1. Section 17.4 The Flow of a Vector Field

2. Often we are concerned with the path an object will travel We can use the information from the velocity vector field in order to determine a path This will depend on the direction and magnitude of the vector as well as the starting point Let’s revisit our flow of the gulf stream example beginning with the vector field and then on to the flow lines Does this sound familiar?

5. Suppose we have a velocity vector field –We will let t be in seconds and use a 2D field Then we have If Then Thus the flow of the field is the general solution to the above system of differential equations

6. Given the system of differential equations and some initial condition we can find the particular flow line through the given field

7. Example Pg. 857, #4 Sketch the vector field and the flow. Find the system of differential equations associated with the vector field and check that the flow satisfies the system. Let’s take a look with Maple