Ordinary and Partial Differential Equations: Fundamentals and Solving Methods

Differential equations are essential mathematical tools for modeling change across science, engineering, and quantitative analysis. Understanding how to solve these equations enables you to analyze dynamic physical and computational systems with confidence. This course guides you through the foundational principles of ordinary differential equations (ODEs) and introduces key techniques for partial differential equations (PDEs). You will start with core definitions, classifications, and solution properties before building step-by-step analytical skills. What you will learn: Learn foundational terminology and classifications of ordinary and partial differential equations. Understand analytical methods for solving first-order linear, separable, and exact equations. Master solution techniques for higher-order linear differential equations. Apply qualitative methods to evaluate solution properties and dynamic behavior. Explore basic integration concepts and separation of variables for partial differential equations. Practice numerical approximation concepts used in modern computational modeling. The reading material begins with key definitions and structural properties, then advances through standard integration methods to introductory partial differential equations. This course is designed for beginners and self-learners looking to grasp differential equations through structured written explanations and worked mathematical examples. Start reading today to master the fundamentals of differential equations.