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Elementary rules of differentiation. Unless otherwise stated, all functions are functions of real numbers (R) that return real values; although more generally, the formulae below apply wherever they are well defined [1][2] — including the case of complex numbers (C). [3]
Ximera is a massive open online course by Ohio State University on Coursera and YouTube. [1] The system was originally known as MOOCulus and Calculus One. [2] The course features over 25 hours of video and exercises. The instructor is Jim Fowler, an associate professor of mathematics at the Ohio State University. [3]
In mathematics education, calculus is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone"), a meaning which still persists in medicine. Because such pebbles were used for ...
Limit (mathematics) In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further ...
e. In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [ a ] the other being differentiation. Integration was initially used to solve problems in mathematics ...
t. e. In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation, or, equivalently, The chain rule may also be expressed in ...
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