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How to enter equation while specifying terms?

Posted 3 months ago
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Hello,

I have tried to learn how to enter an equation and then rearrange it such that I can isolate each variable on one side of the equation. I need to specify instances in which certain terms are constant coefficients, and others where they are variables (functions).
This is an example:
H=BS+KE+AX+CT+J*F,
where in the simplest case B, K, A, C and J are all constants and the rest are variables of independent functions.
I would like to rearrange the equation to express it in terms of each variable (each of S, E, X, T and F isolated on the LHS), while specifying the constants listed above).
Then, I want to specify a cases where one or all of the constant coefficients as originally specified are no longer constant, but variable.
I am relatively inexperienced with Mathematica, more so for symbolic operations. However, I have read more pages from the Mathematica language documentation than I can keep track of, but nothing, so far, seems to address my goals.
Eventually, I will want to derive expressions for the various partial derivatives for the expressions, but I need the expressions first.
I will appreciate any assistance the community may provide, whether sending me to the relevant documentation or providing an exemplary input line.

Best Regards,
Paul

POSTED BY: Paul K
Answer
6 Replies
Posted 3 months ago

There should be a multiplications sign between each of the first first four terms, and the fifth term which is correctly displayed.
I am not sure why the other asterisks are not displayed. They are in my entry, but not in the post.

Paul

POSTED BY: Paul K
Answer
Posted 3 months ago

Hi Paul,

Symbol names that start with a capital letter are reserved for WL built-in symbols, so avoid them to prevent conflicts.

ClearAll[h, b, s, k, e, a, x, c, t, j, f]
eq = h == b*s + k*e + a*x + c*t + j*f

Solve[eq, s]
(* {{s -> (h - f j - e k - c t - a x)/b}} *)

Solve[eq, f]
(* {{f -> (h - e k - b s - c t - a x)/j}} *)

Not sure what you mean by

Then, I want to specify a cases where one or all of the constant coefficients as originally specified are no longer constant, but variable

You can assign a value to a symbol and re-evaluate the expression.

j = 3
Solve[eq, f]
(* {{f -> 1/3 (h - e k - b s - c t - a x)}} *)
Posted 3 months ago

Thanks for the reminder on caps.

As for constant coefficients: in simplest case, b, k, a, c and j are any real number, but constant, so that, for example, d(bs)/ds=b. The later case, where b is a function, say z=b*s and z'=b's+bs'.
Again, not all * symbols post, for some reason.

Thanks,

Paul

POSTED BY: Paul K
Answer
Posted 3 months ago

not all * symbols post, for some reason

Because * and ** have a special meaning (italics and bold) in Markdown. Read the "Post Editor" section here.

Posted 3 months ago

To further elaborate, consider the case for solving the equation for T.

-ct=bs+ke+jf-h gives t=(1/c)h-(b/c)s-(k/c)e-(j/c)f.

Furthermore, the initial h=... equation is an empirically-derived expression that relates the process variables, and empirically derived values are used for the values of the coefficients.
I want to consider cases for which coefficient(s) are actually variables, and thus contribute to non-linear behavior of the linear relationship.

Thanks,
Paul

POSTED BY: Paul K
Answer
Posted 3 months ago

I think I've resolved this. There was no need to specify constant versus non-constant terms in the basic equations.
It is handled when taking derivatives through use of NonConstants{terms}.

Regards,
Paul

POSTED BY: Paul K
Answer
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