Explore the fundamental concepts and applications of differential equations in this comprehensive 10-hour course. Learn to solve various types of differential equations, including first-order, second-order, and systems of equations. Master techniques such as separation of variables, integrating factors, and variation of parameters. Investigate real-world applications in population models, mechanical vibrations, and RCL circuits. Delve into advanced topics like Laplace transforms and power series solutions. Develop problem-solving skills through slope fields, homogeneous and nonhomogeneous equations, and both ordinary and singular points in differential equations.