Explore practical applications of differential equations in this comprehensive 2.5-hour lecture series. Dive into real-world scenarios such as credit card debt, Newton's Law of Cooling for determining time of death, and the cooling rate of beer. Investigate the Logistic Differential Equation and its applications in fish population dynamics and flu spread. Examine mixing problems, including Continuous Stirred Tank Reactors (CSTR) and brine solutions. Conclude with an in-depth look at the Gompertz Differential Equation. Gain valuable insights into how calculus concepts are applied to solve complex problems across various fields.