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	Calculus - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas.
		Leibniz and Newton are usually designated the inventors of calculus, mainly for their separate discoveries of the fundamental theorem of calculus and work on notation.
		The rigorous foundation of calculus is based on the notions of a function and of a limit; the latter has a theory ultimately depending on that of the real numbers as a continuum.
	www.bucyrus.us /project/wikipedia/index.php/Calculus (1852 words)

	Calculus - Wikipedia, the free encyclopedia
		Calculus is one of the most important breakthroughs in modern mathematics, answering questions that had puzzled mathematicians, scientists, and philosophers for more than two thousand years.
		In particular, calculus gave a clear and precise definition of infinity, both in the case of the infinitely large and the infinitely small.
		Today, calculus is used in every branch of science and engineering, in business, in medicine, and in virtually every human endeavor where the goal is an optimum solution to a problem that can be given in mathematical form.
	en.wikipedia.org /wiki/Calculus (2183 words)

	Calculus
		Integral calculus studies methods for finding the integral of a function; which may be defined as the limit of a sum of terms, each of which corresponds to a small strip of area under the graph of a function.
		The modern version of calculus is known as real analysis; this consists of a rigorous derivation of the results of calculus as well as generalisations such as measure theory and functional analysis.
		Calculus has been extended to differential equations, vector calculus, calculus of variations, complex analysis, time scale calculus and differential topology.
	pedia.newsfilter.co.uk /wikipedia/c/ca/calculus.html (1012 words)

	Calculus - Open Encyclopedia (Site not responding. Last check: 2007-11-06)
		Differential calculus is concerned with finding the instantaneous rate of change (or derivative) of a function's value, with respect to changes of the function's arguments.
		Integral calculus studies methods for finding the integral of a function; which may be defined as the limit of a sum of terms (which is called the limit of a Riemann Sum), each of which corresponds to a small strip of area (a rectangle) under the graph of a function.
		Calculus has been extended to differential equations, vector calculus, calculus of variations, complex analysis, time scale calculus infinitesimal calculus, and differential topology.
	open-encyclopedia.com /Calculus (908 words)

	Integral - Wikipedia, the free encyclopedia
		In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total.
		By the Fundamental Theorem of Calculus, $\int_a^b f(x)\,dx = F(b)-F(a) .$
		Many real-world applications of calculus rely on calculating integrals approximately because of the complexity of formulas and since an exact answer is unnecessary.
	www.sterlingheights.us /project/wikipedia/index.php/Integral (1469 words)

	Calculus with polynomials - Wikipedia, the free encyclopedia
		In mathematics, polynomials are perhaps the simplest functions with which to do calculus.
		If one has polynomials with coefficients that are not real or complex numbers (perhaps they are integers, or numbers modulo a prime number) then one can formally define the derivative according to the rules given above.
		This is useful, for example, in determining whether a polynomial will have multiple roots: compute the greatest common divisor of the polynomial and its formal derivative.
	en.wikipedia.org /wiki/Calculus_with_polynomials (208 words)

	Calculus
		Calculus is a branch of mathematics, developed from algebra and geometry.
		Calculus has been extended to differential equations, vector calculus, calculus of variations, and differential topology.
		Nevertheless, the calculus was widely used, as it was a very powerful mathematical tool, but it was not until the nineteenth century that mathematicians like Augustin Louis Cauchy, Bernhard Bolzano[?], and Karl Weierstrass were able to provide a mathematically rigorous exposition.
	www.findword.org /ca/calculus.html (1340 words)

	Encyclopedia: Calculus with polynomials (Site not responding. Last check: 2007-11-06)
		In calculus, the quotient rule is a method of finding the derivative of a function which is the quotient of two other functions for which derivatives exist.
		In calculus, Taylors theorem, named after the mathematician Brook Taylor, who stated it in 1712, gives the approximation of a differentiable function near a point by a polynomial whose coefficients depend only on the derivatives of the function at that point.
		Categories: Calculus Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers, or otherwise is true of all members of an infinite sequence.
	www.nationmaster.com /encyclopedia/Calculus-with-polynomials (1221 words)

	Orthogonal Polynomials and Special Function - Summer Course
		Denote by ${\cal P}(a)$ the algebra of all polynomials (with complex coefficients) modulo the monic polynomial $a(\zeta)$ of exact degree $L$.
		Polynomials orthogonal with respect to a perturbation of certain classical weight functions by the addition of mass points at the end points of the interval $\Omega\subset\mathbb{R}$ are considered.
		The application of this method to the polynomial $C_n^{(l)} (x)$ ($l \in \mathbb{N}$) requires the computation by means of recurrence relations of two auxiliary polynomials, $P(x)$ and $H(x)$, of degrees $2l-2$ and $2l-4$, respectively.
	www.mat.uc.pt /~ajplb/opsf2.htm (3102 words)

	Articles - Polynomial (Site not responding. Last check: 2007-11-06)
		Because of their simple structure, polynomials are very easy to evaluate, and are used extensively in numerical analysis for polynomial interpolation or to numerically integrate more complex functions.
		In linear algebra, the characteristic polynomial of a square matrix encodes several important properties of the matrix.
		As there is no general closed formula to calculate the roots of a polynomial of degree 5 and higher, root-finding algorithms are used in numerical analysis to approximate the roots.
	www.lastring.com /articles/Polynomial (2076 words)

	AP Calculus Review - Polynomial Functions (Site not responding. Last check: 2007-11-06)
		If the polynomial is odd degree, then the range will also be all real numbers, if the polynomial is of even degree there will be a number for which the range is all real values less than or greater than those values.
		If we consider an nth degree polynomial it can be shown that it can have at most n real roots, this corresponds to the factors of the polynomial.
		Polynomials of high degrees can be quite difficult to solve, especially if you rely solely on algebraic techniques and if there are no rational solutions.
	www.smes.com /classes/cozean/apcalcreview/polynomials.htm (1256 words)

	Math 416, Fall 2004: Expanded Cumulative Syllabus
		Calculus useful for bounding and evaluating summations: comparisons with integrals, geometric and harmonic sums, linearity and dominance.
		First, h_x(m), for long string m and short random x mod p, is m evaluated at x mod p, where the entries in m are regarded coefficients of a polynomial, and that polynomial is evaluated at a random x.
		We want numerical alorithms that run in time polynomial in the number of bits in the input, not in the number of integers in the input (and not in the integer inputs themselves).
	www.eecs.umich.edu /~martinjs/math416/syl.html (1041 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-11-06)
		In mathematics, the derivative of a function is one of the two central concepts of calculus.
		Arguably the most important application of calculus to physics is the concept of the "time derivative" — the rate of change over time — which is required for the precise definition of several important concepts.
		Velocity (instantaneous velocity; the concept of average velocity predates calculus) is the derivative (with respect to time) of an object's position.
	pardus.info /index.php?title=Derivative (1994 words)

	The Sensible Calculus Program: Calculus Component.
		As the period of ten years of NSF sponsored calculus reform projects closed in the mid '90's, a summary of these efforts, emphasizing many common features, was presented in [MAA 6, and 7 ].
		Frequently a model is presented for motivation and exploration before the calculus concept or technique as in the treatment of transcendental functions with differential equations.
		The Sensible Calculus' unique approach to probability follows the philosophies of both the NCTM Standards and the California Framework that call for the exploration of probability concepts as a regularly encountered strand in the fabric of mathematics.
	www.humboldt.edu /~mef2/senscalca_x.html (2781 words)

	Analysis (Site not responding. Last check: 2007-11-06)
		Cholewinski developed a version of the umbral calculus for studying differential equations of Bessel type and related topics in [16].
		General papers on orthogonal polynomials and umbral calculus are [29,48,82].
		Banach algebras are used by Di Bucchianico [21] to study the convergence properties of the generating function of polynomials of binomial type and by Grabiner [33,34] to extend the umbral calculus to certain classes of entire functions.
	www.win.tue.nl /~sandro/hypersurvey/node8.html (152 words)

	Math Department Syllabus (Site not responding. Last check: 2007-11-06)
		MATH 115B combines precalculus and calculus topics; the sequence MATH 115B-140B covers the material of MATH 115-140 in a more integrated fashion by virtue of a somewhat different ordering of topics.
		A student who goes from MATH 115B to MATH 140 will be better prepared for calculus topics than a MATH 115 student, but may have to do some additional preparation on a few topics such as triangle trigonometry.
		Calculus topics include limits; derivatives of polynomials and exponential, logarithmic and trigonometric functions; and applications of the derivative in graphing.
	www.math.umd.edu /undergraduate/courses/syllabi/syllabusMATH115B.shtml (211 words)

	Calculus with polynomials
		Polynomials are perhaps the simplest functions to do calculus with.
		Calculus of a Single Variable: Early Transcendental Functions (3rd Edition) by Edwards[?], Hostetler[?], and Larson[?] (2003)
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/ca/Calculus_with_polynomials.html (155 words)

	[No title]
		This is the first in a series of three short courses on financial mathematics that take participants from pre-calculus to stochastic calculus.
		Lectures focus on differential and integral calculus in one dimension.
		Students come away with a clear understanding of what a calculus derivative is and actually use derivatives to derive the Macaulay formula for duration.
	www.risklearning.com /courses/math_1.htm (232 words)

	History of the Calculus -- Differential and Integral Calculus
		Newton are usually designated the inventors of calculus, mainly for their separate discoveries of the fundamental theorem of calculus and work on notation.
		Kowa Seki, lived at the same time as Leibniz and Newton and also elaborated some of the fundamental principles of integral calculus, though this was not known in the West at the time, and he had no contact with Western scholars.
		The modern study of the foundations of calculus is known as
	www.edinformatics.com /inventions_inventors/calculus.htm (1532 words)

	The Sensible Calculus Program: Calculus Component.
		Two (among several) distinctive features of the SCP approach are the extensive use of transformation figures to visualize functions and the early and consistent treatment of modelling situations and especially continuous probability to explore the power of mathematics.
		The SCP Approach: The SCP focuses on the themes of differential equations [FL] and estimation throughout the first year of calculus, using modelling as a central motivation for applications of the calculus [FL2].
		An important and unique feature of the text is that interpretations of calculus concepts consistently refer to both a geometric/tangent view using the graph of a function and a dynamic/motion view using transformation figures to visualize functions.
	www.humboldt.edu /~mef2/senscalca.shtml (1960 words)

	References
		The history of Blissard's symbolic calculus, with a sketch of the inventor's life.
		Polynomial sequences associated with a class of incidence coalgebras.
		Umbral calculus and the theory of multispecies nonideal gases.
	www.win.tue.nl /~sandro/hypersurvey/node12.html (757 words)

	Taylor Polynomials
		The purpose of this lab is to use Maple to introduce you to higher order Taylor polynomial approximations to functions.
		In the previous lab, we introduced quadratic Taylor polynomial approximations.
		In this lab, we investigate higher-order Taylor polynomials.
	www.math.wpi.edu /Course_Materials/Calc3/Labs/node4.html (634 words)

	MAT 123 : Introduction to Calculus
		MAT 123 is a thorough preparation for the calculus sequences at Stony Brook University (MAT 125-126-127, MAT 131-132 and AMS 151-161).
		Its primary objective is strengthening students' grasp of the mathematical tools needed for calculus; functions, graphs, polynomials, exponentials, logarithms, trigonometry and their application.
		Towards the end of the course the first fundamental concepts of calculus (limits and derivatives) will be examined as part of a transition to the beginning of MAT125, 131 or AMS 151.
	www.math.sunysb.edu /~ydkim/123/MAT123 (702 words)

	Calculus WIZ: Wolfram Research's Calculus Tutor
		The Calculus WIZ solvers let you plug in actual homework computations, allowing you to double-check your work and avoid the drudgery of complex computations.
		Calculus WIZ tutorials let you find exactly what you're looking for when you need a little extra help on any given topic.
		Calculus WIZ brings mathematics to life with three-dimensional graphics and charts that help you to better understand the problems you are solving.
	www.wolfram.com /wiz (305 words)

	Quantum Relativity: Calculus Chapter 2: Derivatives of Functions - Polynomials
		It actually happens that sometimes things come up which are not functions, and we want to use calculus anyway: when all you have is a hammer, everything looks like a nail.
		We must remember that the function B is not defined in that region, and, sensibly enough, neither are its derivatives.
		So, we can use calculus on B so long as we remember to stay away from the gaps.
	www.quantumrelativity.com /Calculus/Chapter2.html (2361 words)

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