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Implicit function theorem. Increment theorem. Integral of inverse functions. Integration by parts. Integration using Euler's formula. Intermediate value theorem. Inverse function rule. Inverse function theorem.
Calculus. 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 ...
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras. List of algorithms. List of axioms. List of conjectures. List of data structures. List of derivatives and integrals in alternative calculi. List of equations.
For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory . [2]
Differential calculus. Derivative. Notation. Newton's notation for differentiation. Leibniz's notation for differentiation. Simplest rules. Derivative of a constant. Sum rule in differentiation. Constant factor rule in differentiation.
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 ...
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 ...
As the name implies the curl is a measure of how much nearby vectors tend in a circular direction. In Einstein notation, the vector field has curl given by: where = ±1 or 0 is the Levi-Civita parity symbol . For a tensor field of order k > 1, the tensor field of order k is defined by the recursive relation where is an arbitrary constant vector.
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