Historia del Cálculo en menos de 6 minutos
Summary
Ancient Greek mathematicians like Archimedes revolutionized volume calculations, leading to the development of calculus by mathematicians such as Galileo, Kepler, and Descartes. In the 17th century, Newton and Leibniz made significant contributions such as the discovery of integration, fundamental laws of physics, and refined techniques for calculating areas and volumes using calculus. Leibniz's innovative method of using small rectangles to represent areas under a function's graph laid the foundation for integral calculus, symbolized by the elongated 'S' sign, a crucial tool in modern mathematics, engineering, and statistics.
Origins of Calculus in Ancient Greece
Calculation traces back to ancient Greece in the 3rd century BC with Archimedes initiating volume calculations.
Development of Calculus
Contributions from mathematicians like Galileo, Kepler, Descartes, Fermat, and others led to the development of calculus, focusing on questions about velocity and acceleration.
Method of Exhaustion for Area Calculation
Greeks used the method of exhaustion to calculate areas of circles by inserting smaller triangles, leading to a closer approximation of the circle's area.
Discovery of Integration
In the 17th century, the discovery of integration was made to calculate curved figures, and a British scientist named Isaac Newton further expanded on this during a quarantine period similar to the current COVID-19 situation.
Newton's Discoveries
During his quarantine, Newton discovered the refraction of light, the law of gravity, and his three laws, in addition to contributing to calculus alongside another scholar, Leibniz.
Invention of Integral Calculus
Leibniz introduced the concept of calculus for areas by imagining a network of small rectangles to sum their areas under a function's graph, leading to the development of integral calculus.
Integral Calculus and Its Symbolism
Leibniz symbolized integral calculus with the elongated 'S' signifying summation, defined by geometric interpretations and the Fundamental Theorem of Calculus for obtaining definite integrals within a closed interval.
Process of Definite Integrals
To calculate a definite integral, one needs to find the antiderivative, evaluate it at the integration limits, and compute the difference between these evaluations—a crucial tool for modern mathematics, engineering, and statistics.
FAQ
Q: What is the history of calculus tracing back to?
A: The history of calculus traces back to ancient Greece in the 3rd century BC with Archimedes initiating volume calculations.
Q: How did the Greeks calculate the areas of circles?
A: The Greeks used the method of exhaustion to calculate areas of circles by inserting smaller triangles, leading to a closer approximation of the circle's area.
Q: What major contributions were made in the development of calculus in the 17th century?
A: In the 17th century, the discovery of integration was made to calculate curved figures, and Isaac Newton further expanded on this during a quarantine period, making discoveries like the refraction of light, the law of gravity, and his three laws.
Q: Who introduced the concept of calculus for areas through the use of small rectangles?
A: Leibniz introduced the concept of calculus for areas by imagining a network of small rectangles to sum their areas under a function's graph, leading to the development of integral calculus.
Q: How is integral calculus symbolized?
A: Integral calculus is symbolized by Leibniz with the elongated 'S', signifying summation, defined by geometric interpretations and the Fundamental Theorem of Calculus for obtaining definite integrals within a closed interval.
Q: What is a crucial step in calculating a definite integral?
A: A crucial step in calculating a definite integral is to find the antiderivative, evaluate it at the integration limits, and compute the difference between these evaluations.
Get your own AI Agent Today
Thousands of businesses worldwide are using Chaindesk Generative
AI platform.
Don't get left behind - start building your
own custom AI chatbot now!