Exact Mathematical Analysis Task

A Exact Mathematical Analysis Task is a mathematical analysis task that is an exact mathematical task (which requires the solution to a mathematical statement).

• AKA: Numerical Analysis.
• Context:
  • It can be solved by a Exact Mathematical Analysis System (that implements a exact mathematical anslysis algorithm).
  • It can be the subject of a Exact Mathematical Analysis Domain.
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• Example(s):
  • …
• Counter-Example(s):
  • a Approximate Mathematical Analysis Task.
• See: Function Approximation, Numerical Optimization, Mathematical Analysis, Ordinary Differential Equation, Numerical Approximation, Symbolic Computation, Mathematical Analysis.

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References

2023

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  • An Exact Mathematical Analysis Task is a mathematical analysis task that requires finding an exact, closed-form solution or expression to a mathematical problem, as opposed to an approximate or numerical solution. This type of task often involves the use of algebraic, geometric, and calculus techniques to derive precise expressions, relationships, or formulas for a given problem.
  • Also known as closed-form analysis or symbolic analysis, exact mathematical analysis tasks can be found in various branches of mathematics, such as algebra, calculus, differential equations, and number theory.
  • Context:
    • It can be solved by symbolic computation systems (that implement algebraic manipulation algorithms and symbolic solvers).
    • It can be the subject of study in various mathematical domains, such as real analysis, complex analysis, linear algebra, and more.
    • It can (often) deals with problems that have well-defined, closed-form expressions or solutions, allowing for the derivation of exact results rather than relying on approximations or numerical methods.

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