Leibniz

Definition

Gottfried Wilhelm Leibniz was a German mathematician and philosopher who independently developed calculus around the same time as Isaac Newton. His notation for derivatives and integrals is widely used today.

5 Must Know Facts For Your Next Test

1. Leibniz introduced the notation $\frac{dy}{dx}$ to represent the derivative of a function.
2. He used the integral symbol $\int$ to represent integration, inspired by the elongated letter 'S' for 'summa'.
3. Leibniz's work laid the foundation for much of modern calculus and mathematical analysis.
4. The Fundamental Theorem of Calculus links Leibniz's concepts of differentiation and integration.
5. Leibniz's notation is particularly advantageous because it clearly distinguishes between differentials and integrals, making complex problems easier to solve.

Review Questions

• What is the significance of $\frac{dy}{dx}$ in Leibniz's notation?
• How did Leibniz denote an integral, and what was his inspiration for this symbol?
• Explain how the Fundamental Theorem of Calculus connects differentiation and integration in Leibniz's framework.

Related terms

Newton:

Isaac Newton, an English mathematician who independently developed calculus alongside Leibniz. His approach focused more on limits and fluxions.

$\frac{dy}{dx}$: Leibniz's notation for the derivative of a function, representing an infinitesimal change in $y$ with respect to an infinitesimal change in $x$.

$\int$: The integral symbol introduced by Leibniz, used to represent the process of integration or finding areas under curves.