An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

1) Strictly accurate or correct; precise, as opposed to approximate.
2) The complete solution of an equation. For example, in the equation x² = 7, the positive solution 2.646 is correct to three decimal places. The exact answer is x = 7^1/2.
See also:
→ exact differential, → exact differential equation, → exact science, → accurate, → precise, → rigorous.

From L. exactus, p.p. of exigere, literally "to drive out, thrust out," also "demand, finish, measure," from → ex- "out" + agere "drive, lead, act," → act.

Razin "firm, solid, strong" [Dehxodâ, Steingass], Mid.Pers. razên "firm, strong, secure, solid."

If N(x,y) is a → function of two → independent variables, then dN = (∂N/∂x)dx + (∂N/∂y)dy is the exact differential.

→ exact; → differential.

A → differential equation composed of → continuous  → differentiable functions for which certain conditions are fulfilled. The equation M(x,y)dx + N(x,y)dy = 0 is called exact if M(x,y) and N(x,y) are continuous differentiable functions for which the following relationship is fulfilled: ∂M/∂y = ∂N/∂x, and ∂M/∂y and ∂N/∂x are continuous in some region.

→ exact; → differential; → equation.

A value that is known with complete certainty. Examples of exact numbers are defined numbers, results of counts, certain unit conversions. Some examples: there are exactly 100 centimeters in 1 meter, a full circle is exactly 360°, and the number of students in a class can exactly be 25.

→ exact; → number.

A field of study that admits especially precise predictions and rigorous methods of testing hypotheses, especially reproducible experiments involving quantifiable predictions and measurements.

→ exact; → science.