Foundational Calculus: Limits and Differentiation

Many find calculus daunting, but its core ideas are elegant and powerful. This course demystifies the fundamental concepts that underpin all of calculus, starting with clear, written explanations and practical examples. By the end, you will have a solid grasp of limits, continuity, and differentiation, enabling you to confidently approach more advanced mathematical topics and real-world problem-solving. You will learn to: * Understand the precise definition and intuitive meaning of limits. * Apply algebraic techniques to evaluate various types of limits. * Learn the conditions for continuity and identify discontinuities in functions. * Define the derivative as a limit and interpret its geometric and physical significance. * Master fundamental differentiation rules for common functions. * Practice applying derivatives to analyze function behavior and solve introductory optimization problems. * Develop a strong conceptual framework for understanding rates of change and accumulation. The course begins by establishing a clear understanding of limits, then progresses to continuity, and finally introduces the derivative and its applications. Each concept is explained thoroughly with step-by-step examples and practice exercises. This course is ideal for absolute beginners in calculus or anyone looking to solidify their foundational knowledge. No prior calculus experience is required. Begin your journey into the fascinating world of calculus today.