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Die Differenzenrechnung ist ein Teilgebiet … Die Differenzenrechnung ist ein Teilgebiet der Mathematik, das die diskrete Entsprechung zur Analysis (Differenzial- und Integralrechnung) bildet. Während sich die Analysis mit Funktionen beschäftigt, die auf kontinuierlichen Räumen definiert sind (um einen Grenzwertbegriff etablieren zu können), im Besonderen mit Funktionen auf den reellen Zahlen, interessiert man sich in der Differenzenrechnung für Funktionen auf den ganzen Zahlen ℤ. Die Differenzenrechnung kann zur Berechnung von Reihen angewandt werden.ur Berechnung von Reihen angewandt werden.
, 数学の一部門としての差分法（さぶんほう、英: difference calculus … 数学の一部門としての差分法（さぶんほう、英: difference calculus, calculus of finite difference）あるいは和分差分学（わぶんさぶんがく、英: discrete calculus）は、（微分法および積分法を柱とする）微分積分学の離散版にあたる。微分積分学が（極限の概念を定式化し得る）連続的な空間上の函数（特に実数直線上で定義された函数）に興味が持たれるのに対して、和分差分学では離散的な空間、特に整数全体の成す集合 ℤ 上で定義された函数（すなわち数列）に注目する。差分法は級数の計算にも応用される。ℤ 上で定義された函数（すなわち数列）に注目する。差分法は級数の計算にも応用される。
, Discrete calculus or the calculus of discr … Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change. Discrete calculus has two entry points, differential calculus and integral calculus. Differential calculus concerns incremental rates of change and the slopes of piece-wise linear curves. Integral calculus concerns accumulation of quantities and the areas under piece-wise constant curves. These two points of view are related to each other by the fundamental theorem of discrete calculus. The study of the concepts of change starts with their discrete form. The development is dependent on a parameter, the increment of the independent variable. If we so choose, we can make the increment smaller and smaller and find the continuous counterparts of these concepts as limits. Informally, the limit of discrete calculus as is infinitesimal calculus. Even though it serves as a discrete underpinning of calculus, the main value of discrete calculus is in applications.e of discrete calculus is in applications.
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Discrete calculus or the calculus of discr … Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change.imals", is the study of continuous change.
, Die Differenzenrechnung ist ein Teilgebiet … Die Differenzenrechnung ist ein Teilgebiet der Mathematik, das die diskrete Entsprechung zur Analysis (Differenzial- und Integralrechnung) bildet. Während sich die Analysis mit Funktionen beschäftigt, die auf kontinuierlichen Räumen definiert sind (um einen Grenzwertbegriff etablieren zu können), im Besonderen mit Funktionen auf den reellen Zahlen, interessiert man sich in der Differenzenrechnung für Funktionen auf den ganzen Zahlen ℤ. Die Differenzenrechnung kann zur Berechnung von Reihen angewandt werden.ur Berechnung von Reihen angewandt werden.
, 数学の一部門としての差分法（さぶんほう、英: difference calculus … 数学の一部門としての差分法（さぶんほう、英: difference calculus, calculus of finite difference）あるいは和分差分学（わぶんさぶんがく、英: discrete calculus）は、（微分法および積分法を柱とする）微分積分学の離散版にあたる。微分積分学が（極限の概念を定式化し得る）連続的な空間上の函数（特に実数直線上で定義された函数）に興味が持たれるのに対して、和分差分学では離散的な空間、特に整数全体の成す集合 ℤ 上で定義された函数（すなわち数列）に注目する。差分法は級数の計算にも応用される。ℤ 上で定義された函数（すなわち数列）に注目する。差分法は級数の計算にも応用される。
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Differenzenrechnung
, 和分差分学
, Discrete calculus
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