 |
Vector Notation
In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in . The International Organization for Standardization (ISO) recommends either bold italic serif, as in , or non-bold italic serif accented by a right arrow, as in \vec. In advanced mathematics, vectors are often represented in a simple italic type, like any variable. Vector representations include Cartesian, polar, cylindrical, and spherical coordinates. History In 1835 Giusto Bellavitis introduced the idea of equipollent directed line segments AB \bumpeq CD which resulted in the concept of a vector as an equivalence class of such segments. The term ''vector'' was coined by W. R. Hamilton around 1843, as he revealed quaternions, a system which uses vectors and scalars to span a four-dimensional spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Vector Component
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A '' vector quantity'' is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a '' directed line segment''. A vector is frequently depicted graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \stackrel \longrightarrow. A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word means 'carrier'. It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Lena L
Lena or LENA may refer to: Places * Léna Department, a department of Houet Province in Burkina Faso * Lena, Manitoba, an unincorporated community located in Killarney-Turtle Mountain municipality in Manitoba, Canada * Lena, Norway, a village in Østre Toten municipality in Innlandet county, Norway * Lena, Asturias, a municipality in the Principality of Asturias, Spain Russia * Lena, Russia, a list of names of several rural localities in Russia * Lena (river), the easternmost of the three great rivers in Siberia * Lena Cheeks, a stretch of the river Lena with peculiar rock formations in Kirensky District, Irkutsk Oblast, Russia * Lena Pillars, a natural rock formation along the banks of the Lena River in far eastern Siberia * Lena Plateau, a large plateau in Siberia * Lena-Angara Plateau, a large plateau in Siberia United States * Lena, Illinois, a village in Stephenson County * Lena, Indiana, an unincorporated community in Parke County * Lena, Louisiana, an unincorporated c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Fraktur
Fraktur () is a calligraphic hand of the Latin alphabet and any of several blackletter typefaces derived from this hand. It is designed such that the beginnings and ends of the individual strokes that make up each letter will be clearly visible, and often emphasized; in this way it is often contrasted with the curves of the Antiqua (common) typefaces where the letters are designed to flow and strokes connect together in a continuous fashion. The word "Fraktur" derives from Latin ("a break"), built from , passive participle of ("to break"), which is also the root for the English word "fracture". In non-professional contexts, the term "Fraktur" is sometimes misused to refer to ''all'' blackletter typefaces while Fraktur typefaces do fall under that category, not all blackletter typefaces exhibit the Fraktur characteristics described above. Fraktur is often characterized as "the German typeface", as it remained popular in Germany and much of Eastern Europe far longer than el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Greek Letters
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BC, the Ionic-based Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard throughout the Greek-speaking world and is the version that is still used for Greek writing today. The uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , , , , , , , The Greek alphabet is the ancestor of several scripts, such as the Latin, Gothic, Coptic, and Cyrillic scripts. Throughout antiquity, Greek had only a single uppercase form of each letter. It was written without diacritics and with little punctuation. By the 9th century, Byzantine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Clarendon (typeface)
Clarendon is a slab serif typeface that was released in 1845 by Thorowgood and Co. (or Thorowgood and Besley) of London, a letter foundry often known as the Fann Street Foundry. The original Clarendon design is credited to Robert Besley, a partner in the foundry, and was originally engraved by Punchcutting, punchcutter Benjamin Fox, who may also have contributed to its design. Many copies, adaptations and revivals have been released, becoming almost an entire genre of type design. Clarendon has a bold, solid structure, similar in letter structure to the Didone (typography), "modern" serif typefaces popular in the nineteenth century for body text (for instance showing an 'R' with a curled leg, and ball terminals on the 'a' and 'c'), but bolder and with less contrast in stroke weight. Clarendon designs generally have a structure with bracketed serifs, which become larger as they reach the main stroke of the letter. Mitja Miklavčič describes the basic features of Clarendon designs ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Oliver Heaviside
Oliver Heaviside ( ; 18 May 1850 – 3 February 1925) was an English mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science. Early life Heaviside was born in Camden Town, London, at 55 Kings Street (now Plender Street), the youngest of three children of Thomas, a draughtsman and wood engraver, and Rachel Elizabeth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including websites, Application software, software applications, music, audiovisual, and print materials. The Archive also advocates a Information wants to be free, free and open Internet. Its mission is committing to provide "universal access to all knowledge". The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hundreds of billions of web captures. The Archive also oversees numerous Internet Archive#Book collections, book digitization projects, collectively one of the world's largest book digitization efforts. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Edwin Bidwell Wilson
Edwin Bidwell Wilson (April 25, 1879 – December 28, 1964) was an American mathematician, statistician, physicist and general polymath. He was the sole protégé of Yale University physicist Josiah Willard Gibbs and was mentor to MIT economist Paul Samuelson. Wilson had a distinguished academic career at Yale and MIT, followed by a long and distinguished period of service as a civilian employee of the US Navy in the Office of Naval Research. In his latter role, he was awarded the Distinguished Civilian Service Award, the highest honorary award available to a civilian employee of the US Navy. Wilson made broad contributions to mathematics, statistics and aeronautics, and is well known for producing a number of widely used textbooks. He is perhaps best known for his derivation of the eponymously named Binomial proportion confidence interval#Wilson score interval, Wilson score interval, which is a confidence interval used widely in statistics. Life Edwin Bidwell Wilson was bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Vector Analysis (Gibbs/Wilson)
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from the theory of quaternions by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, ''Vector Analysis'', though earlier mathematicians such as Isaac Newton pioneered the fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Vector Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). The magnitude of the cross product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The units of the cross-product are the product of the units of each vector. If two vectors are parallel or are anti-parallel (that is, they are linearly dependent), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Scalar Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused with scalar multiplication. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see ''Inner product space'' for more). It should not be confused with the cross product. Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Josiah Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American mechanical engineer and scientist who made fundamental theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period) and described the Gibbs phenomenon in the theory of Fourier analysis. In 1863, Yale University awarded Gibbs the firs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |