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Topic: Elementary functions

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	Elementary function - Wikipedia, the free encyclopedia
		In mathematics, an elementary function is a function built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary operations (+ - × ÷).
		The trigonometric functions and their inverses are assumed to be included in the elementary functions by using complex variables (i = √-1) and the relations between the trigonometric functions and the exponential and logarithm functions.
		For polynomials of degree four and smaller there are explicit formulas for the roots (the formulas are elementary functions), but even for higher degree polynomials the fundamental theorem of algebra and the implicit function theorem assures the existence of a function that returns each one of the roots of a polynomial equation.
	en.wikipedia.org /wiki/Elementary_function_(differential_algebra) (477 words)

	PlanetMath: elementary function
		An elementary function is a real function (of one variable) that can be constructed by a finite number of elementary operations (addition, subtraction, multiplication and division) and compositions from constant functions, the identity function (
		), algebraic functions, exponential functions, logarithm functions, trigonometric functions and cyclometric functions.
		This is version 15 of elementary function, born on 2004-10-25, modified 2006-10-14.
	planetmath.org /encyclopedia/ElementaryFunction.html (163 words)

	List of mathematical functions - Wikipedia, the free encyclopedia
		Transcendental functions are functions that are not algebraic.
		Power functions: raise a variable number to a fixed power; also known as Allometric functions; note: if the power is a rational number it is not strictly a transcendental function.
		Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
	en.wikipedia.org /wiki/List_of_mathematical_functions (1002 words)

	MAT114 Elementary Functions
		Students should understand the function concept and should be able to determine the rules and domains of algebraic functions and their combinations.
		Students should understand the relationship between a function and its graph and should be able to sketch graphs of various functions.
		Topics to be covered include exponential and logarithmic functions, complex numbers and polynomial functions, trigonometry, plane analytic geometry, and systems of linear equations and inequalities.
	www.assumption.edu /users/kcarlin/syllabi/MAT114.html (457 words)

	Elementary Functions (Site not responding. Last check: 2007-10-11)
		When the Cycle parameter is specified, the parameter X of the forward trigonometric functions (Sin, Cos, Tan, and Cot) and the results of the inverse trigonometric functions (Arcsin, Arccos, Arctan, and Arccot) are measured in units such that a full cycle of revolution has the given value; otherwise, they are measured in radians.
		The result of the Arcsin function is in the quadrant containing the point (1.0, x), where x is the value of the parameter X. This quadrant is I or IV; thus, the range of the Arcsin function is approximately –π/2.0 to π/2.0 (–Cycle/4.0 to Cycle/4.0, if the parameter Cycle is specified).
		Other accuracy requirements for the elementary functions, which apply only in implementations conforming to the Numerics Annex, and then only in the “strict” mode defined there (see G.2), are given in G.2.4.
	www.adaic.com /standards/05aarm/html/AA-A-5-1.html (1730 words)

	Peter Suber, "Recursive Function Theory"
		Because recursive function theory was developed in part to capture the intuitive sense of effectiveness in a rigorous, formal theory, it is important to the theory that the class of recursive functions can be built up from intuitively effective simple functions by intuitively effective techniques.
		If a function is a rule (for picking a member of the range when given a member of the domain), then it must be computed to reach its result.
		The factorial function is derived by primitive recursion from the functions for multiplication and subtraction.
	www.earlham.edu /~peters/courses/logsys/recursiv.htm (3359 words)

	All Elementary Mathematics - Study Guide - Functions and graphs - Elementary functions and their graphs...
		At n = 2 the function is even and its graph is symmetric relatively an axis Y ; at n = 3 the function is odd and its graph is symmetric relatively an origin of coordinates.
		Such functions are not studied in an elementary mathematics, therefore we consider usually as a function one of its branches: either an upper or a lower branch.
		At a > 0 an exponential function increases, and at a < 0 – decreases.
	www.bymath.com /studyguide/fun/sec/fun9.htm (1564 words)

	Trigonometry and Basic Functions - Numericana
		Polynomial functions: The value y is obtained from the variable x using only a finite number of additions and/or multiplications involving given constants.
		Alternately, such functions may be construed as univalued (ordinary) functions of a variable whose domain is a so-called Riemann surface for which several points may have the same projection on the complex plane.
		Each of those 6 trigonometric functions is the ratio of two sides in a right triangle where one of the acute angles is specified.
	home.att.net /~numericana/answer/functions.htm (4111 words)

	Complex Elementary Functions
		The implementation of the Exp function of a complex parameter X is allowed to raise the exception Constraint_Error, signaling overflow, when the real component of X exceeds an unspecified threshold that is approximately log(Complex_Types.Real'Safe_Last).
		For example, many of the complex elementary functions have components that are odd functions of one of the parameter components; in these cases, the result component should have the sign of the parameter component at the origin.
		Other complex elementary functions have zero components whose sign is opposite that of a parameter component at the origin, or is always positive or always negative.
	www.cs.fsu.edu /~baker/ada/arm_95/RM-G-1-2.html (1326 words)

	Accuracy Requirements for the Elementary Functions
		The prescribed results specified in A.5.1 for certain functions at particular parameter values take precedence over the maximum relative error bounds; effectively, they narrow to a single value the result interval allowed by the maximum relative error bounds.
		The amount by which the result of an inverse trigonometric function is allowed to spill over into a quadrant adjacent to the one corresponding to the principal branch, as given in A.5.1, is limited.
		The versions of the forward trigonometric functions without a Cycle parameter should not be implemented by calling the corresponding version with a Cycle parameter of 2.0*Numerics.Pi, since this will not provide the required accuracy in some portions of the domain.
	www.adaic.org /standards/95aarm/html/AA-G-2-4.html (789 words)

	Functions 2 - maths online Gallery
		is a puzzle type game in which a set of given functional expressions and graphs shall be associated with each other.
		Emphasis is laid on the relation between the geometrically intuitive form of the graphs are the corresponding numerical values.
		As in the previous applet, the functions are of the form
	www.univie.ac.at /future.media/moe/galerie/fun2/fun2.html (304 words)

	Bessel Functions
		An important class of functions can be formed using only the four processes of arithmetic, called the rational functions, and these constitute a connection between the general hazy concept of function, and the concrete realization of functions in terms of numbers.
		Cylinder Functions, and they turn out to be the Bessel Functions because the satisfy the differential equation, but he carefully points out that the converse must be proved, and cannot be assumed from one particular case.
		The generating function is a surprising connection with the exponential, and Bessel's integral connects Bessel and trigonometric function.
	www.du.edu /~jcalvert/math/bessels.htm (1849 words)

	Elementary & Higher Mental Functions
		Elementary functions are natural, and therefore unlearned capacities.
		The central feature of these types of functions is that they involveself-generated stimulation.
		Self -generated stimulation is "the creationand use of artificial stimuli which becomes the immediate causes of behavior."(Lefrancois, 1994).
	www.metu.edu.tr /~e118949/project/index_files/Page836.htm (49 words)

	11. Elementary functions (Site not responding. Last check: 2007-10-11)
		In fact a better class of functions could be the elementary ones introduced by L. Kalmar in 1943.
		He showed that any recursively enumerable function could be achieved as an enumeration of such a simple function.
		The lower elementary functions are functions of polynomial growth--and I think that they should be studied more closely.
	www.hf.uio.no /ifikk/filosofi/njpl/vol1no2/pioneer/node11.html (244 words)

	Calculus and elementary functions
		This is the inverse function of the exponential function,
		This function is used to determine the Taylor series expansion of the inverse of a function "f": if we take "g(var)=var", then "h(f(var))=var" (up to order "degree"), so "h" will be the inverse of "f".
		This function drops all terms of order "degree" or higher in "poly", which is a polynomial in the variable "var".
	yacas.sourceforge.net /refchapter5.html (4572 words)

	Definitive Mathematical Functions Site Now Available
		Elementary mathematical functions, such as sine and cosine, are familiar to anyone who has taken high school mathematics, but in the applications of mathematics to science and engineering--as well as in pure mathematics itself--there are also several hundred so-called "special functions" that have been intensively used for a century or more.
		Says Michael Trott, leader of the project, "The Wolfram Functions Site is the first true semantic website in which a substantial area of human knowledge has been completely encoded in a form that can be not only read but also actually understood by a computer.
		While having already far surpassed previous knowledge bases for mathematical functions, continued growth is planned for The Wolfram Functions Site, with new searching capabilities, external contributions, and new classes of graphics and information.
	www.wolfram.com /news/functionssite.html (567 words)

	Working with Special Functions
		Most special functions have derivatives that can be expressed in terms of elementary functions or other special functions.
		One feature of working with special functions is that there are a large number of relations between different functions, and these relations can often be used in simplifying expressions.
		The Airy functions are related to Bessel functions.
	documents.wolfram.com /v4/MainBook/3.2.13.html (303 words)

	The Math Forum - Math Library - Functions
		An illustrated introductions to the concept of functions, a relationship or correlation where each element of the domain corresponds to one and only one element of the range.
		The site details the interrelationships between the special functions of mathematical physics and the elementary functions of mathematical analysis, as well as the interrelationships between the functions in each group.
		Elementary functions open new teaching and learning possibilities for dynamic geometry, which is characterized particularly by the direct manipulation and production of graphic objects.
	mathforum.org /library/topics/functions (2108 words)

	Courses - Mathematics - Catalog for Academic Year 2005-2006
		Topics include precalculus functions and their graphs, polynomial functions, rational functions, conic sections, exponential and logarithmic functions, systems of equations, sequences and series.
		Definition of the trigonometric functions and their graphic representation; solutions of triangles; graphic representation; polar coordinates and graphs; identities; inverse functions, trigonometric equations; and complex numbers.
		Theory and application of numerical techniques for approximation of functions, solutions of equations of one variable and systems of linear equations, interpolation and curve fitting, integration and differentiation, and solution of ordinary differential equations.
	www.lsus.edu /catalogs/catalog0506/courses_math.asp (2391 words)

	Nonelementary Integrals (Site not responding. Last check: 2007-10-11)
		All of the integrands in the Integration Bee contest are elementary functions, that is, finite combinations of algebraic, trigonometric, and exponential functions, and their inverses.
		But the horrible truth is that many (in some sense most) elementary functions have antiderivatives that cannot be expressed in terms of elementary functions.
		In general, all we know about the integral of an elementary function is the assertion of the Fundamental Theorem of Calculus: Every continuous function has an antiderivative.
	www.math.unt.edu /integration_bee/AwfulTruth.html (247 words)

	26: Real functions
		Real functions are those studied in calculus classes; the focus here is on their derivatives and integrals, and general inequalities.
		Some elementary calculus topics may likewise be appropriate for inclusion in 28: Measure and Integration, 40: Sequences and Series, Approximations and expansions, and so on.
		Convergence of the derivatives of a convergent sequence of functions
	www.math.niu.edu /~rusin/known-math/index/26-XX.html (898 words)

	Elementary functions
		The elementary functions (sine, cosine, tan, exponentials, and logarithms) are the most commonly used mathematical functions in science and engineering.
		Computing these functions quickly and accurately is a major goal in computer arithmetic.
		The purpose is not to give "cookbook recipes" that allow one to implement some given function, but to provide the reader with the knowledge that is necessary to build, or adapt, algorithms to their specific computing environment.
	perso.ens-lyon.fr /jean-michel.muller/book_functions.html (238 words)

	Elementary Functions
		A function ƒ is defined as a set of all ordered pairs (x, y), such that for each element x, there corresponds exactly one element y.
		The inverse of the function ƒ is denoted ƒ
		Odd functions are symmetric about the origin (e.g.
	www.cs.berkeley.edu /~celaine/apcalc/topic1.htm (315 words)

	SparkNotes: Computing Derivatives: Derivatives of Elementary Functions
		In this section we compute the derivatives of the elementary functions.
		Note, as a special case, that the derivative of any constant function f (x) = b is a constant function equal to 0 at every value in its domain: f'(x) = 0.
		We will show in the next section that the derivative of a sum of two functions is equal to the sum of the derivatives of the two functions.
	www.sparknotes.com /math/calcbc1/computingderivatives/section1.html (534 words)

	MA 109 College Algebra Chapter 5
		Since the elementary functions will be defined via infinite series, we need to prove some criteria for checking for the convergence of such series.
		These functions can be restricted to real arguments; when we need to distinguish these restricted functions, we will refer to them as the real sine function, real cosine function, etc.
		By continuity, it follows that the definitions of the trig functions using series corresponds with the definition using the unit circle.
	www.msc.uky.edu /ken/ma109/lectures/elem.htm (2040 words)

	Elementary Functions
		The result of the Arcsin function is in the quadrant containing the point (1.0, x), where x is the value of the parameter X. This quadrant is I or IV; thus, the range of the Arcsin function is approximately -PI/2.0 to PI/2.0 (-Cycle/4.0 to Cycle/4.0, if the parameter Cycle is specified).
		The result of the Arccos function is in the quadrant containing the point (x, 1.0), where x is the value of the parameter X. This quadrant is I or II; thus, the Arccos function ranges from 0.0 to approximately PI (Cycle/2.0, if the parameter Cycle is specified).
		In the following cases, evaluation of an elementary function shall yield the prescribed result, provided that the preceding rules do not call for an exception to be raised:
	www.adaic.org /standards/95aarm/html/AA-A-5-1.html (1695 words)

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