Ordinary and Partial Differential Equations with Practical Applications

Differential equations serve as the mathematical foundation for describing physical, biological, and economic systems. Understanding how to formulate, analyze, and solve these equations is an essential skill for modern engineering, data science, and quantitative analysis. This course provides a comprehensive, step-by-step pathway from basic concepts to practical application. You will start by mastering foundational definitions and first-order ordinary differential equations (ODEs) before progressing to higher-order linear equations. From there, you will explore partial differential equations (PDEs) and learn how to model spatial-temporal phenomena like heat diffusion and wave propagation. What you'll learn: Understand the core classification, order, linearity, and formulation of differential equations; Solve first-order and higher-order ordinary differential equations using analytical methods; Apply Laplace transforms to solve linear differential equations with initial conditions; Formulate and solve basic partial differential equations using separation of variables; Practice modeling real-world physical systems using mathematical equations; Learn modern numerical approximation methods to solve complex equations computationally. The course begins with essential terminology and foundational mathematical concepts, gradually moving toward advanced analytical techniques and modern computational approaches. This course is designed specifically for beginners, students, and professionals looking to build a strong mathematical foundation, with no advanced prerequisites required. Start reading today to unlock the power of mathematical modeling.