Euler models the system that you have With linear changes to the system you had. But if you want continuous behavior Here's what you do You just iterate the integral Halving the time step each time And take it to the limit one more time. You can spend all your time making changes You can spend all your change making time But if you need to find a derivative Here's what you do You just difference your function Then divide by the time And take it to the limit one more time. Take it to the limit, Take it to the limit, Just take it to the limit one more time. When you try to find a function's slope You may be stuck with zip over nil You may still find the local derivative With L'Hopital's Rule: You just take separate derivatives Of run and of rise And take it to the limit one more time. Take it to the limit, Take it to the limit, Just take it to the limit one more time. |