### Foundations

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Calculus is a branch of mathematics that deals with the study of rates of change and slopes of curves, known as differentiation and integration, respectively. It provides a framework for understanding how functions change over time, how they are related to one another, and how they can be modeled and analyzed. Calculus is used in many fields including physics, engineering, economics, and statistics to solve real-world problems. Differentiation involves finding the derivative of a function, which describes the rate of change at any given point, while integration involves finding the area under a curve, which represents the accumulation of a quantity over time. The combination of differentiation and integration is known as a powerful tool in solving problems that require modeling, optimization, and analysis.