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What is calculus?

Calculus is one of the many branches of mathematics; originally it was used to describe the properties of such things as the motion of planets and molecules. Calculus was described in the 18th century by both Sir Isaac Newton and Gottfried Leibniz, they both described calculus as a method of solving physics problems. Strange as it may seem, both of these gentlemen described the subject simultaneously but separately. Calculus tutoring focuses on the two distinct branches of the subject; differential and integral. When properly applied these divisions can solve complex problems as different as calculating the speed of an object at any point in time or the surface area of any complex shape.

Both divisions in calculus rely on the principle that by using approximations which get more and more accurate, you will eventually find the exact result. An example of this is a curve, it can be approximated by a series of straight lines, as the lines get shorter they begin to look like a curve. The same approach can be used to approximate a sphere which is solid. A series of cubes with each iteration getting progressively smaller, will eventually fill the sphere. Calculus allows for the determination of a precise end result.

Differential calculus tutoring centers on the methods employed to find a rate of change function. The function describes something which is constantly changing; perhaps the temperature variances during the course of a full day. The derivative of the function will give rate of temperature change.

Integral calculus is the opposite of differential calculus. If the student is given the rate of change, it is possible to calculate the values that describe the input. When given the derivative, such as temperature change, integration will find the original function. This branch of calculus will also allow for the calculation of the area which sits under a curve or the area or volume of any solid. It is possible to do this because you start with a series of rectangular shapes and make your guesses more and more accurate as you study the limit. Think of the space under the curve divided up into a series of equal width strips, a small number of wide strips will provide an approximation, as the strips get progressively narrower, the area becomes more accurate.

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