Essential Calculus: Continuity and Differentiability

Calculus is the mathematical language of change, but mastering it requires a rock-solid grasp of its foundational building blocks. Understanding how functions behave continuously and how they change at any given point is essential for engineering, data science, and advanced mathematics. This text-only course guides you from the absolute basics to a confident understanding of limits, continuity, and differentiability, equipping you with the analytical skills needed to solve complex calculus problems step by step. What you'll learn: - Understand the core concepts of limits and how they define continuity - Apply fundamental rules and formulas of differentiation to various function types - Analyze functions to identify points of discontinuity and non-differentiability - Master the chain rule, product rule, and quotient rule applications - Solve practical derivative problems using structured, step-by-step workflows - Explore how rates of change apply to modern algorithmic and scientific concepts You will begin with essential terminology and foundational definitions before moving on to algebraic proofs, differentiation rules, and practical problem-solving strategies. The material is structured logically to build your mathematical confidence through reading and written practice. This course is designed for students, self-taught programmers, and beginners who want to build a strong mathematical foundation in calculus. Start reading today and master the core mechanics of calculus.