What is the history of calculus?

Answer 1

There were a few ideas about measuring volumes, areas, and rates of change that date back to the mid-1600s, but they were all rather haphazard and unreliable. For example, we could compute the volume of a sphere, the surface area of a cube, and the acceleration of a runner, but there was no single mathematical system that combined the three concepts.

The closest we got for a long time was in the mid-1600s, when mathematicians like Pierre de Fermat worked on early versions of what we now call calculus, and proofs were written for some basic ideas (such as the notion that a definite integral can be computed using the antiderivative of a function). Calculus was still in its infancy, though, and more ideas needed to be squeezed out of the mathematical world. Bonaventura Cavalieri worked on computing areas and volumes with somewhat awkward methods.

Now enter Gottfried Leibniz and Isaac Newton. Both mathematicians independently developed notation and ideas for unifying those concepts, as well as proving other basic concepts of calculus. Newton concentrated on applying calculus to motion (particularly to astronomical bodies) and on introducing techniques like the product and chain rule, while Leibniz concentrated on unifying the concepts under one notation and giving calculus its name. Although Leibniz published first, Newton had the ideas first. Nevertheless, today, both mathematicians share credit.

Since then, there have only been additions and applications to the fundamental concepts of calculus—a startlingly small number of changes.

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Answer 2

Calculus is a branch of mathematics that deals with the study of change and motion. It was independently developed by Sir Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century. Newton's work on calculus, known as the method of fluxions, was published in 1687 in his famous book "Mathematical Principles of Natural Philosophy." Leibniz, on the other hand, developed his own notation and published his findings in 1684. Both Newton and Leibniz made significant contributions to the development of calculus, and their work laid the foundation for modern calculus.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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