Calculus through Data: Limits and Derivatives

Traditional math courses often focus on abstract formulas, leaving you wondering how calculus actually applies to the real world. This course bridges that gap by teaching you calculus through the lens of practical data analysis and modeling. You will transition from memorizing equations to intuitively understanding how functions change, how to measure that change using derivatives, and how to apply these concepts to real-world datasets. By exploring rate-of-change concepts, you will gain the mathematical foundation necessary for data science, economics, and physical modeling. What you'll learn: - Understand the foundational concepts of functions, limits, and continuity using clear mathematical definitions. - Apply the definition of a derivative to measure sensitivity to change and calculate instantaneous rates of change. - Model real-world scenarios, such as velocity and growth rates, using discrete data points and continuous functions. - Practice numerical differentiation techniques to approximate derivatives using modern data-driven approaches. - Analyze optimization problems by finding maximum and minimum values of functions to make data-driven decisions. The course starts with essential terminology and the foundational concept of a limit before moving on to defining and calculating derivatives. You will progress through written explanations, step-by-step mathematical derivations, and practical modeling exercises designed to build your confidence. This course is designed for beginners with a basic grasp of algebra who want a practical, application-first introduction to calculus. No prior calculus experience is required. Start building your mathematical modeling skills today.