Single Variable Calculus and Approximation Methods

Calculus is the mathematical framework used to describe everything from the trajectory of a satellite to the fluctuations of a heartbeat. This course provides a clear pathway into single-variable calculus, focusing on how these concepts apply to the physical and social sciences. You will develop a strong conceptual grasp of how functions change and how to calculate the accumulation of quantities over time. By the end of this course, you will be able to translate real-world scenarios into mathematical models and use approximation techniques to solve complex problems. What you'll learn: - Understand the foundational definitions of limits, continuity, and change - Master the mechanics of differentiation to find rates of change and optimize systems - Apply integration techniques to calculate areas, volumes, and total accumulation - Utilize Taylor series to approximate functions and simplify complex calculations - Practice modeling real-world phenomena in engineering and the social sciences - Explore modern numerical methods for analyzing discrete data sets The course starts with essential terminology and the basic building blocks of functions before moving into practical applications and series approximations. It is designed for beginners who want a solid mathematical foundation without needing prior calculus knowledge. Begin your journey into the mathematics of change.