Foundations of Differentiation for IIT and Math Olympiads

Mastering calculus is the gateway to cracking competitive engineering examinations and mathematical olympiads. This course breaks down the core concepts of differentiation into clear, digestible written explanations, helping you build a rock-solid mathematical foundation. You will progress from understanding the fundamental definition of a limit to confidently applying advanced differentiation rules. By working through structured written examples and step-by-step proofs, you will develop the analytical thinking required to tackle complex competitive exam problems. What you will learn: Understand the foundational concept of limits and the first principles of derivatives; Master key differentiation rules including the power, product, quotient, and chain rules; Apply derivatives to find tangents, normals, and rates of change in physical systems; Analyze functions to determine maxima, minima, and points of inflection; Explore how differentiation connects to modern computational fields like optimization and machine learning algorithms; Practice solving Olympiad-style problems through detailed, written step-by-step walkthroughs. The course starts with basic definitions and algebraic intuition described through text, gradually building up to rigorous techniques and competitive-level problem-solving strategies. This text-only course is designed for high school students, IIT aspirants, and math enthusiasts preparing for competitive exams who have a basic background in algebra and trigonometry. No prior calculus experience is required. Start reading today to unlock a deeper understanding of calculus and elevate your mathematical problem-solving skills.