Foundational Calculus: Limits, Continuity, and Differentiation

Are you ready to demystify calculus and unlock its foundational concepts? This course provides a clear, step-by-step introduction to the building blocks of advanced mathematics. By the end of this course, you will possess a solid conceptual understanding of limits, continuity, and differentiation. You will be equipped to analyze functions, solve related problems, and confidently progress to more complex calculus topics, forming a robust base for any STEM field. What you'll learn: * Understand the precise definitions and properties of limits of functions * Apply various techniques to evaluate limits, including algebraic manipulation and L'Hôpital's rule * Grasp the concept of continuity and identify different types of discontinuities in functions * Learn the fundamental rules of differentiation and their geometric interpretation * Practice calculating derivatives of various functions using product, quotient, and chain rules * Explore applications of derivatives, such as finding tangent lines and rates of change The course progresses logically, starting with the intuitive idea of limits before delving into formal definitions and computational methods. It then builds upon these concepts to explore continuity and, finally, the powerful tools of differentiation and their practical uses. This course is designed for absolute beginners in calculus, students needing to strengthen their foundational understanding, and anyone preparing for introductory mathematics courses. No prior knowledge of calculus is required, only basic algebra skills. Begin your journey into the fascinating world of calculus today.