Single Variable Calculus: Differentiation and Applications

Differentiation is the mathematical language of change, used to describe everything from the trajectory of a satellite to the fluctuations of a market. Understanding how variables interact and evolve is an essential skill for anyone entering technical, scientific, or analytical fields. This course provides a clear path to mastering the mechanics of derivatives and their real-world utility. You will transition from basic algebraic concepts to a deep understanding of how to calculate and interpret rates of change across various functions. By the end of the course, you will be able to apply these mathematical tools to approximate complex systems and solve optimization problems. What you'll learn: - Understand the conceptual foundations of the derivative as a rate of change - Apply differentiation rules to calculate derivatives of power, trigonometric, and exponential functions - Practice using Taylor series for function approximation and local linearization - Analyze optimization problems to find maximum and minimum values in practical scenarios - Learn the basics of numerical differentiation used in modern computational modeling - Explore applications of differentiation in physics, engineering, and economics The course begins with foundational definitions and the concept of limits before moving into formal differentiation techniques and the power of Taylor series. You will progress through written explanations and exercises designed to reinforce your conceptual and practical understanding. This course is designed for beginners and students in the sciences or engineering who have a basic background in algebra. No prior calculus experience is required. Start building your mathematical foundation with this comprehensive text-based guide to differentiation.