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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [2] [3] [4] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation, it resembles repeated application of a local smoothing ...
A net = is said to be frequently or cofinally in if for every there exists some such that and . [5] A point is said to be an accumulation point or cluster point of a net if for every neighborhood of , the net is frequently/cofinally in . [5] In fact, is a cluster point if and only if it has a subnet that converges to . [6] The set of all ...
A quadratic equation is one which includes a term with an exponent of 2, for example, , [40] and no term with higher exponent. The name derives from the Latin quadrus , meaning square. [ 41 ] In general, a quadratic equation can be expressed in the form a x 2 + b x + c = 0 {\displaystyle ax^{2}+bx+c=0} , [ 42 ] where a is not zero (if it were ...
Polynomial equation – equation in which a polynomial is set equal to another polynomial. Transcendental equation – equation involving a transcendental function of one of its variables. Functional equation – equation in which the unknowns are functions rather than simple quantities. Differential equation – equation involving derivatives.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Expected loss is the sum of the values of all possible losses, each multiplied by the probability of that loss occurring. In bank lending (homes, autos, credit cards, commercial lending, etc.) the expected loss on a loan varies over time for a number of reasons.