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2. 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 ...

3. Desmos - Wikipedia

   en.wikipedia.org/wiki/Desmos

   [5] The name Desmos came from the Greek word δεσμός which means a bond or a tie. [6] In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7]

4. 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 ...

5. Taylor series - Wikipedia

   en.wikipedia.org/wiki/Taylor_series

   The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions include: The partial sums (the Taylor polynomials) of the series can be used as approximations of the function ...

6. 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] ¯ = ().

7. Function space - Wikipedia

   en.wikipedia.org/wiki/Function_space

   Function spaces appear in various areas of mathematics: In set theory, the set of functions from X to Y may be denoted {X → Y} or Y X. As a special case, the power set of a set X may be identified with the set of all functions from X to {0, 1}, denoted 2 X. The set of bijections from X to Y is denoted .

8. 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 (+,,, /).

9. Concave function - Wikipedia

   en.wikipedia.org/wiki/Concave_function

   A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield.