"a course, especially a fixed course of study at a college, university, or school," 1824, from a Modern Latin transferred use of classical Latin curriculum "a running, course, career" (also "a fast chariot, racing car"), from currere "to run" (from PIE root *kers- "to run"). Used in English as a Latin word since 1630s at Scottish universities.
late 14c., "of or manifesting life," from Latin vitalis "of or belonging to life," from vita "life," related to vivere "to live," from PIE root *gwei- "to live." The sense of "necessary or important" is from 1610s, via the notion of "essential to life" (late 15c.). Vital capacity recorded from 1852. Related: Vitally.