Course Overview
Core Concepts of Calculus
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Limits
A limit describes the value a function approaches as the input gets closer to a certain point. It forms the base of both differentiation and integration. -
Derivatives (Rate of Change)
A derivative tells how fast something is changing at any instant.
For example:
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Velocity = rate of change of position
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Acceleration = rate of change of velocity
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Integrals (Accumulation)
An integral gives the total accumulation of a quantity.
For example:
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Total distance from velocity
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Area under a curve
🔹 Fundamental Theorem of Calculus
This important concept connects differentiation and integration, showing they are inverse processes.
ddx∫axf(t)dt=f(x)\frac{d}{dx}\int_a^x f(t)dt = f(x)dxd∫axf(t)dt=f(x)
🔹 Real-Life Applications
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In Physics: calculating motion, force, energy
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In Chemistry: reaction rates and concentration changes
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In Biology: growth models and population dynamics
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In Engineering: designing systems and structures
🔹 Simple Example
If you know the speed of a car at every moment, calculus helps you find:
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How far it traveled (integration)
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How its speed is changing (differentiation)
