Fields Deriving from a Potential

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Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

Covers the concept of convex functions and their applications in optimization problems.

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Explores boundary conditions for D and E at material interfaces and in capacitors, emphasizing the impact of dielectrics.

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

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.