In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean space as well as a finite-dimensional real vector space. This calculus is also known as advanced calculus, especially in the United States. It is similar to multivariable calculus but is somewhat more sophisticated in that it uses linear algebra (or some functional analysis) more extensively and covers some concepts from differential geometry such as differential forms and Stokes' formula in terms of differential forms. This extensive use of linear algebra also allows a natural generalization of multivariable calculus to calculus on Banach spaces or topological vector spaces.
Calculus on Euclidean space is also a local model of calculus on manifolds, a theory of functions on manifolds.
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mathematics, calculusonEuclideanspace is a generalization of calculus of functions in one or several variables to calculus of functions onEuclideanspace R n...
Multivariable calculus may be thought of as an elementary part of advanced calculus. For advanced calculus, see calculusonEuclideanspace. The special...
This is a list of calculus topics. Limit (mathematics) Limit of a function One-sided limit Limit of a sequence Indeterminate form Orders of approximation...
multivariable calculus; for this, see CalculusonEuclideanspace This disambiguation page lists articles associated with the title Advanced calculus. If an...
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a...
fields, primarily in three-dimensional Euclideanspace, R 3 . {\displaystyle \mathbb {R} ^{3}.} The term vector calculus is sometimes used as a synonym for...
honors-level course might spend more time on conic sections, Euclidean vectors, and other topics needed for calculus, used in fields such as medicine or engineering...
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals...
in its current form by Élie Cartan in 1899. The resulting calculus, known as exterior calculus, allows for a natural, metric-independent generalization...
differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the...
magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A Euclidean vector is frequently represented by...
product) of Euclideanspace even though it is not the only inner product that can be defined onEuclideanspace; see also inner product space. double integral...
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let h ( x ) = f (...
Gregory's Euclidean Proof of the Fundamental Theorem of Calculus at Convergence Isaac Barrow's proof of the Fundamental Theorem of Calculus Fundamental...
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and...
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...
terms would not change a series' convergence/divergence. Dawkins, Paul. "Calculus II - Alternating Series Test". Paul's Online Math Notes. Lamar University...
(1983), Calculus with analytic geometry (Alternate ed.), Prindle, Weber & Schmidt, p. 516, ISBN 0-87150-341-7 Rinaldo B. Schinazi: From Calculus to Analysis...
function itself for any bounded continuous function on (0,∞), and this can be done by using the calculus of finite differences. Specifically, the following...
of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve...
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input...
are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional...
geometry (also known as combinatorial geometry), etc.—or on the properties of Euclideanspaces that are disregarded—projective geometry that consider only...
Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector...
Placement (AP) Calculus (also known as AP Calc, Calc AB / BC, AB / BC Calc or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and...
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