Foundational Calculus: Functions of One and Several Variables

Do you need a strong, analytical foundation in calculus before tackling advanced mathematics, physics, or engineering topics? This course provides a rigorous introduction to the behavior of functions. You will move beyond rote calculation to develop a deep understanding of core concepts like limits, differentiability, and optimization, preparing you for higher-level analysis. What you'll learn: * Understand the rigorous definition of limits, continuity, and differentiability for single-variable functions. * Apply techniques for finding extrema (maxima and minima) and solving optimization problems in one dimension. * Explore vector-valued functions and the geometry of curves in two and three dimensions. * Master partial derivatives, the chain rule, and the gradient for analyzing functions of several variables. * Practice using Taylor series and power series representations for functions and analyzing their convergence. * Learn foundational concepts of integration and fundamental theorems of calculus in both single and multi-variable contexts. The course begins with foundational concepts in real analysis, establishing the behavior of single-variable functions. It then systematically expands these principles to functions of multiple variables, covering differentiation, optimization, and basic integration theory. This course is designed for absolute beginners in advanced calculus or those needing a solid refresher in mathematical analysis. No prior knowledge of calculus is required, only basic algebra skills. Start building your analytical foundation today.