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Topic: Calculus

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In the News (Thu 23 May 19)

  calculus.org - THE CALCULUS PAGE .
Calculus demonstrations that you can use in the classroom to spice up your lectures and prevent those nodding heads.
Single Variable Calculus Mika Seppälä of Florida State University and the University of Helsinki presents classroom type notes on calculus, in pdf and powerpoint format.
Math Applets for Calculus at SLU: Mike May at St. Louis University has a selection of applets to illustrate important concepts of single and multivariable calculus.
www.calculus.org   (1238 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   (1444 words)

  Calculus (mathematics) - MSN Encarta
Calculus (mathematics), branch of mathematics concerned with the study of such concepts as the rate of change of one variable quantity with respect to another, the slope of a curve at a prescribed point, the computation of the maximum and minimum values of functions, and the calculation of the area bounded by curves.
The two branches into which elementary calculus is usually divided are differential calculus, based on the consideration of the limit of a certain ratio, and integral calculus, based on the consideration of the limit of a certain sum.
Every application of differential calculus stems directly or indirectly from one or both of the two interpretations of the derivative as the slope of the tangent to the curve and as the rate of change of the dependent variable with respect to the independent variable.
encarta.msn.com /encyclopedia_761568582/Calculus_(mathematics).html   (2150 words)

  Calculus - Wikipedia, the free encyclopedia
Calculus is built on two major complementary ideas, both of which rely critically on the concept of limits.
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   (2269 words)

 calculus. The Columbia Encyclopedia, Sixth Edition. 2001-05
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.bartleby.com /65/ca/calcul.html   (1087 words)

 Category:Calculus - Wikipedia, the free encyclopedia
Calculus is a branch of mathematics, developed from algebra and geometry.
Calculus focuses on rates of change (within functions), such as accelerations, curves, and slopes.
The development of calculus is credited to Archimedes, Bhaskara, Madhava of Sangamagrama, Leibniz and Newton; lesser credit is given to Barrow, Descartes, de Fermat, Huygens, and Wallis.
en.wikipedia.org /wiki/Category:Calculus   (140 words)

 Lambda calculus - Wikipedia, the free encyclopedia
In lambda calculus, every expression stands for a function with a single argument (argument::input of a function); the argument of the function is in turn a function with a single argument, and the value of the function is another function with a single argument.
A function of two variables is expressed in lambda calculus as a function of one argument which returns a function of one argument (see currying).
Barendregt, Henk, The lambda calculus, its syntax and semantics, North-Holland (1984), is the comprehensive reference on the (untyped) lambda calculus; see also the paper Introduction to Lambda Calculus.
en.wikipedia.org /wiki/Lambda_calculus   (2426 words)

 Calculus - Uncyclopedia, the content-free encyclopedia   (Site not responding. Last check: )
There is no one-size-fits-all formula for integration; sophomore calculus students can be seen wandering the halls of The Complex, scratching their heads like monkeys and cramming long lists of case studies into their brains, each of which applies only to a narrow class of calculus crime.
Really hard calculus was invented by Chris Bamford immediately after he was struck upon the head by a falling cinder block (brick) accelerating at 9.81 meters per second squared.
This new paradigm surpassed the difficulty of hard calculus to such an extent that the only people capable of comprehending it are those in a state of being struck upon the head by falling cinder blocks accelerating at 9.81 meters per a second squared.
uncyclopedia.org /wiki/Calculus   (1118 words)

 Basic Mathematics - Calculus
Calculus is a style of mathematic invented by Sir Isaac Newton.
My Calculus teacher used to tell us that calculus really isn't that hard, all you have to imagine is that calculus is focused more narrowly on a particular equation than a simple a + b = c.
Calculus is used to take into account stops and starts, twists and turns in the road, time it take entering and exiting the vehicle - things like that that will result in a much more realistic equation.
astronomyonline.org /Science/Calculus.asp   (455 words)

Calculus is a branch of mathematics, developed from algebra and geometry, built on two major complementary ideas.
Leibniz and Newton are usually designated the inventors of calculus, mainly for their discovery of the fundamental theorem of calculus and work on notation.
Calculus has been extended to differential equations, vector calculus, calculus of variations, complex analysis, time scale calculus, infinitesimal calculus, and differential topology.
www.math.ucdavis.edu /~temple/MAT21B/SUPPLEMENTARY-ARTICLES/1HistoryOfCalc.html   (1866 words)

 Lambda calculus - Wikipedia, the free encyclopedia
Lambda calculus can be used to define what a computable function is. The question of whether two lambda calculus expressions are equivalent cannot be solved by a general algorithm, and this was the first question, even before the halting problem, for which undecidability could be proved.
Lambda calculus is universal in the sense that any computable function can be expressed and evaluated using this formalism.
The most prominent counterparts to lambda calculus in programming are functional programming languages, which essentially implement the calculus augmented with some constants and datatypes.
www.wikipedia.org /wiki/Lambda_calculus   (2426 words)

Calculus was invented by Newton and Leibnitz at the end of the 17th century.
Calculus involves a convenient representation of certain limiting processes, which were hinted at in earlier mathematics, but were very difficult to use, and then only in particular problems.
Advanced calculus is a good place to tie all these things together, one final survey of the field, and a proper goal for the undergraduate.
www.du.edu /~jcalvert/math/calculus.htm   (1655 words)

 Why Calculus?
The foundations of calculus were not secure at the time of invention, and the limitations of calculus were obvious to many critics.
Calculus is fundamentally a theory of continuous objects.
However, calculus is about calculating and with the advent of computers it has become possible to attack non-linear problems.
www.math.nus.edu.sg /aslaksen/teaching/calculus.shtml   (1398 words)

 Math.com Online Solvers Calculus   (Site not responding. Last check: )
Calculus is a vast topic, and it forms the basis for much of modern mathematics.
At school, you are introduced to differential calculus by learning how to find the derivative of a function in order to determine the slope of the graph of that function at any point.
Integral calculus is often introduced in school in terms of finding primitive functions (indefinite integrals) and finding the area under a curve (definite integrals).
www.math.com /students/solvers/calculus/calculus.htm   (230 words)

 1.2 What Is Calculus and Why do we Study it?
And you have a qualitative notion of calculus.
The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes.
In fact calculus was invented by Newton, who discovered that acceleration, which means change of speed of objects could be modeled by his relatively simple laws of motion.
www-math.mit.edu /~djk/calculus_beginners/chapter01/section02.html   (1520 words)

 CALCULUS REFORM PAGE   (Site not responding. Last check: )
Calculus&Mathematica is a computer-based calculus reform project developed at the University of Illinois and Ohio State University.
The Calculus, Concepts, Computers and Cooperative Learning (C4L) program is the result of a National Science Foundation funded research and development project begun at Purdue University under the direction of Ed Dubinksky and Keith Schwingendorf.
The Old Dominion University Calculus Project was initially developed under a grant from the State Council for Higher Education in Virginia (SCHEV).
www.math.okstate.edu /archives/calcrefm.html   (281 words)

 NAMEzero - Web Directory: Browse
Calculus AP Problems of the Week - Archive of questions and solutions in relation to the Calculus Advanced Placement Exam for high school students.
Calculus Solutions - Reference site with a vast amount of information and example problems which are alphabetically listed by topic.
Calculus and Physics Practice Exams - Practice exams for applied calculus and physics in PDF and HTML formats.
kevdb.infospace.com /info.direct/kevdb?KCFG=dmoz&otmpl=dmoz/dmoz-out.htm&qk=50&qcat=Top/Science/Math/Calculus   (732 words)

 Calculus history
In fact, although Barrow never explicitly stated the fundamental theorem of the calculus, he was working towards the result and Newton was to continue with this direction and state the Fundamental Theorem of the Calculus explicitly.
His results on the integral calculus were published in 1684 and 1686 under the name 'calculus summatorius', the name integral calculus was suggested by Jacob Bernoulli in 1690.
After Newton and Leibniz the development of the calculus was continued by Jacob Bernoulli and Johann Bernoulli.
www-groups.dcs.st-and.ac.uk /~history/HistTopics/The_rise_of_calculus.html   (1696 words)

 PSU Math - Calculus   (Site not responding. Last check: )
The engineering-science calculus sequence begins with Math 140 (4 credits), followed by Math 141 (4 credits), which, together, cover one variable differential and integral calculus and an introduction to sequences and series.
But calculus is more than a technical tool - it is a collection of fascinating and exciting ideas that have interested thinking people for centuries.
Many people consider calculus to be one of the greatest achievements of the human intellect.
www.math.psu.edu /courses/calcpage.html   (545 words)

 Calculus Lesson Plans
Calculus Reform: Sample Materials- Syllabi, homework, exams, handouts from the four terms of Calculus, as taught at Stony Brook.
Extreme Values and Calculus- Students should be familiar with defining functions on specific intervals and viewing windows on a graphing calculator.
Momentum- One useful consequence of Newton's 3rd law is the conservation of momentum, as is shown by analyzing the recoil of a cannon.
www.teach-nology.com /teachers/lesson_plans/math/calculus   (246 words)

 Calculus - Content Standards (CA Dept of Education)
When taught in high school, calculus should be presented with the same level of depth and rigor as are entry-level college and university calculus courses.
Consideration of the College Board syllabi for the Calculus AB and Calculus BC sections of the Advanced Placement Examination in Mathematics may be helpful in making curricular decisions.
Calculus is a widely applied area of mathematics and involves a beautiful intrinsic theory.
www.cde.ca.gov /be/st/ss/mthcalculus.asp   (875 words)

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