Calculus is a branch of mathematics that studies continuous change. It helps us understand how things change over time and space, like the motion of objects or the growth of populations.
Calculus has two main branches. Differential calculus studies rates of change, like how fast something is moving at any given moment. Integral calculus studies accumulation, like finding the total distance traveled or the area under a curve.
Limits are the foundation of calculus. A limit describes what happens to a function as the input approaches a certain value. This concept allows us to understand behavior at points where functions might not be defined.
Calculus has countless applications across many fields. In physics, it describes motion, velocity, and acceleration. Engineers use it for optimization and design problems. In economics, it helps find marginal costs and maximize profits.
To summarize what we have learned: Calculus is the mathematical study of continuous change. It has two main branches - differential and integral calculus. Limits provide the foundation for all calculus concepts. Its applications are vast, spanning physics, engineering, economics, and many other fields where we need to model and understand how things change.