07 Integracion (El Universo Mecanico)
Daniel Palma・14 minutes read
Isaac Newton and Gottfried Wilhelm Leibniz were pivotal in the discovery of calculus in the 17th century, building upon the integration method for calculating areas of curved figures and contributing to the first fundamental theorem of calculus. Despite differences in their methods, both Newton and Leibniz made significant strides in connecting integration and differentiation, with Newton's calculus revealed in a book titled "The Method of Inflections" published posthumously in 1969.
Insights
- Integration and differentiation, foundational concepts in calculus, were independently developed by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, leading to the first fundamental theorem of calculus.
- The history of calculus is intertwined with the contributions of various scientists like Archimedes, Johannes Kepler, and Isaac Barrow, each adding essential elements to the development of calculus, culminating in Newton and Leibniz's groundbreaking work on integration and differentiation.
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Recent questions
Who discovered calculus?
Newton and Leibniz
What is the significance of integration?
Calculate areas of curved figures
How did ancient civilizations use geometry?
Measuring land surfaces
What were Archimedes' contributions to calculus?
Quadrature of a segment of a parabola
How did Newton and Leibniz contribute to calculus?
First fundamental theorem of calculus
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Summary
00:00
Discovery of Calculus in the 17th Century
- Integration was discovered in the 17th century as a method to calculate areas of curved figures.
- Isaac Newton, a unique and somewhat lazy boy from a farming family, astounded with his discovery of calculus in the 17th century.
- Gottfried Wilhelm Leibniz, a scholarly diplomat from Hanover, was another key figure in the discovery of calculus, known for his practical nature.
- Calculus, a culmination of many ideas, was built upon questions posed by various scientists like Galileo and Kepler.
- Geometry, with practical applications like measuring land surfaces, had roots in ancient civilizations like Egypt and Greece.
- The Greeks approximated curved figures with inscribed polygons using the exhaustion method to find areas, establishing mathematical standards.
- Archimedes made significant discoveries in calculus, including the quadrature of a segment of a parabola.
- Johannes Kepler and two Frenchmen made strides towards calculus, with the Frenchmen introducing rectangular coordinates and derivatives.
- Isaac Newton, influenced by Isaac Barrow, discovered his own calculus method called the method of fluctuations, explaining the movement of bodies in space.
- Newton and Leibniz, despite differences in their calculus methods, both contributed to the remarkable connection between integration and differentiation, leading to the first fundamental theorem of calculus.
24:59
Newton's Calculus Delayed Publication by Editor
- Newton's calculus was published in a book called "The Method of Inflections," although it was not written by him but by Johnson; Newton's own manuscript on calculus was not published until 1969, possibly due to the editor's delay or other issues.
