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AERO BOARD PREP 2014CALCULUSJGG DECENAContentsFunctionLimitsDifferentiationIntegration

AERO BOARD PREP 2014CALCULUSJGG DECENAA Brief History of CalculusCalculus was created by Isaac Newton, a British scientist, as well as Gottfried Leibniz, a self-taught German mathematician, in the 17th century. It has been long disputed who should take credit for inventing calculus first, but both independently made discoveries that led to what we know now as calculus. Newton discovered the inverse relationship between the derivative (slope of a curve) and the integral (the area beneath it), which deemed him as the creator of calculus. Thereafter, calculus was actively used to solve the major scientific dilemmas of the time, such as:•calculating the slope of the tangent line to a curve at any point along its length•determining the velocity and acceleration of an object given a function describing its position, and designing such a position function given the object's velocity or acceleration•calculating arc lengths and the volume and surface area of solids•calculating the relative and absolute extrema of objects, especially projectilesFor Newton, the applications for calculus were geometrical and related to the physical world - such as describing the orbit of the planets around the sun. For Leibniz, calculus was more about analysis of change in graphs. Leibniz's work was just as important as Newton's, and many of his notations are used today, such as the notations for taking the derivative and the integral.

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AERO BOARD PREP 2014CALCULUSJGG DECENAFUNCTIONSANDRELATIONS

AERO BOARD PREP 2014CALCULUSJGG DECENA

AERO BOARD PREP 2014CALCULUSJGG DECENAWhat is a Relation?