Limits, differentiation, integration, and their mathematical relationships. General applied modeling remains in Applied Mathematics.
Test your knowledge with these top questions!
How did Isaac Newton mark rates of change in his calculus notation?
Newton's dot notation is still common in physics for quantities that change with time.
Leibniz based the integral sign on a word from which language?
The sign comes from "summa," Latin for sum, because integration adds small pieces into a total.
Which society investigated the calculus dispute while Isaac Newton was its president?
Newton secretly drafted the committee's report, making him both a disputant and an author of the verdict.
Which rival of Isaac Newton published his calculus first?
Newton developed his methods earlier but published later, so discovery and publication pointed to different men.
In calculus, what does the limit of a function describe?
A limit cares about nearby inputs, so a function can approach a value it never actually reaches.
In calculus, what does the derivative of a curve measure at a single point?
Zooming far into a smooth curve makes it look straight, and the derivative gives that line's steepness.
What does a car speedometer display as the derivative of distance traveled?
A speedometer ignores the whole trip and reports how fast distance is changing at that instant.
What pair does the Fundamental Theorem of Calculus link together?
The theorem shows differentiation and integration undo each other, like rewinding a recorded trip.
In calculus, what does the +C in an indefinite integral stand for?
Constants vanish when derived, so reversing the process restores an unknown constant C.
What does shrinking the time interval toward zero give for a moving car in calculus?
Average speed over shorter intervals settles toward the speedometer reading at that instant.