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Lecture 23: Existence and Uniqueness for ODEs: Picard–Lindelöf Theorem
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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/
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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.
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