항목
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Singularity 특이점 (해석학), Singularity (mathematics)In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. See Singularity theory for general discussion of the geometric theory...출처 영어 위키백과
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Residue 유수 (복소해석학), Residue (complex analysis)In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f: \mathbb{C} \setminus \{a_k\}_k...출처 영어 위키백과
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Complex analysis 복소해석학, 複素解析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. It is useful in many branches of mathematics, including algebraic geometry, number theory, applied mathematics; as well as...출처 영어 위키백과
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Harmonic analysis 조화해석학, 調和解析Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two...출처 영어 위키백과
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Liouville's theorem 리우빌의 정리 (복소해석학), Liouville's ..In complex analysis, Liouville's theorem, named after Joseph Liouville, states that every bounded entire function must be constant. That is, every holomorphic function f for which there exists a positive number M such that |f(z)| \leq M for all z in \mathbb{C} is constant. Equivalently...출처 영어 위키백과
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Open mapping theorem 열린 사상 정리 (함수해석학), Open mappi..In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is surjective then it is an open map. More precisely...출처 영어 위키백과
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Pole 극점 (복소해석학), Pole (complex analysis)In the mathematical field of complex analysis, a pole of a meromorphic function is a certain type of singularity that behaves like the singularity of \frac{1}{z^n} at z = 0. For a pole of the function f(z) at point a the function approaches infinity as z approaches a. Formally, suppose U is an...출처 영어 위키백과
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Hurwitz's theorem 후르비츠의 정리 (복소해석학), Hurwitz's the..In mathematics and in particular the field of complex analysis, Hurwitz's theorem is a theorem associating the zeroes of a sequence of holomorphic, compact locally uniformly convergent functions with that of their corresponding limit. The theorem is named after Adolf Hurwitz. Theorem statement...출처 영어 위키백과
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Hartogs' theorem 하르톡스의 정리 (복소해석학), ハルトークスの定理In mathematics, Hartogs' theorem is a fundamental result of Friedrich Hartogs in the theory of several complex variables. Roughly speaking, it states that a 'separately analytic' function is continuous. More precisely, if F:{\textbf{C}}^n \to {\textbf{C}} is a function which is analytic in each...출처 영어 위키백과
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미적분으로 해결할 수 없는 것들상금보다 더 많은 돈을 썼다. 18세기 말부터 수학자들은 복소수를 적극적으로 받아들이기 시작했고 가우스는 1811년에 해석학의 원칙을 복소수에 적용했다. 복소수를 이용한 해석학(복소 해석학)은 실수(實數)에 적용되는 법칙의 상당수가 복소수에도 똑같이 적용되기 때문에 가능해졌다. 현대 해석학은 많은 부분에서...
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미적분학에는 어떤 종류가 있을까?‘수학적 해석학이란?’에서 언급한 대로 미적분학은 극한을 구하는 과정을 포함하는 여러 무한과정을 사용한다. 그리고 이런 미적분 함수들을 해결하기 위해 변하는 양들에 적용되는 여러 형식적인 수학적 규칙들을 포함한다. 수학자들은 미적분학을 두 분야로 분류한다. 첫 번째 분야는 적분학으로, 다각형 모양을...
