Applet objetive
To interpret geometrically a differential equation of the first order and to bring a solution near by means of Euler's method.
Input data
For keyboard:
- Value of the step h
- Value of A
- The differential equation that is wanted to aproximate
- To show the representation in the graph the button will be touched " Draw Euler ".
On the graph:
- The sliders "longitud" and "densidad".
- The slider "h".
- The point A can crawl.
Output data
Field of vectors
Approximation by means of Euler's method.
Observations
The button " Draw Euler " will transport to the graph the information introduced by keyboard.
The button " Calculate table " will realize the calculations taking the information introduced by the keyboard. The menu of the table is retractable, since it can reach a troublesome size.
First steps
- It draws the field of vectors associated to and ' = y.cos (x). By means of the mouse it changes the point of beginning To to see how it changes the path.
- We know that and = sen x is a solution of and ' = cos x, and (0 =0). It draws Euler's approximation and diminishes the step h to see if it improves the approximation.
- We consider and ' =2*x*y - 1/x, and (0.2) = 0.1. It locates a region so that changing the point of beginning changes qualitatively the approximation.
