Solving Differential Equations with Euler's Method

Differential equations are essential for describing change in the physical world, but many cannot be solved with simple algebra. Euler's Method provides a powerful, intuitive way to find numerical solutions when exact formulas are out of reach. This text-based course takes you from the basic concept of slope fields to confidently calculating step-by-step approximations, bridging the gap between theoretical calculus and practical computation. You will transform your understanding of mathematical modeling by learning how to discretize continuous functions. By the end of this program, you will be able to set up initial value problems and use iterative logic to predict system behavior across various scientific domains. What you'll learn: - Understand the fundamental theory behind first-order ordinary differential equations and initial value problems - Apply Euler's Method to approximate values of unknown functions using iterative steps - Analyze the impact of step size on the accuracy and stability of numerical solutions - Identify the difference between local and global truncation errors in approximation - Practice implementing the method through structured written exercises and mathematical logic - Explore how these numerical patterns form the basis for modern computational algorithms used in data science and physics The course begins with foundational definitions of differential equations and derivatives before moving into the step-by-step mechanics of the algorithm and error analysis. You will work through clear, written explanations that demonstrate how to move from a rate of change to a concrete numerical path. This course is designed for beginners in calculus, engineering, or physics who have a basic grasp of derivatives and want to learn practical numerical analysis. No prior experience with numerical methods is required. Start building your numerical analysis skills today.