Lecture
Ordinary Differential Equations: Basics
Description
This lecture covers the basics of ordinary differential equations (ODEs), starting with the Cauchy equation y' = f(t, y) and exploring questions about global solutions, uniqueness, and local solutions. It then delves into higher dimensions and higher-order derivatives of y, establishing a strong connection between the two generalizations. The lecture also discusses Lipschitz functions, the transformation of differential equations into integral equations, and finding solutions for ODEs with various initial conditions.
Official source
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