Anyone can describe how euler's method works?

[ddcamp]

let's say we do not know the proof.
then how do you guys describe it conceptually?
hm...><

 

[henry_m]

http://en.wikipedia.org/wiki/Euler_method"

 

[timthereaper]

It's a method to extrapolate the next point in a curve if you only have the starting point and the equation for its slope, since Euler's method is 1st order. Graphically, you're starting at a point and drawing the slope of a line until the horizontal component of the line equals your step size. Then you mark the end point and then based on that point, you calculate the slope of the line at that point and then draw another line. From there, it's lather-rinse-repeat.