Part 1/7:

Understanding Differentials and Linear Approximations in Calculus

In the world of calculus, the concept of differentials plays a pivotal role, particularly in the realm of linear approximation. In this article, we will delve into the fundamentals of differentials, providing a clear understanding of their application in approximating values close to a known point on a curve.

Introduction to Differentials

Differentials are a notation used to express the change in a function with respect to its independent variable. To grasp this concept, let's consider a function ( y = f(x) ). In the context of differentials, we denote ( dx ) as a small change in ( x ), leading us to define ( dy ), the corresponding change in ( y ).