FUNCTIONS

1. FUNCTIONS

2. In mathematics, a function is of course comparing elements of a number of elements of another set so that each element of the first set is compared to just one element of the second set. Graphic of cubic function

3. Functions are being examined in many units of mathematics and serve to define other mathematical objects. Depending on the important properties of the particular application and the required accuracy a function may be specified by a formula using graph by algorithm by describing its properties or description of its relationship with other functions.

5. z (x, y) = x4 + y4 - 2 x2 + 4 x y - 2 y2

6. z = x2 - y2

8. Functions are found in all areas of mathematics and natural sciences, but different areas have different names, different ideas about the properties of functions and even different definition.

10. Set theory functions considered in the larger community. The only property that requires a function to compare a single value to every admissible argument. Not required or argument values are numbers, such as the function that compares each country's capital, does not set numerical relationship between sets.

11. In algebra functions are usually expressed using algebraic operations. The functions tested in the analysis usually have extra features such as continuity or diferentsiruemost. An example of such a function is sine function. Usually there learning functions can be expressed in a single formula. In complex analysis are considered analytic functions that can be expressed through the development stage in order.

12. In complex analysis are considered a special class of multivalued functions that can be matched more than one value of an argument. Although formally speaking, they are not functions, they have very similar properties to the properties of analytic functions. Unlike set theory in lambda-calculus functions are primitive and object are defined by sets. In most areas of mathematics terms map, image transformation and operator are used as synonyms for the function.

13. Functions definition An approximate definition of a function is as follows: Let A and B are sets. Function from A to B is a rule that matches each element of A exactly one element of B. This intuitive understanding of the functions used since ancient times and still occurs in places where strict definition is not required

14. Objects by contemporary understandings considered functions were considered in ancient times. In ancient Babylon, as found tables of squares and cubes of natural numbers. Ptolemy calculated the lengths of chords in a circle, which essentially means that it is used trigonometric funktsii.Funktsiite he is considered, today called differentiable functions and are the most common type of function. For them make sense notions limit and derivative.

15. Later in 1755 g.Leonard Euler gives in his book Institutiones calculi differentialis modern understanding of function, namely the dependence between two variables, where changes in one variable leads to change the other. Despite this definition, however, Euler considered only continuous functions can be expressed by a formula consisting of terminal and infinite algebraic operations.

16. Functions are abstract mathematical categories to describe the processes occurring in nature, the macrocosm and microcosm. Described by mathematical formulas and an idealized representation of the laws and regularities observed in the surrounding landscape and space.

17. Made by • Milen Minev, • Tihomir Zhelev , • Martin Stoikov • 2011 • SOU ZHELEZNIK • Stara Zagora