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A Brief History Of Calculus
Calculus is usually associated with Isaac Newton and Gottfried Wilhelm Leibniz, who are commonly called its founders. This is true in the sense that they created calculus as a general symbolic method, but the ideas behind calculus developed over many centuries. Long before Newton and Leibniz, mathematicians were already studying problems involving areas, volumes, tangents, curves, limits, and infinite processes.
In modern calculus courses, differentiation is often introduced before integration because derivatives are usually easier to understand and compute. Historically, however, the development went in the opposite direction. The earliest calculus-like problems were problems of integration: finding areas, volumes, and lengths of curved figures.
Archimedes and the Beginning of Integral Ideas
The first major steps toward calculus were made by ancient Greek mathematicians, especially Archimedes. His work represents the peak of ancient mathematics and the beginning of what later became integration.
Archimedes used the method of exhaustion, which involved approximating curved figures by simpler shapes, such as inscribed and…
