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20 relations: Antiderivative, Cauchy's integral theorem, Cauchy–Riemann equations, Chain rule, Complex analysis, Complex number, Connected space, Conservative vector field, David Tall, Function (mathematics), Fundamental theorem of calculus, Green's theorem, Holomorphic function, Line integral, Mathematics, Open set, Path (topology), Real number, Smoothness, Up to.
Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Cauchy's integral theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane.
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Cauchy–Riemann equations
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.
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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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Conservative vector field
In vector calculus, a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential.
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David Tall
David Orme Tall (born 15 May 1941) is Emeritus Professor in Mathematical Thinking at the University of Warwick.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.
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Green's theorem
In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green, though its first proof is due to Bernhard Riemann and is the two-dimensional special case of the more general Kelvin–Stokes theorem.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Path (topology)
In mathematics, a path in a topological space X is a continuous function f from the unit interval I.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
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Anti-derivative (complex analysis), Antiderivative of a complex function, Antiderivative of complex function, Complex antiderivative.
References
[1] https://en.wikipedia.org/wiki/Antiderivative_(complex_analysis)
