"The textbook for that class is very thin."
Uhg. Let's see, です is not a verb first of all. です is a copula. This coupled with a noun, they form a predicate in a sentence, for example, 「これは教科書です。」"This is a textbook".
However 薄い is not a noun is an i-adjective, and i-adjectives are a special kind of predicate in Japanese grammar, they already have a copula built-in, which is the い at the end. That word 薄い already expresses the state of being, is an adjective but a verbal kind of adjective, if you say「これは薄い。」that would mean "this is thin", including the "IS" part. You don't need です or だ for that.
Even then you would ask, why is です added after i-adjectives in some sentences? well, that's only done to softening the statement done by the adjective. です at the end of i-adjectives is an exception and is only done for politeness' sake.
「その授業の教科書はとても薄い。」is the plain non-polite form of→
Does that make sense?