Calculus Foundations: Limits, Continuity, and Differentiability

Calculus can feel intimidating when presented as a wall of complex formulas, yet understanding its core principles is essential for advanced mathematics, physics, and modern computer science. This course breaks down the fundamental concepts of limits, continuity, and differentiability into clear, logical steps. Through detailed written explanations and structured practice problems, you will transition from memorizing rules to truly understanding how functions behave, how to analyze their limits, and how to determine their rate of change. What you'll learn: 1. Understand the foundational concept of a limit and how to evaluate limits analytically. 2. Apply algebraic techniques to resolve indeterminate forms and evaluate infinite limits. 3. Master the definition of continuity and use it to analyze function behavior at specific points. 4. Practice proving differentiability using first principles and understand its geometric meaning. 5. Learn how these calculus principles form the basis of modern optimization algorithms used in data science. The course begins with basic definitions of functions and limits before moving systematically through continuity criteria, differentiability rules, and practical problem-solving applications. This text-based course is designed for beginners, high school students preparing for exams, and anyone looking to build a strong mathematical foundation with no prior calculus experience required. Start reading today to master the core principles of calculus.