Differential and Difference Equations for Modeling

Mathematical models are essential tools for understanding complex dynamic processes in physics, economics, and engineering. Differential and difference equations allow you to formalize real-world behaviors, predict future states, and derive actionable insights from mathematical frameworks. This written course guides you through core modeling techniques step by step. You will start with key definitions and fundamental terminology, then progress to analytical solutions and practical stability analysis for both continuous and discrete systems. What you will learn: Understand core terminology and foundational concepts of continuous and discrete mathematical models. Solve first-order and higher-order ordinary differential equations using analytical methods. Analyze linear difference equations to evaluate discrete-time economic and physical models. Assess system stability, equilibria, and long-term behavior across various scenarios. Practice applying mathematical formulations to model physical and economic phenomena. Explore fundamental numerical solution methods for approximating complex models. The course begins with clear definitions and theoretical fundamentals before moving into detailed written explanations and worked mathematical examples. Designed for beginners in applied mathematics, data analysis, economics, or engineering looking to build confidence in mathematical modeling. Start reading today to build a strong foundation in differential and difference equations.