MIT 18.100B Real Analysis, Spring 2025 - Lecture 17: Taylor Polynomials; Remainder Term; Riemann Integrals

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG We begin by estimating how close the Taylor expansion approximates a function. To do so means that we need to bound the remainder term. After that, we turn to constructing the Riemann integrals. Integrals plays a key role in all of mathematics and was originally constructed to calculate areas of complicated figures. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.