Calculus is the branch of mathematics that studies continuous change and is the principal precursor of modern mathematical analysis. It rests on two complementary divisions: differential calculus, which examines instantaneous rates of change and the slopes of curves, and integral calculus, which studies the accumulation of quantities and areas under curves. The two divisions are connected by the fundamental theorem of calculus, and both rest on the concept of a limit applied to infinite sequences and series.
Facts
Central QuestionCalculus studies continuous change: how the instantaneous rate at which a quantity changes (the derivative) and the total accumulation of a changing quantity (the integral) can each be defined rigorously and are related to one another through the fundamental theorem of calculus. 1 Key DebateIsaac Newton and Gottfried Wilhelm Leibniz each independently formulated infinitesimal calculus in the late 17th century, and when both published, a bitter priority dispute broke out over which mathematician, and therefore which country, deserved credit; it divided English-speaking mathematicians from continental European mathematicians for many years. 1 Classification
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Source Calculus (Wikipedia)
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Source Cavalieri's Quadrature Formula (Wikipedia)
Source Chain rule (Wikipedia)
Source Differentiation Rules (Wikipedia)
Source Divergence (Wikipedia)
Source Gradient Theorem (Wikipedia)
Source Integral of the Secant Function (Wikipedia)
Source Limit of a Function (Wikipedia)
Source Quotient Rule (Wikipedia)
Source Second Derivative (Wikipedia)
Source Squeeze Theorem (Wikipedia)
Source Vector Field (Wikipedia)
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1. Calculus (Wikipedia)
Wikimedia FoundationLead section
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus.
History section, Newton and Leibniz passage
When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit.
Associated With: Analysis, Wikipedia lead paragraph, Calculus
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis.
View the Source Chain rule (Wikipedia)
Includes: Chain Rule, Lead sentenceQuote, Includes: Chain Rule, Lead sentence
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y
Gradient Theorem (Wikipedia)
Includes: Gradient Theorem, Lead sentenceQuote, Includes: Gradient Theorem, Lead sentence
theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field
Squeeze Theorem (Wikipedia)
Includes: Squeeze Theorem, Lead sentenceQuote, Includes: Squeeze Theorem, Lead sentence
In calculus, the squeeze theorem (also known as the sandwich theorem, the two policeman and a drunk theorem among other names) is
Differentiation Rules (Wikipedia)
Includes: Differentiation Rules, Lead sentenceQuote, Includes: Differentiation Rules, Lead sentence
les for computing the derivative of a function in calculus.
Quotient Rule (Wikipedia)
Includes: Quotient Rule, Lead sentenceQuote, Includes: Quotient Rule, Lead sentence
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functio
Vector Field (Wikipedia)
Includes: Vector Field, Lead sentenceQuote, Includes: Vector Field, Lead sentence
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean spac
Limit of a Function (Wikipedia)
Includes: Limit of a function, Lead sentenceQuote, Includes: Limit of a function, Lead sentence
e limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular
Second Derivative (Wikipedia)
Includes: Second Derivative, Lead sentenceQuote, Includes: Second Derivative, Lead sentence
In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f.
Cavalieri's Quadrature Formula (Wikipedia)
Includes: Cavalieri's Quadrature Formula, Lead sentenceQuote, Includes: Cavalieri's Quadrature Formula, Lead sentence
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral ∫
Divergence (Wikipedia)
Includes: Divergence, Lead sentenceQuote, Includes: Divergence, Lead sentence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that
Integral of the Secant Function (Wikipedia)
Includes: Integral of the Secant Function, Lead sentenceQuote, Includes: Integral of the Secant Function, Lead sentence
In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expres
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