# Taylor Expansion Without Variables?

• Poppop

#### Poppop

This is just part of a larger problem, but I have a basic equation r'=k-g*r, where k and a start out as constants, but then I need to treat everything as if it can vary slightly from the average. For this, I set r=r_ave+dr, g=g_ave+dg, and k=k_ave+dk. Now I need to work these into the first equation, so I guess I need to Taylor expand them, but I don't see how to do that with this sort of equation. Any suggestions?

Is r' the derivative of r? You say you "need to treat everything as if it can vary slightly from the average", but what do you want do do with it? What problem are you trying to solve? I don't think you need to expand this into a Taylor's series, just substitute:
r'= k_ave+ dk- (g_ave+ dg)(r_ave_+ dr)
Now, are you thinking of dk, dg, and dr as functions of some variable (apparently r is since you are using r' but you didn't say what the variable is) or just numbers? If numbers just go ahead and multiply it out. If dk, dg, and dr are very small, you can ignore products like (dg)(dr) and simplify a bit.