Monday, July 20, 2009

calculus - slope fields


There are three levels of visualization to be gleaned from this illustration. The segments themselves give a low-resolution picture of the family of curves which satisfy the differential equation. Secondly, the solution curves can be viewed with the click of a button. Finally, a set of tracing points can be sent along their respective curves, illustrating the concept of initial values. The sketch is simple, but it covers the basics in a way that any visual learner will appreciate. The sketch works nicely when dy/dx is a function of x, but if dy/dx is implicitly defined, the construction is more complex and the differential equation is not easily changed.
Keywords: slope fields, direction fields, anti-derivative, anti-differentiation, integral curves, solution curves, family of solutions, differential equations, dy/dx

2 comments:

  1. Thanks so much for allowing me to use this sketch in my Calculus class. I think it is really going to help.

    B. Gallis
    Central High School
    Philadelphia

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