LEC08 - ELEC2102 - Lec 8 Differential equations Sec 8.4 8.6...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
ELEC2102 ELEC2102 - Lec Lec 8 Differential equations Sec 8.4 – 8.6 Classifications of DE’s Classifications of DE’s Restrict ourselves to equations with derivatives with respect to time t Generally can put the time derivatives explicitly on one side Start with a first order DE (,) dx f xt dt =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Classifications of DE’s 2 Classifications of DE’s 2 If there is no explicit time dependence the equation is autonomous , that means knowing the x value only, we know where the solution will go next Of course there is still implicit time dependence in the derivative dx/dt (,) dx f xt dt = first order nonlinear first order nonlinear automonous automonous DE DE 2 xx dx dt - = Graph with dfield5/6/7 (Rice University) x=1 is an unstable equilibrium equilibrium, x=0 is stable Unstable, ball on top of hill, 2 nd deriv>0 Stable, ball in valley, 2 nd deriv<0.
Background image of page 2
2 first order linear 2 first order linear automonous automonous DE’s DE’s ( 29 ( 29 ,, d x dy f x y gxy d t dt == f and g are linear functions of x and y
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 03/20/2011.

Page1 / 7

LEC08 - ELEC2102 - Lec 8 Differential equations Sec 8.4 8.6...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online