Difference between revisions of "Calculus"
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The discovery of the branch of [[mathematics]] known as '''calculus''' was motivated by two classical problems: how to find the [[slope]] of the [[tangent line]] to a curve at a [[point]] and how to find the [[area]] bounded by a curve. What is surprising is that these two problems are fundamentally connected and, together with the notion of limits, can be used to analyse instantaneous [[rate]]s of change, accumulations of change, [[volume]]s of irregular [[solid]]s, and much more. | The discovery of the branch of [[mathematics]] known as '''calculus''' was motivated by two classical problems: how to find the [[slope]] of the [[tangent line]] to a curve at a [[point]] and how to find the [[area]] bounded by a curve. What is surprising is that these two problems are fundamentally connected and, together with the notion of limits, can be used to analyse instantaneous [[rate]]s of change, accumulations of change, [[volume]]s of irregular [[solid]]s, and much more. | ||
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== Calculus in Math Competitions == | == Calculus in Math Competitions == | ||
Revision as of 02:17, 31 October 2006
This article is a stub. Help us out by expanding it.
The discovery of the branch of mathematics known as calculus was motivated by two classical problems: how to find the slope of the tangent line to a curve at a point and how to find the area bounded by a curve. What is surprising is that these two problems are fundamentally connected and, together with the notion of limits, can be used to analyse instantaneous rates of change, accumulations of change, volumes of irregular solids, and much more.
Limits are heavily used in calculus. The formal notion of a limit is what "differentiates" (hehe, pun) calculus from precalculus mathematics.
Student Guide to Calculus
The following topics provide a good introduction to the subject of calculus:
Calculus in Math Competitions
The use of calculus in pre-collegiate mathematics competitions is generally frowned upon. However, many physics competitions require it, as does the William Lowell Putnam competition.
Additional Note
The subject dealing with the rigorous foundations of calculus is called analysis, specifically real analysis.
