I love Newton. He is my idol.
If we didn't have Newton, then we wouldn't have AP Calculus courses, which would be two less A's in my report card.
Also, Newton's calculus contributed to his 3 laws, and are very important in the fields of mathematics, physics, and numerous other disciplines such as gynecology and courses like: "The Science of Batman".
If you would like to worship Newton, like numerous others do, please contact your local Newton obsessor ASAP.
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Newton "invented" "applied mathematics" and calculus.
Series in calculus are important for many reasons. One of them is the ability to differentiate or integrate a series that represents a function much easier than the function itself.
Calculus; by a long shot.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
It is certainly used in calculus, just as calculus can be used in trigonometry.