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2. Domain of a function - Wikipedia

   en.wikipedia.org/wiki/Domain_of_a_function

   The term domain is also commonly used in a different sense in mathematical analysis: a domain is a non-empty connected open set in a topological space. In particular, in real and complex analysis , a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} or the complex coordinate space C n ...

3. Calculus of variations - Wikipedia

   en.wikipedia.org/wiki/Calculus_of_Variations

   The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). [2] It immediately occupied the attention of Jacob Bernoulli and the Marquis de l'Hôpital , but Leonhard Euler first elaborated the subject, beginning in 1733.

4. Domain (mathematical analysis) - Wikipedia

   en.wikipedia.org/wiki/Domain_(mathematical_analysis)

   In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.

5. Newton's method - Wikipedia

   en.wikipedia.org/wiki/Newton's_method

   If f has an incomplete domain, it is possible for Newton's method to send the iterates outside of the domain, so that it is impossible to continue the iteration. [19] For example, the natural logarithm function f ( x ) = ln x has a root at 1, and is defined only for positive x .

6. Initial value problem - Wikipedia

   en.wikipedia.org/wiki/Initial_value_problem

   In multivariable calculus, an initial value problem [a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to

7. Domain theory - Wikipedia

   en.wikipedia.org/wiki/Domain_theory

   In addition, the domain of computation is equipped with an ordering relation, in which the "undefined result" is the least element. The important step to finding a model for the lambda calculus is to consider only those functions (on such a partially ordered set) that are guaranteed to have least fixed points. The set of these functions ...