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2. Symbolab - Wikipedia

   en.wikipedia.org/wiki/Symbolab

   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.

3. Envelope (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Envelope_(mathematics)

   Envelopes can be used to construct more complicated solutions of first order partial differential equations (PDEs) from simpler ones. [4] Let F(x,u,Du) = 0 be a first order PDE, where x is a variable with values in an open set Ω ⊂ R n, u is an unknown real-valued function, Du is the gradient of u, and F is a continuously differentiable ...

4. List of open-source software for mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_open-source...

   The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.

5. Mean of a function - Wikipedia

   en.wikipedia.org/wiki/Mean_of_a_function

   In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1] ¯ = ().

6. Function (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Function_(mathematics)

   On the other hand, if a function's domain is continuous, a table can give the values of the function at specific values of the domain. If an intermediate value is needed, interpolation can be used to estimate the value of the function. For example, a portion of a table for the sine function might be given as follows, with values rounded to 6 ...

7. Rolle's theorem - Wikipedia

   en.wikipedia.org/wiki/Rolle's_theorem

   The graph of the absolute value function. If differentiability fails at an interior point of the interval, the conclusion of Rolle's theorem may not hold. Consider the absolute value function = | |, [,]. Then f (−1) = f (1), but there is no c between −1 and 1 for which the f ′(c) is zero.

8. Calculus of variations - Wikipedia

   en.wikipedia.org/wiki/Calculus_of_Variations

   Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]

9. Closed-form expression - Wikipedia

   en.wikipedia.org/wiki/Closed-form_expression

   The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).