Intro Real Analysis, Lec 19, Part 1: Conditions for Riemann Integrability

Part 2 of Lecture 19: https://www.youtube.com/watch?v=TZWkAWO3FlI. Real Analysis course textbook ("Real Analysis, a First Course"): https://amzn.to/3421w9I. "Hands On Start to Mathematica": https://amzn.to/2MycspH. Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. Real Analysis Playlist: https://www.youtube.com/watch?v=EaKLXK4hFFQ&list=PLmU0FIlJY-MngWPhBDUPelVV3GhDw_mJu

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Lecture 19, Part 1.

(0:00) Theorems to know about Riemann integrability.
(1:00) Riemann integrable functions are bounded (this is not contradicted by the existence of improper integrals for certain unbounded functions).
(4:00) Continuous functions are Riemann integrable.
(5:25) Monotone functions are Riemann integrable.
(7:10) Equivalent condition for Riemann integrability in terms of the oscillation of a function.
(19:42) Mathematica code to illustrate these ideas.

Bill Kinney, Bethel University Department of Mathematics and Computer Science. St. Paul, MN.

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Видео Intro Real Analysis, Lec 19, Part 1: Conditions for Riemann Integrability канала Bill Kinney