns Hopkins.

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530_343lecture06 - ME 530.343: Design and Analysis of...

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