Understanding Positive and Negative Orientation in Curves

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Covers Green's Theorem, transforming 2D integrals into 1D line integrals.

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

Explores closed and non-closed surfaces, divergence theorem, Stokes theorem, and fluid properties in fluid dynamics and electromagnetism.

Explains curvilinear integrals, conservative fields, and their relationship with potentials.

Covers curvilinear integrals in R^n, focusing on continuous functions and curves.

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Introduces the divergence and Stokes' theorems, comparing surface and volume integrals, and explains parameterization of surfaces and boundaries.

Explores surface integrals, emphasizing physical interpretation and mathematical calculations in vector fields and domains.

Covers the definitions of gradient and divergence, including the Cartesian coordinate system and the divergence theorem.