Vector Fields and Potentials

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Related lectures (31)

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Local Invertibility: Vector Fields

Covers local invertibility of vector fields and the Inverse Function Theorem.

Mayer-Vietoris Sequence

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.

Electric Fields: Curl and Path Integrals, Spherical Coordinates Supplement

Explores the integration of electric fields along paths and solutions for constant and radial fields.

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Curvilinear Integrals: Fundamentals

Covers the fundamentals of curvilinear integrals and their calculations, emphasizing the importance of orientation in integrals.

Green-Riemann Formula: Curvilinear Integrals

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

Spectrum of Hyperbolic Surfaces

Explores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.