Euler's method of solving the initial value problem is conceptually important. One way or another all practical methods come down to the same idea: Add small increments to your functions corresponding to derivatives multiplied by step sizes.
where the 
are the first time derivatives of the 
.
The Euler method is not very accurate (compared to others discussed below), sometimes unstable and generally not recommended for any practical use. This is because the derivative is computed at the start of the interval h and assumed to hold over the whole interval. In fact then,
Where the error term 
is only one order down on the increment
term hf 
.