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The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...
Just as the integration by parts above reduced the integral of secant cubed to the integral of secant to the first power, so a similar process reduces the integral of higher odd powers of secant to lower ones. This is the secant reduction formula, which follows the syntax:
In Newton's notation or the dot notation, a dot is placed over a symbol to represent a time derivative. If y {\displaystyle y} is a function of t {\displaystyle t} , then the first and second derivatives can be written as y ˙ {\displaystyle {\dot {y}}} and y ¨ {\displaystyle {\ddot {y}}} , respectively.
In mathematics, the problem of differentiation of integrals is that of determining under what circumstances the mean value integral of a suitable function on a small neighbourhood of a point approximates the value of the function at that point.
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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
An object at height h above the ground and slant range R forms an angle α that can be calculated through sin α = h / R.By re-arrangement, R = h / sin α, or R = h csc α. The radar equation states that the signal received from an object, P e, varies inversely with the 4th power of range and directly as the square of the antenna gain, G, such that P e ~ G 2 / R 4.
The nabla is a triangular symbol resembling an inverted Greek delta: [1] or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word νάβλα for a Phoenician harp, [2] [3] and was suggested by the encyclopedist William Robertson Smith in an 1870 letter to Peter Guthrie Tait.