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In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions , vectors , matrices , polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The individual terms in the sum are not. When the basis is changed, the components of a vector change by a linear transformation described by a matrix. This led Einstein to propose the convention that repeated indices imply the summation is to be done. As for covectors, they change by the inverse matrix. This is designed to guarantee that the ...
Loosely speaking, a function is Riemann integrable if all Riemann sums converge as the partition "gets finer and finer". While not derived as a Riemann sum, taking the average of the left and right Riemann sums is the trapezoidal rule and gives a trapezoidal sum. It is one of the simplest of a very general way of approximating integrals using ...
Is a subfield of calculus [30] concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve. [31] differential equation Is a mathematical equation that relates some function with its derivatives. In applications ...
The integral symbol is U+222B ∫ INTEGRAL in Unicode [5] and \int in LaTeX.In HTML, it is written as ∫ (hexadecimal), ∫ and ∫ (named entity).. The original IBM PC code page 437 character set included a couple of characters ⌠ and ⌡ (codes 244 and 245 respectively) to build the integral symbol.
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.
In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories of summation equations and integral equations can be unified as integral equations on time scales [ 1 ] using time scale calculus .
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.