Advanced Analysis II: Spherical Coordinates

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Explores volume calculation of revolution bodies using mathematical formulas and inequalities.

Covers the basics of spherical coordinates and their applications in volume calculations.

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

Covers cylindrical and spherical coordinates, transformations between coordinate systems, and rotations in physics.

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Covers spherical coordinates, transformations, and volume calculations in integrals.

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

Explores differentiability and coordinate transformations between polar and spherical systems.

Explores the similarity of convex bodies, affine transformations, the Johen's Theover theorem, and KKT conditions.

Covers the transformation of vectors and tensors in quantum physics.