Calculus Foundations: Single Variable Functions and Approximations

Calculus is the mathematical language of change, shaping everything from physical laws to modern machine learning algorithms. Understanding functions and how they behave is the essential first step to mastering this powerful tool. This written course guides you through the core concepts of single-variable calculus, focusing on conceptual clarity and practical applications. You will transition from basic algebraic representations to analyzing complex mathematical models, gaining the skills needed to solve real-world problems in engineering, physics, and data science. What you'll learn: - Understand the foundational properties of single-variable functions and their graphical representations. - Analyze limits and continuity to describe function behavior at critical points. - Apply Taylor series and approximation techniques to simplify complex mathematical expressions. - Explore how calculus principles underpin modern computational optimization and data modeling. - Practice solving applied problems in the physical, social, and engineering sciences through written exercises. You will begin with basic definitions and terminology before moving systematically through functions, limits, and foundational approximation theories. The material combines clear written explanations with step-by-step mathematical derivations and practical exercises to reinforce your learning. This course is designed for beginners starting their journey in science, technology, engineering, or quantitative social sciences, requiring only a basic background in high school algebra. Start reading today to build a rigorous and practical understanding of calculus.