.. _sphx_glr_api_gallery_calculus_newton_leibniz:

Newton and Leibniz
------------------

The two central facts of the calculus of Newton and Leibniz: the
derivative is a limiting difference quotient, and the definite integral
is a limiting sum.


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    <div class="sphx-glr-thumbcontainer" tooltip="The calculus of Newton and Leibniz rests on two limits: the derivative dy/dx is the limit of a difference quotient, and the integral \int f\,dx is the limit of a sum of thin strips. This example watches secant slopes (via central_difference) close in on the tangent slope, and trapezoidal sums (via TrapezoidalRule) close in on the area under the curve -- and then checks that the two operations undo each other, as the fundamental theorem of calculus says they must.">

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