WHAT DID LATER MATHEMATICANS NEED TO DO TO COMPLETE THE THEORY OF CALULUS AND WHO WERE THEY AND WHAT DID THEY CONTRIBUTE?
WE ALWAYS READ ABOUT NEWTON AND LEIBNIZ however, there is more and i would like to know who else contributed in a meaningful way. thank you
There were many mathematicians a little before Newton and Liebniz who had portions of calculus sorted out, including Barrow, Fermat, Descartes and Wallis. Barrow had completed some work on tangents, Descartes had worked out methods of getting the equivalent to a derivative, Fermat and Wallis had determined ways of doing integration of specific curves including polynomials and fractional exponents.
After Newton and Liebniz calculus became more widespread but it was also not accepted as being completely rigorous. The first person to put calculus on a modern footing was Cauchy in dispensing with infinitesimals. This was in the 1820s, about 150 years after Newton/Leibniz.
Cauchy's work was then formalized by Weierstrauss in the 1820s.
The formalization of integration was first done by Reimann in the mid 1800s and then extended by Lebesgue in the early 1900s.
Many aspects of calculus are still being worked on by researchers today, including real and complex analysis, non-standard analysis manifolds, and multi-dimensional calculus.