Foundational Single-Variable Calculus

Calculus is the mathematical language used to describe change, motion, and optimization, making it indispensable for modern engineering, physics, and data science. A solid grasp of its core principles is crucial for success in any STEM field. This course guides you through the fundamental concepts of single-variable calculus, transforming abstract definitions into practical problem-solving skills. You will gain confidence in interpreting complex relationships and applying powerful mathematical tools to model real-world phenomena. What you'll learn: * Understand the precise definitions of limits, continuity, and their role in function analysis. * Master differentiation rules and apply them to solve practical optimization and rate-of-change problems. * Practice various techniques for calculating definite and indefinite integrals, including substitution and integration by parts. * Analyze the fundamental theorem of calculus and its connection between differentiation and integration. * Determine the convergence or divergence of sequences and infinite series, including power series and Taylor expansions. * Apply foundational calculus concepts to accurately model and interpret real-world systems involving change. We begin by establishing the theoretical foundation of limits and continuity before moving into the core techniques of differentiation and integration. The course concludes with an in-depth study of infinite sequences and series. This course is specifically designed for absolute beginners and requires no prior knowledge of college-level mathematics. If you are preparing for technical studies or simply want to build a strong mathematical mindset, this course is for you. Start mastering the language of change today.