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 | + | 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. |
[[Limit]]s are heavily used in calculus. The formal notion of a limit is what "differentiates" (hehe, pun) calculus from precalculus mathematics. | [[Limit]]s 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: | ||
| + | |||
| + | * [[Derivative]] | ||
| + | * | ||
| + | {{stub}} | ||
| + | |||
| + | == Calculus in Math Competitions == | ||
The use of calculus in pre-collegiate [[mathematics competitions]] is generally frowned upon. However, many [[Physics competitions | physics competitions]] require it, as does the [[William Lowell Putnam Mathematical Competition|William Lowell Putnam competition]]. | The use of calculus in pre-collegiate [[mathematics competitions]] is generally frowned upon. However, many [[Physics competitions | physics competitions]] require it, as does the [[William Lowell Putnam Mathematical Competition|William Lowell Putnam competition]]. | ||
| + | == Additional Note == | ||
The subject dealing with the rigorous foundations of calculus is called [[analysis]], specifically [[real analysis]]. | The subject dealing with the rigorous foundations of calculus is called [[analysis]], specifically [[real analysis]]. | ||
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== See also == | == See also == | ||
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* [[Analysis]] | * [[Analysis]] | ||
| + | * [[Derivative]] | ||
* [[Fundamental Theorem of Calculus]] | * [[Fundamental Theorem of Calculus]] | ||
* [[Chain Rule]] | * [[Chain Rule]] | ||
| + | * [[Integral]] | ||
Revision as of 10:52, 12 August 2006
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:
This article is a stub. Help us out by expanding it.
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.
