Advanced Analysis II: Laplacian and Coordinates

Related lectures (28)

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Explores the physics of a point particle sliding on a curved surface without friction, focusing on differential equations, forces, and dynamics.

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

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

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

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

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Covers a vertical metronome's forces, angle equation, equilibrium positions, and stability.

Covers separable differential equations of order 1, defining separable equations and providing examples.