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Topic: Piecewise

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	PlanetMath: piecewise
		The word “piecewise” is used widely in mathematics, primarily in the analysis of functions of a single real variable.
		Piecewise is typically applied to a set of mathematical properties on a function.
		This is version 7 of piecewise, born on 2006-04-12, modified 2006-11-13.
	planetmath.org /encyclopedia/Piecewise.html (296 words)

	What's New in Mathematica 5.1: Fully Integrated Piecewise Functions
		Piecewise functionality is of wide-ranging importance across many different fields, especially in engineering.
		Mathematica supports traditional 2D formatting of piecewise definitions, for both output and input.
		Piecewise functions work with domain specification in Mathematica, enabling close-form solutions to a broad range of problems.
	www.wolfram.com /products/mathematica/newin51/piecewise.html (177 words)

	Piecewise - Wikipedia, the free encyclopedia
		The term piecewise is also used as an adverb to describe a property of a piecewise function that holds on each interval but may not hold on the whole function.
		That is an example of a piecewise linear function: its graph is made up of a number of parts of the graphs of linear functions.
		The definitions of piecewise continuous, piecewise differentiable and so on are therefore made, to require that the 'pieces' of the function are continuous (resp.
	en.wikipedia.org /wiki/Piecewise (304 words)

	Piecewise linear - Wikipedia, the free encyclopedia
		Important sub-classes of piecewise linear functions include the continuous piecewise linear functions and the convex piecewise linear functions.
		The idea of a piecewise linear (PL) structure on a topological manifold M is used in geometric topology.
		A more slick definition is to use a sheaf, locally isomorphic to the sheaf of piecewise linear functions on Euclidean space.
	en.wikipedia.org /wiki/Piecewise_linear (242 words)

	MuPAD documentation
		Whenever an object of type piecewise is evaluated, the truth of the conditions is checked again for the current values and the current properties of the identifiers involved.
		Most unary functions are overloaded for piecewise by mapping them to the objects in all branches of the input.
		This simplifies the use of piecewise: it is always allowed to enter p:=piecewise(...) and to call some method of piecewise with p as argument.
	www.mupad.de /doc/31/eng/stdlib_piecewis.html (2759 words)

	Medium Level Interactive Vision
		An intermediate representation is to use piecewise polynomials to represent a continuous boundary of arbitrary shape, in which perhaps one polynomial is used to represent each segment of the curve separated by peaks in
		The piecewise approximation technique may be applied to higher order polynomials in principle, but in a computer vision system this is rarely useful in view of the lack of accuracy of the segmented description derived from the image data.
		Piecewise functions offer a direct way of achieving local control and simpler functional representations.
	homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/MARBLE/medium/contours/poly.htm (602 words)

	Workshop on Piecewise Isometries
		Piecewise Isometries are two and higher dimensional generalizations of well-known interval exchange transformations.
		Recent wide interest in the subject is partially driven by (a) analogies with one dimensional maps, (b) spectacular fractal mosaics of cells, as well as, (c) potential applications.
		Thisuses only elementary tools such as complexity function and graph of words, and might be useful to understand more general piecewise isometries.
	math.sfsu.edu /goetz/conference/pi (1371 words)

	MUG: piecewise function trouble (25.2.98)
		I think that this should be changed for the next releases, and a smarter piecewise function can verify whether the argument is outside the allowed range, and then prevent undesired evaluation.
		An alternative is to avoid the use of piecewise, instead defining a procedure using an if statement.
		The function piecewise is never entered, because the expression 1/0 causes _before_ an error message.
	www.math.rwth-aachen.de /mapleAnswers/html/491.html (792 words)

	Piecewise Cubic Bézier curves (Site not responding. Last check: 2007-10-16)
		This is a single minimum piece of a piecewise Bézier curve.
		Piecewise cubic Bézier curves like their most general Bézier counterparts cannot exactly represent a circle.
		Except in the trivial case of a straight line, it isn't possible to create a Bézier curve that is parallel to another.
	astronomy.swin.edu.au /~pbourke/curves/bezier/cubicbezier.html (698 words)

	"Piecewise" or "Case by case" Functions (Site not responding. Last check: 2007-10-16)
		These are called piecewise functions and are useful as examples as well as for representing behavior whose governing law switches at some point in the domain.
		When graphing piecewise functions it is important to indicate what happens at the ends of the pieces.
		An alternative method is to use square and round brackets as one would to indicate open and closed intervals.
	oregonstate.edu /instruct/mth251/cq/FieldGuide/piecewise/lesson.html (332 words)

	Mathematica Documentation: Piecewise
		that yields True is returned as the value of the piecewise function.
		do not literally yield False, the Piecewise function is returned in symbolic form.
		• Piecewise can be used in such functions as Integrate, Minimize, Reduce, DSolve and Simplify, as well as their numeric analogs.
	documents.wolfram.com /mathematica/functions/Piecewise (136 words)

	INFOR: Stochastic optimization of a hydroelectric reservoir using piecewise polynomial approximations
		We propose a method for optimizing a single hydro-electric reservoir using a piecewise polynomial approximation of the future value functions.
		However, due to the piecewise linear revenues, our function V^sub t^(s^sub t^) is not as smooth as in Chen et al.
		Some authors have also addressed the problem of approximating the value function of a multireservoir system by a piecewise linear function, using linear programming and Benders decomposition: Pereira and Pinto (1991) assume the reward is proportional to the energy produced and Archibald et al.
	www.findarticles.com /p/articles/mi_qa3661/is_200302/ai_n9188254 (1337 words)

	Math Forum - Ask Dr. Math Archives: Piecewise Functions
		I know piecewise functions are based on expressions between specific intervals, but I do not know how to describe this function family.
		I have a series of points on a graph that form a piecewise equation that 'steps' down as x increases.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/drmath/sets/select/dm_piecewise.html (220 words)

	Piecewise Functions
		Piecewise functions generally decide what formula to put a number into on the basis of "where" the number is found.
		On the other hand, I could ask the computer to plot thousands of values and paint the background different colors according to which function was being plotted.
		Piecewise functions can be a difficult concept to master.
	kerbaugh.uncfsu.edu /piecewise/piecewise.html (1971 words)

	piecewise vs which
		All Piecewise functions have a default value of zero on their undefined intervals.
		The Piecewise function returns 0 as a default value when a domain isn't given for an argument.
		Bradley, If you examine the Help for Piecewise you will see that it is possible to include, as a last argument, a return value if none of the conditions are True, and that the default value for this return value is 0.
	www.codecomments.com /message589138.html (1915 words)

	Questions on Piecewise Functions (Site not responding. Last check: 2007-10-16)
		Special care needs to be taken in for piecewise functions as explained in the exposition.
		Graph the following piecewise functions and evaluate for the given values of x.
		Write the defining rule for a piecewise function T(x) giving the tax owed by a person whose taxable income is $x, where x is less than $117,950.
	oregonstate.edu /instruct/mth251/cq/FieldGuide/piecewise/quiz.html (238 words)

	Piecewise Functions
		We use these types of functions so regularly in science and business that you could almost say they are the most "real" of our applications of functions.
		Be able to use the calculator to graph piecewise functions more easily.
		The calculator is a very useful tool for graphing piecewise functions once you have a set of formulas.
	fym.la.asu.edu /~tturner/MAT_117_online/piecewisefunction/Piecewise.htm (759 words)

	Integration of Piecewise Functions with Applications -- from Mathematica Information Center
		They are intended for working with piecewise continuous functions, and also generalized functions in the case of PiecewiseIntegrate.
		They support all the standard Mathematica piecewise functions such as UnitStep, Abs, Max, as well as Floor and other arithmetic piecewise functions.
		The arguments of the piecewise functions can be non-algebraic and contain symbolic parameters.
	library.wolfram.com /infocenter/MathSource/5117 (102 words)

	Seeing Math Secondary: Piecewise Linear Grapher: User's Guide
		The Seeing Math™ Piecewise Linear Grapher was developed to support learning of linear functions through the use of piecewise functions—functions that are described by different rules for different intervals of the domain.
		The Seeing Math™ Piecewise Linear Grapher (PLG) provides a real-time, two-way connection between symbolic and graphic representations of piecewise linear functions, so that changes in one representation instantly cause changes in the other.
		To remove an entire piecewise function at once — all of its segments or rays — click the Delete Function button next to that function.
	seeingmath.concord.org /Interactive_docs/PLG_UsersGuide.htm (1422 words)

	Graphing Piecewise Functions on the TI-83/84 -- TC3 (Brown) (Site not responding. Last check: 2007-10-16)
		But a piecewise function will legitimately have gaps, and therefore you want to select dot mode.
		One particular problem with piecewise functions is that the TI-83/84 may try to connect the pieces.
		Make sure you are in dot mode, not connected mode: look on the Y= screen for three dots next to your equation.
	www.acad.sunytccc.edu /instruct/sbrown/ti83/funcpc.htm (331 words)

	Piecewise Graphs (Site not responding. Last check: 2007-10-16)
		A piecewise defined graph is a graph whose behavior is defined in pieces.
		This is a nice introduction to the notion of piecewise defined graphs.
		It was the first assignment regarding piecewise graphs that I gave to my students - A nice first exercise for those with little previous piecewise graphing experience.
	home.columbus.rr.com /mathparty/pw.html (238 words)

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