1. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 10.3: Slope Fields Section 10.3 Slope Fields

2. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example A differential equation gives us information about the rate of change of a function. A differential equation gives us information about the slope of the graph of the function.

3. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Constructing a Direction Field

4. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example

5. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example

6. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example

7. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved............... Example

8. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved............... Example

9. Which of the following graphs could be a solution to the differential equation

10. Example Which of the following graphs could be a solution to the differential equation Slopes are positive when x 0 Slopes are negative when x > 0 and y > 0 When x=0, dy/dx = 0 When y=0, dy/dx = 0