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• W2927300083 abstract "This note tries to show that a re-examination of a first course in analysis, using more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to extreme, namely we present two proofs of Extreme Value Theorem: the programmer that suggests a method (which is practical in down-to-earth settings) to approximate, to any required precision, extreme values of given function in a metric space setting, and an abstract space proof (the level-set proof) for semicontinuous functions defined on compact topological spaces. Next, in intermediate part, we consider Intermediate Value Theorem, generalize it to a wide class of discontinuous functions, and re-examine meaning of intermediate value property. The trek reaches final frontier when we discuss Uniform Continuity Theorem, generalize it, re-examine meaning of uniform continuity, and find optimal delta of given epsilon. Have fun!" @default.
• W2927300083 created "2019-04-11" @default.
• W2927300083 creator A5017467848 @default.
• W2927300083 date "2007-09-27" @default.
• W2927300083 modified "2023-09-27" @default.
• W2927300083 title "Fun with Analysis I: basic theorems in calculus revisited" @default.
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