Calculus Foundations: Limits and Derivatives from Scratch

Calculus often feels intimidating, but mastering its foundation does not have to be. Understanding limits and derivatives is the key to unlocking advanced mathematics, physics, and modern machine learning optimization. This text-based course guides you step-by-step through the core principles of calculus, helping you transition from basic algebra to analyzing continuous change. What you'll learn: - Understand the fundamental concept of a limit and how functions behave near specific points. - Evaluate limits analytically and numerically using standard algebraic techniques. - Define continuity and identify where functions fail to be continuous. - Master the definition of the derivative as an instantaneous rate of change. - Apply core differentiation rules, including the power, product, quotient, and chain rules. - Explore modern applications of derivatives in optimization and algorithmic thinking. You will start with foundational definitions and key mathematical terminology before moving on to guided practice problems. The curriculum flows logically from the concept of limits to the mechanics and applications of differentiation, ensuring you build confidence with each reading. This course is designed for absolute beginners, students preparing for college-level math, or professionals looking to refresh their mathematical foundations. No prior calculus experience is required. Start reading today to build a rock-solid foundation in calculus.