Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced.

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

Derivatives may be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector.

Derivative (finance)

In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and often called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Bombay Stock Exchange, while most insurance contracts have developed into a separate industry. Derivatives are one of the three main categories of financial instruments, the other two being stocks (i.e., equities or shares) and debt (i.e., bonds and mortgages).

Collateralized debt obligation

Derivative (chemistry)

In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction.

In the past, derivative also meant a compound that can be imagined to arise from another compound, if one atom or group of atoms is replaced with another atom or group of atoms, but modern chemical language now uses the term structural analog for this meaning, thus eliminating ambiguity. The term "structural analogue" is common in organic chemistry.

In biochemistry, the word is used for compounds that at least theoretically can be formed from the precursor compound.

Chemical derivatives may be used to facilitate analysis. For example, melting point (MP) analysis can assist in identification of many organic compounds. A crystalline derivative may be prepared, such as a semicarbazone or 2,4-dinitrophenylhydrazone (derived from aldehydes or ketones), as a simple way of verifying the identity of the original compound, assuming that a table of derivative MP values is available. Prior to the advent of spectroscopic analysis, such methods were widely used.

Swap

Swap or SWAP may refer to:

Finance

Science and technology

Other

See also

Swap (computer science)

In computer programming, the act of swapping two variables refers to mutually exchanging the values of the variables. Usually, this is done with the data in memory. For example, in a program, two variables may be defined thus (in pseudocode):

(In many programming languages where the swap function is built-in; in C++, overloads are provided allowing std::swap to swap some large structures in O(1) time.) After swap() is performed, x will contain the value 0 and y will contain 1; their values have been exchanged. Of course, this operation may be generalized to other types of values, such as strings, aggregated data types and comparison sorts, utilize swaps to change the positions of data.

Using a temporary variable

The simplest and probably most widely used method to swap two variables is to use a third temporary variable:

While this is conceptually simple and in many cases the only convenient way to swap two variables, it uses extra memory. Although this should not be a problem in most applications, the sizes of the values being swapped may be huge (which means the temporary variable may occupy a lot of memory as well), or the swap operation may need to be performed many times, as in sorting algorithms.

Swåp

Swåp are an Anglo-Swedish band that produce a musical fusion of traditional nordic music and celtic music.

Biography

Swåp was formed in 1995 by Karen Tweed (piano accordion), Ian Carr (guitar) (both UK), Ola Bäckström (fiddle, viola d'amore) and Carina Normansson (fiddle, vocals) (both Sweden). Together they have made four albums exploring a fusion of many different genres of folk music, including traditional Swedish music, English music, and the music of Brittany and Ireland. Karen Tweed left the band in 2007.

Discography