MIT 18.100B Real Analysis, Spring 2025 - Lecture 23: Existence & Uniqueness for ODEs: Picard–Lindelöf Theorem

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 show existence and uniqueness of first order ordinary differential equations (ODEs). This is the Picard-Lindelof theorem and is a wonderful application of much of the material in the class. It will use the theory of metric spaces as well as the contracting mapping theorem. The solution to an ODE will be constructed as a fix point of a contracting map. Here the contracting map is defined on the Cauchy complete metric space of continuous functions on a compact interval. 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.