Differential Calculus Foundations: Single-Variable Functions

Understanding how quantities change is at the heart of mathematics, physics, and modern computational science. Single-variable differential calculus provides the essential analytical framework needed to model motion, optimize processes, and interpret rates of change. This text-based course guides you through core mathematical concepts from the ground up, giving you a clear theoretical and practical foundation in mathematical analysis. What you'll learn: Understand key definitions, set notation, limits, and function continuity; Calculate derivatives and differentials using foundational rules and formulas; Apply major analysis theorems such as Rolle's, the Mean Value Theorem, and L'Hôpital's rule; Analyze function behavior, critical points, extrema, concavity, and asymptotes; Connect calculus concepts to real-world optimization problems and algorithmic thinking. The course begins with core terminology and limit principles before guiding you through practical differentiation techniques, general analysis theorems, and full function investigation routines. Designed for absolute beginners, students, and self-learners, this course requires only basic algebra skills to get started. Start reading today to master the principles of continuous change.