Newton's Calculus: What He Came Up With & Notation Used

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SUMMARY

Isaac Newton significantly contributed to the development of calculus, focusing on real-world applications and the concept of limits. While much of the modern notation is attributed to Gottfried Wilhelm Leibniz, Newton's work laid the foundation for calculus through his use of geometric principles. Newton did not formalize the notation for derivatives and integrals as we know it today, such as (d/dx)(sin x) = cos x, but his methodologies were crucial in the evolution of these concepts.

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  • Understanding of basic calculus concepts, including limits and derivatives.
  • Familiarity with Newtonian physics and its mathematical implications.
  • Knowledge of Leibniz's notation and its historical context.
  • Awareness of the differences between Newton's and Leibniz's approaches to calculus.
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  • Research the historical context of Newton's and Leibniz's contributions to calculus.
  • Study Newton's method of fluxions and its application in calculus.
  • Examine the evolution of calculus notation from Newton to modern usage.
  • Explore the implications of limits in calculus and their significance in Newton's work.
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Students of mathematics, historians of science, and educators seeking to understand the foundational differences between Newton's and Leibniz's calculus approaches.

pi-r8
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How much calculus did Newton himself actually come up with? And what did it look like? I've read that most of the notation we use today was actually invented by Leibniz- if that's true, then what did Newton's notation look like?
 
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Netwon went a long way and for this reason 'credit' for the 'invention' of calculus is often shared as Newton was based primarily on true reality nad the use of limits where as Leibniz was far mroe embracing of the abstract and infinite.

Perhaps this reflects the very different way they approached the problem due to their situations.
 
So did Newton come up with the equations for equations for derivatives and integrals that we use today? I'm thinking of things like (d/dx)(sinx) = cosx, and such.
 

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