Foundations of Ordinary Differential Equations

Many phenomena in science, engineering, and economics are described by how things change over time or space. Ordinary Differential Equations (ODEs) provide the essential mathematical framework to understand, predict, and control these dynamic systems. By the end of this course, you will possess a solid understanding of various types of ordinary differential equations and the analytical methods required to solve them, enabling you to approach complex problems with confidence. What you'll learn: * Understand the fundamental definitions, classifications, and properties of ordinary differential equations. * Apply various analytical techniques to solve first-order and higher-order ODEs, including linear and non-linear types. * Model real-world scenarios using differential equations, from population growth to electrical circuits. * Interpret the behavior of solutions qualitatively and analyze stability using phase-plane analysis for simple systems. * Explore numerical methods for approximating solutions when analytical methods are intractable. This course begins with essential terminology and foundational definitions, then systematically progresses through different types of ODEs, their solution methods, and practical applications. You will learn step-by-step through clear explanations and practical examples. This course is designed for absolute beginners with a basic understanding of calculus, who are looking to build a strong foundation in ordinary differential equations. No prior experience with differential equations is required. Start your journey into the world of dynamic systems today.