Calculus

advanced math · change and motion · problem-solving

Two main branches. Differential calculus figures out how fast something is changing at any exact moment, like the speed of a car. Integral calculus does the opposite: it adds up tiny pieces to find total amounts, like the total distance traveled.

Two sides, one truth. The fundamental theorem of calculus connects these two branches together, showing that speeding up and totaling are actually mirror images of each other.

Infinity made useful. Calculus uses infinite sequences and series, which are endless lists of numbers that get closer and closer to a target value, to solve real problems with precision.

Slopes of curves. Instead of just measuring straight lines, calculus lets mathematicians study curved lines and understand exactly how steep they are at any point.