## Write

**y**/*t*=**f***'*(*t*,**y**) **y**= *t***f***'*(*t*,**y**).## Start with known values

**y***n*at*tn*(initial values).## Then

**y***n*+1 at*tn*+1 =*tn*+*h*is:**y***n*+1 =**y***n*+*h***f***'*(*tn*,**y***n*)

*h*is called the*step size*.## Integration is not symmetric: derivative evaluated only at start of step error term

*O*(*h*2), from Taylor series. So, Euler's method is__first order__.