Calculus is the mathematical study of continuous change. While basic math handles static values, Calculus allows us to understand the world in motion. At its heart lies the concept of the "Rate of Change"—the bridge between the known and the evolving.

The Instantaneous Velocity

Imagine you are driving a car. Your speedometer shows your speed at a single, exact moment. That is a **Rate of Change**. In traditional algebra, we find average speed by dividing distance by time. However, Calculus allows us to shrink that time interval to zero, giving us the exact speed at any instant.

Slopes and Tangents

Geometrically, the derivative is simply the slope of a curve. If a curve represents a journey, the derivative tells us exactly how steep that journey is at any point. On JAY Spark, I aim to show that these aren't just numbers on a page—they are the laws that govern how planets orbit and how economies fluctuate.

Real-World Applications

Why does Jayanta Majumder study Calculus? Because it is everywhere:

• Physics: Calculating the acceleration of a rocket leaving the atmosphere.
• Biology: Modeling the rate at which a virus spreads through a population.
• Economics: Determining the marginal cost to maximize profit in business.
• Engineering: Designing safe curves for bridges and high-speed railways.

"Calculus is the language God used to write the universe."