Advanced Analysis II: Spherical Coordinates

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Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.

Explains multiple integration using spherical coordinates to calculate volumes of spheres and ellipsoids.

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Covers the inverse function theorem, Jacobian matrix, injective functions, bijective functions, and spherical coordinates.

Explains polar, cylindrical, and spherical coordinates in physics, emphasizing their advantages in simplifying motion analysis.

Covers the conversion and applications of spherical coordinates in mathematical and physical contexts.

Covers the analytical expression of orthogonal projections and reflections in 2D space.

Covers cylindrical and spherical coordinates, vector positions, velocities, accelerations, and rotations.

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.