Compact Subsets of R^n, Bolzano-Weierstrass Theorem, Extreme Value Theorem

Part 27, Honors Linear Algebra and Multivariable Calculus, Math 340 This is the twenty seventh of a series of videos for the Honors Linear Algebra and Multivariable Calculus course that I teach at the University of Maryland. The course involves some proofs along with the discussion of linear algebra and multivariable calculus. In this video I discuss compact sets. I discuss the Bolzano-Weierstrass Theorem, and the Extreme Value Theorem. Compact Sets: 0:45 Examples for Compact Sets: 1:15 Bounded Sets: 9: Example for Bounded Sets: 9:15 Bolzano-Weirestrass Theorem: 14:30 Extreme Value Theorem: 29:50