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For example, one might conjecture that a differential operator ought to satisfy a certain boundedness condition "for nice test functions," or one might state that some interesting topological invariant should be computable "for nice spaces X." object Anything that can be assigned to a variable and for which equality with another object can be ...
In most cases, however, the important general case of ordinary differential equations exists for a sought-after variable : Due to the laws of nature or the model assumptions, a functional relation is known that specifies how the deriativey ′ of the function to be determined can be calculated from and from the (unknown) value (). In addition ...
del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform. dim – dimension of a vector space. div – divergence of a vector field. DNE – a solution for an expression does not exist, or is undefined.
Linear equations are so-called, because when they are plotted, they describe a straight line. The simplest equations to solve are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. As an example, consider:
However, he used different symbols than those that are now standard. Later, René Descartes (17th century) introduced the modern notation for variables and equations ; in particular, the use of x , y , z {\displaystyle x,y,z} for unknown quantities and a , b , c {\displaystyle a,b,c} for known ones ( constants ).
Fundamental theorem of algebra – states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero. Equations – equality of two mathematical expressions
The plus–minus sign, ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign. For example, y = x ± 1 represents the two equations y = x + 1 and y = x − 1. Sometimes, it is used for denoting a positive-or-negative term such as ±x.
The word algorithm is derived from the Latinization of Al-Khwārizmī's name, Algoritmi, and the word algebra from the title of one of his works, Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa'l-muqābala (The Compendious Book on Calculation by Completion and Balancing).
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