Differential Equations
Study of equations involving derivatives and their applications.
Practical Applications
Physics: Motion and Forces
Describing Movement with Math
Motion, like a ball thrown in the air, is described using differential equations involving velocity and acceleration.
Example: Free Fall
\( \frac{dv}{dt} = -g \), where \( g \) is the acceleration due to gravity.
Why Is This Useful?
It helps engineers design safe roller coasters, predict the path of a rocket, or figure out how long it takes for something to hit the ground.
Examples
Calculating how high a basketball will go before falling.
Predicting the landing spot of a launched projectile.