1 6.1 Slope Fields and Euler's Method Objective: Solve differential equations graphically and numerically.

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Presentation transcript:

1 6.1 Slope Fields and Euler's Method Objective: Solve differential equations graphically and numerically.

2 Slope Fields: a graphical approach Solving some DEs can be difficult or even impossible  Take a graphical approach Consider y’= F ( x, y )  At each point (x, y) in the xy-plane where F is defined, the DE determines the slope y’= F ( x, y ) of the solution at that point.  If you draw a short line segment with slope F ( x, y ) at selected points (x, y) in the domain of F, these line segments form a slope field.  A slope field shows the general shape of all the solutions

3 Sketch the slope field for the differential equation y’= x - y

4

5 Match the slope field to the DE

6 Sketch the slope field for the differential equation y’= 2x + y Use your slope field to sketch the solution that passes through (1,1)

7 Sketch the slope field for the differential equation y’= 2x + y Use your slope field to sketch the solution that passes through (1,1)