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Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart.
Field equations can be classified in many ways: classical or quantum, nonrelativistic or relativistic, according to the spin or mass of the field, and the number of components the field has and how they change under coordinate transformations (e.g. scalar fields, vector fields, tensor fields, spinor fields, twistor fields etc.).
His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, Al-Jabr. [40] On the Calculation with Hindu Numerals, written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
The reception of Arabic numerals in the West was gradual and lukewarm, as other numeral systems circulated in addition to the older Roman numbers. As a discipline, the first to adopt Arabic numerals as part of their own writings were astronomers and astrologists, evidenced from manuscripts surviving from mid-12th-century Bavaria.
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. A tensor field of order greater than one may be decomposed into a sum of outer products, and then the following identity may be used: = ().
Al-Khwārizmī wrote several important books on the Hindu–Arabic numerals and on methods for solving equations. His book On the Calculation with Hindu Numerals (c. 825), along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and numerals to the West. Al-Khwarizmi did not claim the numerals as Arabic, but over ...
1 Hindu-Arabic numerals. 2 Latin. 3 Greek. 4 Other scripts. Toggle Other scripts subsection. 4.1 Hebrew. 4.2 Cyrillic. ... Tav (number) Cyrillic. Л Lobachevsky ...