Lyapunov Functions: Construction and Properties

Related lectures (28)

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Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Covers differential forms, invariant measures, and integration on manifolds with examples and illustrations.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Covers a review of vector calculus and the Maxwell equations in electromagnetism.

Covers the derivation of geometric properties from spectral side functions.