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Differential equations are the language of change, describing everything from population growth to electrical circuits. Mastering them is crucial for understanding dynamic systems across science and engineering. This course provides a comprehensive, text-based introduction to ordinary differential equations, equipping you with the analytical and conceptual tools to solve a wide range of problems. By the end, you will confidently approach mathematical models that describe evolution and interaction over time. What you'll learn: Understand fundamental definitions, classifications, and properties of differential equations. Solve various types of first-order ordinary differential equations using analytical techniques. Master methods for solving higher-order linear ordinary differential equations with constant coefficients. Apply differential equations to formulate and analyze mathematical models for real-world phenomena. Learn foundational numerical methods for approximating solutions to ordinary differential equations. Analyze systems of linear ordinary differential equations and their applications. The course begins with core concepts and classifications, then systematically progresses through analytical solution techniques for first-order and higher-order equations, before introducing modeling applications and essential numerical approaches. This course is designed for absolute beginners with a basic understanding of calculus. No prior experience with differential equations is required. Start your journey into the powerful world of differential equations today.