Explore advanced mathematical concepts in this 18-hour course covering ordinary differential equations, improper integrals, series solutions, Bessel functions, Laplace transformations, and partial differential equations. Delve into the solution methods for first-order and first-degree ODEs, approximate solutions for initial value problems, and homogeneous linear equations. Study the properties and applications of Bessel functions, master Laplace transformation techniques, and apply them to solve various problems. Investigate one-dimensional wave and heat equations, and gain a comprehensive understanding of differential equations, including first-order higher degree, second-order linear, and higher-order linear equations. Examine geometric interpretations and explore the Euler-Cauchy theorem to enhance your mathematical problem-solving skills.