|
Integral Symbol
The integral symbol: : (Unicode), \displaystyle \int (LaTeX) is used to denote integrals and antiderivatives in mathematics, especially in calculus. History The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz in 1675 in his private writings; it first appeared publicly in the article "" (On a hidden geometry and analysis of indivisibles and infinites), published in '' Acta Eruditorum'' in June 1686. The symbol was based on the ſ (long s) character and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands. Typography in Unicode and LaTeX Fundamental symbol The integral symbol is in Unicode and \int in LaTeX. In HTML, it is written as ∫ (hexadecimal), ∫ ( decimal) 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. These were deprecated in subse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic scripts, as well as symbols, emoji (including in colors), and non-visual control and formatting codes. Unicode's success at unifying character sets has led to its widespread and predominant use in the internationalization and localization of computer software. The standard has been implemented in many recent technologies, including modern operating systems, XML, and most modern programming languages. The Unicode character repertoire is synchronized with Universal Coded Character Set, ISO/IEC 10646, each being code-for-code identical with the other. ''The Unicode Standard'', however, includes more th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IBM PC
The IBM Personal Computer (model 5150, commonly known as the IBM PC) is the first microcomputer released in the IBM PC model line and the basis for the IBM PC compatible de facto standard. Released on August 12, 1981, it was created by a team of engineers and designers directed by Don Estridge in Boca Raton, Florida. The machine was based on open architecture and third-party peripherals. Over time, expansion cards and software technology increased to support it. The PC had a substantial influence on the personal computer market. The specifications of the IBM PC became one of the most popular computer design standards in the world. The only significant competition it faced from a non-compatible platform throughout the 1980s was from the Apple Macintosh product line. The majority of modern personal computers are distant descendants of the IBM PC. History Prior to the 1980s, IBM had largely been known as a provider of business computer systems. As the 1980s opened, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Integral
In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a scalar as a value) over the surface, or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a ''surface'' as shown in the illustration. Surface integrals have applications in physics, particularly with the theories of classical electromagnetism. Surface integrals of scalar fields Assume that ''f'' is a scalar, vector, or tensor field defined on a surface ''S''. To find an explicit formula for the surface integral of ''f'' over ''S'', we need to parameterize ''S'' by defining a system of curvilinear coordinates on ''S'', like the latitude and longitude on a sphere. Let such a paramet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Manifold
In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has only ''non-compact'' components. Examples The only connected one-dimensional example is a circle. The sphere, torus, and the Klein bottle are all closed two-dimensional manifolds. A line is not closed because it is not compact. A closed disk is a compact two-dimensional manifold, but it is not closed because it has a boundary. Open manifolds For a connected manifold, "open" is equivalent to "without boundary and non-compact", but for a disconnected manifold, open is stronger. For instance, the disjoint union of a circle and a line is non-compact since a line is non-compact, but this is not an open manifold since the circle (one of its components) is compact. Abuse of language Most books generally define a manifold as a space that is, locally, homeomorphic to Euclidean space (along with some other technical con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counterclockwise
Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite sense of rotation or revolution is (in Commonwealth English) anticlockwise (ACW) or (in North American English) counterclockwise (CCW). Terminology Before clocks were commonplace, the terms "sunwise" and "deasil", "deiseil" and even "deocil" from the Scottish Gaelic language and from the same root as the Latin "dexter" ("right") were used for clockwise. " Widdershins" or "withershins" (from Middle Low German "weddersinnes", "opposite course") was used for counterclockwise. The terms clockwise and counterclockwise can only be applied to a rotational motion once a side of the rotational plane is specified, from which the rotation is observed. For example, the daily rotation of the Earth is clockwise when viewed from above the South P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clockwise
Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite sense of rotation or revolution is (in Commonwealth English) anticlockwise (ACW) or (in North American English) counterclockwise (CCW). Terminology Before clocks were commonplace, the terms " sunwise" and "deasil", "deiseil" and even "deocil" from the Scottish Gaelic language and from the same root as the Latin "dexter" ("right") were used for clockwise. " Widdershins" or "withershins" (from Middle Low German "weddersinnes", "opposite course") was used for counterclockwise. The terms clockwise and counterclockwise can only be applied to a rotational motion once a side of the rotational plane is specified, from which the rotation is observed. For example, the daily rotation of the Earth is clockwise when viewed from above the South Pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contour Integral
In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is closely related to the calculus of residues, a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods. Contour integration methods include: * direct integration of a complex-valued function along a curve in the complex plane (a '' contour''); * application of the Cauchy integral formula; and * application of the residue theorem. One method can be used, or a combination of these methods, or various limiting processes, for the purpose of finding these integrals or sums. Curves in the complex plane In complex analysis a contour is a type of curve in the complex plane. In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined. A curve i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadruple Integral
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, or . Integrals of a function of two variables over a region in \mathbb^2 (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in \mathbb^3 (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration. Introduction Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the -axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where ) and the plane which contains its domain. If there are more variables, a multiple integral will yield hypervolumes of multidime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triple Integral
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, or . Integrals of a function of two variables over a region in \mathbb^2 (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in \mathbb^3 (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration. Introduction Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the -axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where ) and the plane which contains its domain. If there are more variables, a multiple integral will yield hypervolumes of multidimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Integral
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, or . Integrals of a function of two variables over a region in \mathbb^2 (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in \mathbb^3 (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration. Introduction Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the -axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where ) and the plane which contains its domain. If there are more variables, a multiple integral will yield hypervolumes of multidime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Esh (letter)
Esh ( majuscule: Ʃ Unicode U+01A9, minuscule: ʃ Unicode U+0283) is a character used in conjunction with the Latin script, which represents the voiceless postalveolar fricative (English ''sh''). Form, usage, and history Its lowercase form ʃ is similar to a long s ſ or an integral sign ∫; in 1928 the Africa Alphabet borrowed the Greek letter sigma for the uppercase form Ʃ, but more recently the African reference alphabet discontinued it, using the lowercase esh only. The lowercase form was introduced by Isaac Pitman in his 1847 Phonotypic Alphabet to represent the voiceless postalveolar fricative (English ''sh''). It is today used in the alphabets of some African languages, as well as in the International Phonetic Alphabet. The International Phonetic Alphabet (IPA) uses to represent a voiceless palato-alveolar sibilant. Related obsolete IPA characters include , , and . is used in the Teuthonista phonetic transcription system. Variations of esh are used for other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miscellaneous Technical
Miscellaneous Technical is a Unicode block ranging from U+2300 to U+23FF, which contains various common symbols which are related to and used in the various technical, programming language, and academic professions. For example: * Symbol ⌂ (HTML hexadecimal code is ⌂) represents a house or a home. * Symbol ⌘ (⌘) is a "place of interest" sign. It may be used to represent the ''Command key'' on a Mac keyboard. * Symbol ⌚ (⌚) is a watch (or clock). * Symbol ⏏ (⏏) is the "Eject" button symbol found on electronic equipment. * Symbol ⏚ (⏚) is the "Earth Ground" symbol found on electrical or electronic manual, tag and equipment. It also includes most of the uncommon symbols used by the APL programming language. Miscellaneous Technical (2300–23FF) in Unicode In Unicode, ''Miscellaneous Technical'' symbols placed in the hexadecimal range 0x2300–0x23FF, (decimal 8960–9215), as described below. (2300–233F) :1. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
