The Current Language of Derivative – Assignment Example

The paper "The Current Language of Derivative" is a great example of a math assignment.
Differential equation first appeared explicitly in a geometric language. In 1687 Sir Isaac Newton published a book called Mathematical principal which credits him as the inventor of calculus. In his book, Newton introduces two principals that define the laws of a derivative.
The first law stipulates that a body subject to a force has the same acceleration in the same direction as the force with which is proportional to the force and inversely proportional to the mass(Newton, 1687), thus he develops a formula that captures this statement as (F=ma).
The second law by this great scientist stipulates that two bodies attract with the force aligned along the line between them, which is directly proportional to the product of their masses and is inversely proportional to the square of the distance separating them (Newton 1687). These laws combine to form differential equations and equations for the position of the body in terms of their derivatives.
For example, if we have two bodies of mass m1 and m2 respectively and are freely moving under the gravitational force, then their position can be denoted by a time (t) in a vector with respect to their origin x1(t) and x2(t). Thus the acceleration of these bodies is the second derivatives. X1”(t) and x2”(t) with respect to time in their position. Thus combining the two laws of Newton then we obtain the first force of the body as
M1x1”(t) = G m1m2/(||x2-x1||) (x2-x1)/(||x2-x1||)
This also applies to the force of the second object. The gravitational force of proportionality is independent of the bodies, their position and is universal.