MAT320/640 LECTURE 23 (11/24/2021): DARBOUX AND RIEMANN INTEGRALS
• Announcements: Happy Thanksgiving to everyone!!
• Video 1: Preliminary definitions. Download file or watch below
• Video 2: Upper and lower integrals and (Darboux) integrability. Download file or watch below
• Video 3: Two examples. Download file or watch below
• Video 4: Lower integral is smaller than or equal to upper integral. Download file or watch below
• Video 5: Necessary and sufficient condition for (Darboux) integrability. Download file or watch below
• Lecture Notes (static file from above video): PDF file
Note: Due to time restrictions, we are not discussing what are Riemann sums, as you typically learn in Calculus, nor why the notions of Darboux and Riemann integrability are indeed equivalent, as claimed in lecture today. For all practical matters, you can just take that to be true -- but if you are curious to read more details about it (and I would certainly encourage you to!) then please take a look at pages 275--279 of the book by Ross.
Last updated: Nov 24, 2021, 2:00pm EST