I would suspect that a financial maths book would introduce the following, but I am only a novice and so would cherish your recommendations. The following is motivated by pp 304-305, ETFs for Canadians for Dummies (2013; by Russell Wild and Bryan Borzykowski). (which only invokes arithmetic and no further maths). Please simply recommend resources if any answers my question. Denote:
$D$ = Dollar value of your current portfolio
$S_i$ = Dollar value of financial instrument $i$ (eg a common stock)
$p_i$ = Proportion of your portfolio in $S_i$, where $0 \le p_i \le 1$.
Thus $ D= \sum_{1 \le i \le n} p_iS_i$.
You desire to change your portfolio by amount $C$, and desire your changed portfolio to become:
$D + C = \sum_{1 \le i \le n} p_i'S_i'$. You decide and so know $p_i'$, but how do you solve for $S_i'$ for each $i$?