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Slope Fields

Part 5: Summary

  1. How is a slope field generated from a differential equation?

  2. What geometric property of a slope field corresponds to slope information that depends only on the dependent variable?

  3. What geometric property of a slope field would correspond to slope information that depends only on the independent variable? Draw a slope field for dP/dt = t2, and explain how this picture supports your answer.

  4. What distinguishes different solutions on the same slope field?

  5. For a given slope field and a given point (t0,P0), how many different solution curves do you think can possibly go through (t0,P0)? Explain.

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Last modified: October 7, 1997