Volume element

Related lectures (31)

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Explores changing variables in double integrals, showcasing practical applications and emphasizing the importance of the Jacobian determinant.

Explores differentiability, coordinate changes, Jacobian determinant, gradient transformation, and chain rule.

Explores cylindrical and spherical coordinates with visual aids and practical experiments.

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

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

Covers the calculation of volumes of solid bodies using slices and integrating the cross-sectional area.

Discusses Newton's 2nd Law in fluid dynamics and incompressible Newtonian fluids.

Covers the calculation of the center of gravity in analytical geometry.

Delves into the linear request problem, infinitesimal perturbations, transport plans, and the main theorem from 2018.