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Usage Examples English
- The Gauss-Legendre algorithm can be proven to give results converging to π using only integral calculus. This is done here and here.
- With the invention of integral calculus came a universal method for area calculation.
- As a mathematician, his greatest achievement was the development of the main ideas of differential and integral calculus, independently of Isaac Newton's contemporaneous developments, and mathematicians have consistently favored Leibniz's notation as the conventional and more exact expression of calculus.
- John Wallis's infinitesimals differed from indivisibles in that he would decompose geometrical figures into infinitely thin building blocks of the same dimension as the figure, preparing the ground for general methods of the integral calculus.
- In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (...).
- In 1789 he submitted in Strasbourg a major report on the differential and integral calculus to the Académie des Sciences in Paris which was never published.
- The development of integral calculus in the late 17th century provided tools that could subsequently be used for computing more complicated areas, such as the area of an ellipse and the surface areas of various curved three-dimensional objects.
- The elements of differential and integral calculus extend naturally to vector fields.
- It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve.
- As a privatdozent he lectured on differential and integral calculus.
- Louis Couturat studied integral calculus with Picard in 1891-1892, taking detailed notes of the lectures. These notes were preserved and now are available in three cahiers from Internet Archive.
- The concept of weighted average can be extended to functions. Weighted averages of functions play an important role in the systems of weighted differential and integral calculus.
- It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves.
- The third volume includes the solution of several dynamical problems by means of the calculus of variations; some papers on the integral calculus; a solution of a Fermat's problem: given an integer [...] which is not a perfect square, to find a number [...] such that [...] is a perfect square; and the general differential equations of motion for three bodies moving under their mutual attractions.
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Contains translations by TU Chemnitz and Mr Honey's Business Dictionary (German-English only).
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