Calculus Paper

1. Calculus is split into two branches, differential calculus and integral calculus. Differential calculus is used to find the rates of change for geometric curves. This means that differential calculus is used to find the slope or tangent along a specific direction of a geometric curve. This relates directly to change, because finding the slope or tangent of a geometric curve is essentially finding the rate of change for that geometric curve. The other branch of calculus, integral calculus, is concerned with finding the area under a curve. This is accomplished by using small towers, to find the closest area of the curve. This relates to change because you can find the difference in area of the curve, depending on the equation’s curve’s restrictions. The relationship between these two branches is that they are inverse operations. This means that taking a derivative after finding an integral, would leave you with the original equation. 2. The method of exhaustion is a process that is still used today in order to find the area of irregular shapes that typically have curved bounded areas. The process uses regular polygons to approximate the area of irregular polygons. This is done by the process of circumscription, which means that a regular polygon is placed around the irregular polygon, but each of the corners of the regular polygon will touch the edge of the circle. Then, another regular polygon is inscribed within the irregular polygon. This means that the regular polygon is placed within the irregular polygon, with each of the corners just touching the edges of the irregular polygon. The word exhaustion is accurately used in the description of this method, because by adding more and more regular polygons to inscribe and circumscribe around the irregular polygon, the extra space is actually exhausted so that the closest area approximation can be found.

3. Isaac Barrow was an English mathematician, and was the teacher of Isaac Newton. Barrow is credited