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Topic: Derivative calculus

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	Calculus - Wikipedia, the free encyclopedia
		Today, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimal solution to a problem that can be given in mathematical form.
		Calculus avoids division by zero by using the concept of the limit which, roughly speaking, is a method of controlling an otherwise uncontrollable output, such as division by zero or multiplication by infinity.
		Calculus continues to be further generalized, such as the development of the Lebesgue integral in 1900.
	en.wikipedia.org /wiki/Calculus (2260 words)

	Derivative - Wikipedia, the free encyclopedia
		If the second derivative is positive at a critical point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
		The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
		Perhaps the most natural situation is that of functions between differentiable manifolds; the derivative at a certain point then becomes a linear transformation between the corresponding tangent spaces and the derivative function becomes a map between the tangent bundles.
	en.wikipedia.org /wiki/Derivative (2317 words)

	HighBeam Encyclopedia - calculus
		The calculus is characterized by the use of infinite processes, involving passage to a limit —the notion of tending toward, or approaching, an ultimate value.
		The calculus and its basic tools of differentiation and integration serve as the foundation for the larger branch of mathematics known as analysis.
		The branch of calculus concerned with both the integral as the limit of a sum and the integral as the antiderivative of a function is known as the integral calculus.
	www.encyclopedia.com /html/c1/calcul.asp (1363 words)

	KryssTal : Introduction to Calculus
		The derivative of a sine is the cosine.
		The derivative of the natural logarithm of a function is the reciprocal of the function multiplied by the derivative of the function.
		The derivative of a number raised to the power of a function is the number raised to the function multiplied by the derivative of the function multiplied by the log of the number.
	www.krysstal.com /calculus.html (2657 words)

	More on Derivatives
		In mathematics, the derivative of a function is one of the two central concepts of calculus.
		Points on the graph of a function where the derivative is undefined or equals zero are called critical points or sometimes stationary points (in the case where the derivative equals zero).
		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.
	www.artilifes.com /derivatives.htm (2418 words)

	CHAPTER B2. MAXIMIZATION AND OPTIMIZATION TECHNIQUES
		In the calculus, the derivative of a function that measures the rate of change of the function is conventionally represented as dy/dx, read "the derivative of y with respect to x." The value of the derivative may be computed by the formula
		The second derivative is the derivative of the first derivative; it measures the rate of change of the rate of change of the original function, i.e., the rate of acceleration of the original function.
		The calculus concept of the derivative may be used as a measure of the economic concept of the marginal.
	facweb.furman.edu /~dstanford/mecon/b2.htm (6307 words)

	Calculus Calculators
		Tools for Using the Derivative -- A number of tools for using the derivative, including Newton's method for solving an equation, plotting the tangent line to a function, computing a polynomial approximation for a function, and computing the first N terms of the power series of a function.
		Visual Calculus -- "Visual Calculus is a collection of modules which can be used in the study or teaching of calculus." Topics include pre-calculus, limits and continuity, derivatives, integration, and sequences and series.
		Calculus -- Interactive applets and animation that help visualize a large variety of analytic geometry and calculus topics (e.g., the volume of a solid of revolution, the rectangle approximation method, the fundamental theorem of calculus, etc).
	www.ifigure.com /math/calculus/calculus.htm (591 words)

	A redefinition of the derivative
		Properly derived and analyzed, the derivative equation cannot yield an instantaneous velocity, since the curve always presupposes a subinterval that cannot approach zero; a subinterval that is, ultimately, always one.
		Therefore, all the machinations of calculus, all the dx's and dy's and limits, are not applicable.
		You either apply the calculus to the real-life curve, where there are points in space, or you apply it to the curve on the graph, where there are not.
	geocities.com /mileswmathis/are.html (14271 words)

	Dr. Sloane's Calculus I
		The concept of the limit of a function is central to the study of calculus.
		The Derivative of a function is the slope of the line tangent to the curve (original function) at a given point.
		Calculus professors thought "the derivative of" would be too easy to understand, so they started using d/dx to make it look confusing.
	svr-www.eng.cam.ac.uk /~kkc21/calculus/calculus2.html (2494 words)

	Lee Lady: Topics in Calculus
		It is a mistake to think of calculus, or mathematics in general, as primarily a tool for finding answers (although it is also a mistake to think, as many graduate students do, that calculating is an inferior, unworthy aspect of mathematics).
		Although this Second Derivative Test has theoretical value and is sometimes convenient, in many cases it is simpler to simply decide whether the function is increasing or decreasing in the intervals between critical points by looking at the values the function takes or checking the sign of the first derivative.
		This is understandable, since almost all the functions encountered in a calculus course (and in common applications of calculus) are analytic, and the singularities that occur are usually poles.
	www.math.hawaii.edu /~lee/calculus (2553 words)

	Calculus graphics -- Douglas N. Arnold
		The diagram illustrates the local accuracy of the tangent line approximation to a smooth curve, or--otherwise stated--the closeness of the differential of a function to the difference of function values due to a small increment of the independent variable.
		The proof is based on a diagram depicting a circular sector in the unit circle together with an inscribed and a circumscribed triangle.
		A brief graphical exploration of a continuous, nowhere differentiable function fits very well in the first semester of calculus, for example, to provide a strong counterexample to the converse of the theorem that differentiability implies continuity; or to show that it is only differentiable functions which look like straight lines under the microscope.
	www.ima.umn.edu /~arnold/graphics.html (1432 words)

	More on Calculus
		Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas.
		Applications of integral calculus arise whenever the problem is to compute a number that is in principle (approximately) equal to the sum of the solutions of many, many smaller problems.
		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.artilifes.com /calculus.htm (1869 words)

	Rate of Change and Tangent
		The inevitable conclusion is that a prerequisite to a successful study of calculus is an abstract-general concept of a variable at or near the point of reification.
		Since the derivative is usually constructed as the limit of the slopes of secant lines, these students were demonstrating knowledge that is useful in the study of the derivative.
		Some calculus and post-calculus students drew a line tangent to the curve at the point of interest and used the slope of that line to judge the rate of growth.
	www.mste.uiuc.edu /murphy/Papers/RateOfChangeA.html (5539 words)

	Mathlets: Derivative Calculator
		Calculates the derivative of an expression specified using a simple expression syntax.
		The result of one derivative evaluation step will be entered back into the text input field.
		The button next to the "Variable" label displays a pop-up menu which can be used to select a variable for partial derivatives.
	cs.jsu.edu /mcis/faculty/leathrum/Mathlets/derivcalc.html (240 words)

	Calculus Primer Calculus Tutorial
		Among other things, calculus involves studying analytic geometry (analyzing graphs).
		Having determined the derivative, we can put it to use by the previous example when we calculated the slope for x=3.
		The derivative of a constant (for example the number 7) is always zero.
	www.1728.com /calcprim.htm (1252 words)

	World Web Math: Calculus Summary
		Differential calculus studies the derivative and integral calculus studies (surprise!) the integral.
		The derivative and integral are linked in that they are both defined via the concept of the limit: they are inverse operations of each other (a fact sometimes known as the fundamental theorem of calculus): and they are both fundamental to much of modern science as we know it.
		You may be wondering about the derivatives of your favorite trigonometric functions.
	web.mit.edu /wwmath/calculus/summary.html (911 words)

	Open Directory - Science: Math: Calculus (Site not responding. Last check: 2007-10-24)
		Calculus and Physics Practice Exams - Practice exams for applied calculus and physics in PDF and HTML formats.
		Calculus Solutions - Reference site with a vast amount of information and example problems which are alphabetically listed by topic.
		The University of Minnesota Calculus Initiative - Offers calculus application examples for the mathematical properties of a rainbow, the fundamental theorem of calculus, methods of maximizing structural beams in a building, and modeling population growth.
	dmoz.org /Science/Math/Calculus (926 words)

	Differentiation 1 - maths online Gallery
		is a dynamical diagram displaying the derivative as the slope of the tangent to a graph.
		The necessary preliminaries the user should be familiar with are the slope of a straight line and the graph of a function (see the two applets The slope of a straight line und Function and graph).
		helps to understand the concept of the second derivative (the rate of change of the rate of change) of a function.
	www.univie.ac.at /future.media/moe/galerie/diff1/diff1.html (295 words)

	Differential Calculus: The Derivative
		A derivative is the slope of a line tangent to a curve at a point.
		You may remember something else having that same defintion...symbolically a derivative is written as the ratio we have already discussed: dy/dx.
		Now that you should be comfortable with the overall concept of the derivative, let's find out how to get the derivative of a function.
	members.shaw.ca /mathematica/ahabTutorials/calcDiffDerivitive.html (1983 words)

	Total Derivative (Site not responding. Last check: 2007-10-24)
		The n partial derivatives are equal to v dotted with the n unit vectors that point along the axes.
		It represents the derivative, or the total derivative, of f at p.
		This is analogous to the one dimensional case, where a local maximum or minimum requires a derivative of 0.
	www.mathreference.com /ca-mv,total.html (624 words)

	TI-83/84 Plus BASIC Calculus Programs - ticalc.org
		This program is an extensive collection of calculus tools including approximating definite integrals using Reimann sums, graphing slope fields of first order differential equations, and many other useful items.
		CALCULUS is a suite of 5 tools useful in precalculus and calculus courses for the TI-83/TI-83+/TI-84+/SE.
		This program provides a variety of tools for slope fields: you can enter a differential equation, render the resultant field, edit the window settings, find the slope value at a specific (x,y) point, and trace an antiderivative over the field to verify that it is correct.
	www.ticalc.org /pub/83plus/basic/math/calculus (4252 words)

	Visual Calculus - Definition of derivative
		Objectives: Now that we have defined the derivative of a function at a point, in this tutorial, we define a function which is the derivative at all points of an interval.
		We use the definition of a derivative to find the derivative of some functions.
		We have used the notation f' to denote the derivative of the function f.
	archives.math.utk.edu /visual.calculus/2/definition.12/index.html (425 words)

	Career Calculus
		In basic calculus we learned that the first derivative of a function is the "rate of change" of the value of that function with respect to another variable.
		Focusing on the first derivative can be very difficult to do, as our natural inclination is to focus on C itself.
		The key to a great career is to focus on L, the first derivative of the equation.
	software.ericsink.com /Career_Calculus.html (1836 words)

	Math Tools Browse
		Sketchpad Activities for Introducing Calculus Topics is a series of five activities designed to introduce students to the basic concepts of calculus.
		Uses the definition of derivative to prove that the absolute value function is not differentiable at x = 0.
		Use polar coordinates to visualize the derivative of e^x.
	mathforum.org /mathtools/cell/c,15.5,ALL,ALL (489 words)

	Online Education - Calculus Concepts - How To Guide
		To be able to look at a graph and recognize the limit and the derivative of a function at a specific point.
		Beginning with the history of why calculus was developed, Sir Isaac and I go on to talk about the limit, continuity, the derivative and the integral in a way that even you non math people can appreciate.
		The Derivative; The Ups and Downs of Calculus - The derivative is one of the major areas of study in calculus.
	search.universalclass.com /i/search/11553.htm (1302 words)

	Fractional Calculus (Site not responding. Last check: 2007-10-24)
		Miscellaneous Functions 8 Techniques in the Fractional Calculus 8.1 Laplace Transformation 8.2 Numerical Transformation 8.
		Furthermore, papers related to Fractional Calculus Modelling by promoters and/or their associates can be down-loaded.
		The Fractional Calculus Project is an interdisciplinary collaboration of mathematicians, statisticians, physicists and hydrologists to develop...
	www.fractionalcalculus.info (298 words)

	Amazon.co.uk: Financial Calculus: An Introduction to Derivative Pricing: Books (Site not responding. Last check: 2007-10-24)
		Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities.
		This unique, modern and up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world.
		The two books are very different to each other, though, and it is worth the reader considering his preferred approach before parting with cash.
	www.amazon.co.uk /exec/obidos/ASIN/0521552893 (1252 words)

	Martin Flashman's courses- Math 106 Fall, '02
		Derivatives, integrals; velocity, curve sketching, area; marginal cost, revenue, and profit, consumer savings; present value.
		SCOPE: This course will deal with the theory and application to Business and Economics of what is often described as "differential and integral calculus." Supplementary notes and text will be provided as appropriate.
		Use of Office Hours and Optional "5th hour"s: Many students find beginning calculus difficult because of weakness in their pre-calculus background skills and concepts.
	www.humboldt.edu /~mef2/Courses/m106f02.html (1556 words)

	Amazon.com: Financial Calculus : An Introduction to Derivative Pricing: Books: Martin Baxter,Andrew Rennie (Site not responding. Last check: 2007-10-24)
		Introduction to the Mathematics of Financial Derivatives by Salih N. Neftci
		The discussion is very lucid and easy to understand, and they explain why the conditions in the definition of Brownian motion make its use nontrivial; namely, one must pay attention to all the marginals conditioned on all the filtrations (or histories).
		The method is not really different in principle from the standard short derivation given in Hull, but it does provide a nice, clear example of what is meant by replication and self-financing in the terminology of Brownian motion/sde's.
	www.amazon.com /exec/obidos/tg/detail/-/0521552893?v=glance (2689 words)

	Mathtools.net : Fortran/Calculus
		By applying the chain rule of derivative calculus repeatedly to these operations, derivatives of arbitrary order can be computed automatically, and accurate to working precision.
		The following list of automatic differentiation tools provides a short introduction into the capabilities of the listed AD tool, as provided by their developers and provides pointers to developers and additional information.
		This is a free, portable library for the direct solution of finite difference approximations to two dimensional Helmholz equations in Cartesian, polar, cylindrical, interior spherical coordinates, and surface spherical coordinates, with various combinations of periodicity, normal derivative, or solution of the boundaries of a regular domain.
	www.mathtools.net /Fortran/Calculus/index.html (866 words)

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