Dive into a comprehensive 7-hour video series on advanced differential equations and mathematical functions. Explore series solutions for ordinary and singular points, Legendre polynomials, and the Frobenius method. Master techniques for solving first-order and higher-degree differential equations, including Clairaut's equation and simultaneous linear differential equations. Delve into Bessel's functions, studying their recurrence relations, orthogonal properties, and practical applications. Examine Legendre polynomials, covering Rodrigues formula, generating functions, and orthogonal properties. Tackle partial differential equations, focusing on homogeneous and non-homogeneous cases, complementary functions, and particular integrals. Conclude with essential advice on protecting yourself during the coronavirus pandemic.