Foundations of Differential Equations

Many phenomena in science, engineering, and economics can be described using differential equations. This course provides a clear, text-based introduction to this fundamental mathematical tool, helping you understand how rates of change are modeled and analyzed. By completing this course, you will build a robust foundation in differential equations, enabling you to identify, classify, and solve common types of ordinary differential equations, and interpret their solutions in practical contexts. What you'll learn: * Understand the core definitions, terminology, and classifications of differential equations * Solve first-order ordinary differential equations using various analytical techniques * Apply methods for solving higher-order linear ordinary differential equations with constant coefficients * Formulate and solve initial and boundary value problems * Explore foundational concepts of numerical methods for approximating solutions to differential equations * Interpret the behavior of solutions and their real-world implications This course begins with the essential definitions and concepts, progressing through analytical solution techniques for different types of ordinary differential equations, and concludes with an introduction to numerical approximation methods. Each section builds upon the previous one, reinforced with clear explanations and practice problems. This course is designed for absolute beginners with a basic understanding of calculus, who are looking for a comprehensive introduction to differential equations. No prior knowledge of differential equations is required. Start your journey into the world of mathematical modeling and problem-solving today.