1. Section 11.3 Euler’s Method

2. We have seen how to draw a solution curve given a slope field and some initial value
Now we are going to see how to find solutions to differential equations by calculating the slope at a point and using it to guide us to the next point
At the next point we will recalculate the slope and see where our next point is
We continue to do this to find our numerical solution
This is called Euler’s Method

3. Let’s apply Euler’s Method to
We will start at the point (1, 0) and find the solution for when x = 2
Using 2 steps
Using 5 steps

4. Let’s apply Euler’s Method to
We will start at the point (1, 0) and find the solution for when x = 2
Using 2 steps
Using 5 steps

5. Let’s revisit our Yam problem with our temperature of 20° when t = 0 for the first 5 minutes
dT/dt: (200-T)
Exact Solution:
e-.025t 20
4.50
20.00 1
24.5
4.39
24.44 2
28.89
4.28
28.78 3
33.17
4.17
33.01 4
37.34
4.07
37.13 5
41.41
3.96
41.15

6. When is Euler’s method an overestimate and when is it an underestimate?
Remember how it works:
It uses the rate of change locally
It basically uses tangent lines for estimates