Foundational Mathematics: Limits, Derivatives, and Series

Do you struggle with the foundational mathematical concepts that bridge algebra and calculus? Understanding limits, derivatives, and infinite series is essential for success in engineering, physics, data science, and advanced mathematics. This course provides a thorough, text-based revision of these critical topics, equipping you with the algebraic tools and conceptual clarity needed to confidently solve complex problems and prepare for academic exams or technical challenges. What you'll learn: * Understand the rigorous definition of a limit and apply limit theorems to evaluate indeterminate forms. * Master the rules of differentiation (product, quotient, chain rule) and interpret the derivative as a rate of change. * Analyze arithmetic and geometric sequences and series, including formulas for the nth term and sums. * Practice advanced algebraic manipulation techniques essential for simplifying functions before applying calculus rules. * Apply derivatives to practical optimization problems and determine tangent and normal lines to curves. The course begins with a review of fundamental function theory and algebraic manipulation. We then systematically explore limits, continuity, and the definition of the derivative, followed by an in-depth study of sequences and series, reinforcing concepts through detailed examples and written exercises. This course is designed for absolute beginners or students needing a structured, comprehensive revision of foundational mathematical concepts. No prior calculus knowledge is required, only basic algebra skills. Start building your strong mathematical foundation today.