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The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function. The first part of the theorem, sometimes called the first fundamental theorem of calculus , states that one of the antiderivatives (also called indefinite integral ), say F , of some function f may be ...
Institutiones calculi integralis (Foundations of integral calculus) is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations .It was written after "Institutiones calculi differentialis" (1755) and "Introductio in ...
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover. [1]
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic .
In mathematical analysis, Schwarz's theorem (or Clairaut's theorem on equality of mixed partials) [9] named after Alexis Clairaut and Hermann Schwarz, states that for a function : defined on a set , if is a point such that some neighborhood of is contained in and has continuous second partial derivatives on that neighborhood of , then for all i ...
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...