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I was working on some applied differential equations problem in physics, and I was wondering if there was any simple notion to indicate that a variable in an equation is constant (similar to how x ∈ R indicates x is a real number in 1 dimension).

Example: When I write my solution involving hookes law (F = k Δl), indicate that variable k is constant other than writing in plain english ", k is constant"

David G. Stork
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01penguin
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    No. Especially in physics it's important to say in what conditions that parameter is a constant. In your case, $k$ is a constant for a particular spring. It depends on the material, the cross section, the uncompressed length, etc. – Andrei Oct 06 '21 at 20:08
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    $k=\text{const}$, but you should generally avoid symbology and write things like $x ∈ R$ in plain English as much as possible. It makes your text more readable. – Conifold Oct 06 '21 at 20:08

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Even if it is a physical constant, $k$ may be the unknown - that'd be an inverse problem. What is known and not known should not change the model itself, so the logical order is to introduce all variables and discuss their physical meaning and relationship, and then before studying the mathematical problem, say what is data and what is unknown for your present work.

In general, this can take the form of stating your problem as

Find $(F,\Delta l) \in \mathbb{R}^2$, such that $$F=k\Delta l$$ and ...

So, to come back to your question, it is usually "the other way around": we list the variables which are not known constants.

Some of the data may be also explicitly referred to in that statement of the problem, especially when there are restrictions on them (e.g., "Find..., such that... with $k \in \mathbb{R}^{+*}$")

Joce
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