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Advanced Analysis II: Laplacian and Coordinates
This lecture covers the advanced analysis of the Laplacian operator in different coordinate systems, focusing on spherical coordinates. It explains the definition and properties of Laplacian in spherical coordinates, emphasizing the transformation between Cartesian and spherical coordinates. The lecture also discusses the convergence of sequences defined by functions and the differentiability of functions. The Laplacian in polar and spherical coordinates is explored, along with the application of Laplacian in solving differential equations. The instructor reviews the Laplacian operator in polar and spherical coordinates, highlighting its significance in mathematical analysis.