Calculus AB covers the fundamental concepts of differential and integral calculus, preparing students for advanced mathematical applications.
Differential equations help us describe systems where things are changing and those changes depend on the current state—like populations or cooling coffee!
It’s an equation involving a function and its derivative, like \( \frac{dy}{dx} = 3x \). Solving it tells us how something changes over time.
Slope fields are visual maps showing the direction a solution curve would travel at any point. Each little dash shows the slope at that spot.
Many real-world processes—like the growth of bacteria or how heat spreads—are modeled by differential equations.
Slope fields help us visualize all possible solutions without solving the equation exactly.
Sketching the slope field for \( \frac{dy}{dx} = x \) to see possible solution curves.
Solving \( \frac{dy}{dx} = 2y \) by separating variables and integrating.
Differential equations describe changing systems; slope fields show solution directions visually.