Introduction to Differential Equations: Solve and Model Real-World Change

How do we predict the spread of a virus, the cooling of a cup of coffee, or the motion of a pendulum? Differential equations are the mathematical language of change, allowing us to model how systems evolve over time. This written course guides you through the core concepts of differential equations, translating complex calculus into practical, step-by-step problem-solving skills. By reading through clear explanations and practicing with targeted written exercises, you will build a solid foundation in modeling and solving equations. You will transition from understanding basic definitions to confidently analyzing first- and second-order equations, and even exploring modern computational methods used to solve them numerically. What you'll learn: Understand key terminology, classifications, and the foundational concepts of differential equations. Solve first-order differential equations using separation of variables and integrating factors. Apply second-order linear equations to model mechanical oscillations and physical systems. Use Euler's method and modern numerical approaches to approximate solutions when analytical methods fail. Model real-world scenarios in biology, physics, and finance using systems of differential equations. Practice step-by-step mathematical proofs and solving techniques through structured written exercises. We begin with the absolute basics, defining what differential equations are and how they are classified, before moving systematically through analytical solving techniques and modern numerical modeling applications. This course is designed for students, self-learners, and aspiring data analysts or engineers who want a beginner-friendly path into differential equations without needing advanced prerequisites beyond basic calculus. Start reading today to unlock the mathematics of change.