Probably not. As a general rule we do not buy textbooks for the library’s collection, though some professors put their textbooks on course reserve, and you can ask your professors to do so.
You can use the Library Search on the library homepage to check if your textbooks happen to be in the library's collection. You may request these books from other UW campuses using Library Search. But you should not rely on using textbooks from libraries for your courses. Many libraries do not purchase current textbooks, and if they do, they often reserve them for their own students. Loan periods for textbooks are typically short (about one month) with limited (if any) renewals.
The campus bookstore's website lists required textbooks for every class.