Change of Variables Formula

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Introduces vectors in a solid reference frame and explains the importance of determinants in interpreting vector products and coordinate changes.

Covers coordinate changes, focusing on polar and spherical coordinates and their transformations, determinants, and invertibility.

Explores coordinate changes between polar and Cartesian coordinates, and introduces the spherical coordinate system.

Introduces Cartesian equations of planes in space and their parametric representations.

Explores differentiability and coordinate transformations between polar and spherical systems.

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

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers polar coordinates, the Jacobian matrix, and examples of calculating areas in polar coordinates.