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What does the verb ''prescribe'' mean in these sentences?

two initial conditions$$y(x_{0})=K_{0},\ \ y'(x_{0})=K_{1}$$ prescribe values ${K_0}$ and ![${K_1}$ of the solution and its first derivative (the slope of it's curve) at the same point $x=x_{0}$

one prescribes the initial temperature u(x,0)=f(x) (f given) and boundary conditions at x=0 and x=L for all $t\geq 0$ ,for instance, $u(0,t) = 0,{\rm{ }}u(L,t) = 0$

a problem in which T is prescribed on one portion of the boundary and ${{\partial T} \over {\partial n}}$on the other portion is called a mixed boundary value problem.

Three given distinct points $z_{1},z_{3},z_{3}$ can always be mapped onto three prescribed distinct points $w_{1},w_{3},w_{3}$ by one, and only one, linear fractional transformation $w=f(z)={{az+b}\over{cz+d}}$

I searched in all available dictionaries and The only meaning Which seems appropriate is this: ''to specify with authority''

What do you think is the true meaning of this word?

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  • Why do you not think that 'specify' and 'specified' are not the meanings? Commented Apr 9, 2022 at 15:04
  • I don't think prescribe is used in math or statistics like that.
    – Lambie
    Commented Apr 9, 2022 at 15:25
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    @MichaelHarvey I think this might be appropriate:" specify beforehand" but I'm not quite sure. Commented Apr 9, 2022 at 15:31
  • @Lambie These texts are from the following book: " Advanced engineering mathematics" by "Erwin kreyszig" Commented Apr 9, 2022 at 15:45
  • Ok, then, go with the dictionary definition. specify with authority.
    – Lambie
    Commented Apr 9, 2022 at 15:55

2 Answers 2

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In mathematical contexts like these, "prescribe X" is roughly synonymous with "specify the value of X", usually at the beginning of an argument where you use the specified value in further calculation.

In the first example, the initial conditions allow you to specify - in this case to determine - the two constants \kappa_0 and \kappa_1, which you then use for the rest of the analysis.

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The word "prescribe" can be used in that sort of context. I have seen it so used. I would define it as "set", "fix" or "specify".

But I have seen it much more often used in legal or governmental contexts, where it usually means "order" or "dictate", and of course in a medical context where it means "specify a medicine or other remedy", no doubt derived from the sense of "order" or "specify.

Let's check some dictionary definitions.

Merriam-Webster gives:

Definition of prescribe

intransitive verb

  1. : to lay down a rule : dictate
  2. [Middle English, from Medieval Latin praescribere, from Latin, to write at the beginning] : to claim a title to something by right of prescription
  3. : to write or give medical prescriptions
  4. : to become by prescription invalid or unenforceable

transitive verb
1a : to lay down as a guide, direction, or rule of action : ordain
b : to specify with authority
2 : to designate or order the use of as a remedy prescribed a painkiller

Cambridge gives, in addition to the strictly medical senses:

prescribe verb (MAKE RULE)
[ T ] formal
to tell someone what they must have or do, or to make a rule of something:

  • Penalties for not paying taxes are prescribed by law.
  • [ + that ] The law prescribes that all children must go to school.
  • [ + question word ] Grammatical rules prescribe how words may be used together.

to tell someone what he or she must have or do, or to give as a rule:
A secretary of education cannot and should not prescribe the curriculum of the nation’s colleges.

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