# Solving coefficients of a function having boundary conditions

I have a function F=c+dz, which has particular boundary values, say F(z=1)=2 and F(z=-1)=1, Then I can determine the coefficients: c=1.5 and d=0.5. However, the following does not work!

ClearAll;
F[c_, d_, z_] = c + d*z;
Print[F[c, d, 1]]; Print[F[c, d, -1]];
Solve[{F[c, d, 1] == 2, F[c, d, -1] == 1}, {c, d}];
Print["c=", c, " d=", d];


Where's the mistake?

PS. There's a question of similar title here, which hasn't received an answer (and looks complicated too).

You need to understand how to define a function and how replacement rules work. This is a nice start point.

f[c_, d_, z_] := c + d z
s = Solve[{f[c, d, 1] == 2, f[c, d, -1] == 1}, {c, d}]

(* {{c -> 3/2, d -> 1/2}} *)

Print["c=", c /. s[], " d=", d /. s[]]

(* c=3/2 d=1/2 *)

• What if I just use s = Solve[{f[c, d, 1] == 2, f[c, d, -1] == 1}] in the second line (omitting {c,d} part)? Seems that works too. Anyway still c and d don't take their values (What is Print[c,d];?). How does s become an array? – hbaromega Jan 4 '15 at 16:55
• @hbaromega Solve[] doesn't return "values" but "replacement rules". Please read the docs and this – Dr. belisarius Jan 5 '15 at 5:14
• Thanks. I have read this. Still it's not clear what's the point of mentioning c and d, if Solve cannot return them! Anyway, granting that, could you explain me how it stores in an array s? Say, what would s[] mean and when can I use that? – hbaromega Jan 5 '15 at 7:31
• – Dr. belisarius Jan 5 '15 at 14:28

In addition to @belisarius' solution, you might want to look at StringForm

Clear[f]

f[c_, d_, z_] = c + d z; (* either Set or SetDelayed works *)

s = Solve[{f[c, d, 1] == 2, f[c, d, -1] == 1}, {c, d}];

StringForm["c = 1, d = 2", c, d] /. s[] 