Foundational Differential Calculus: From Rates of Change to Derivatives

Differential calculus is the mathematical foundation behind analyzing change, motion, and optimization in the real world. Understanding how variables change instantaneously is crucial for fields ranging from physics and engineering to modern data science and economics. This text-based course guides you from the absolute basics of functions and limits to the practical application of derivatives, ensuring you build a strong intuitive and mathematical foundation. What you'll learn: • Understand the fundamental concept of limits and how they define continuity • Analyze rates of change and transition from average to instantaneous rates • Master key derivative rules including the power, product, quotient, and chain rules • Apply differentiation to solve real-world optimization and rate-of-change problems • Practice solving calculus problems step-by-step through guided written exercises. The course begins with foundational definitions of functions, graphs, and limits, establishing a solid baseline before introducing the definition of a derivative. From there, you will progress through standard differentiation rules and explore how these mathematical tools are applied to real-world scenarios. This course is designed for beginners with a basic background in algebra; no prior calculus experience is required. Start reading today to unlock the power of calculus and elevate your analytical skills.