Calculus is a generic term referring to any form of mathematics which has axioms and at least one fundamental theory. Some examples of mathematics that can be categorized as calculus are: algebra, geometry, arithmetic, etc.
Due to corruption of the definition over time, in modern usage "calculus" almost exclusively refers to "The Calculus." The Calculus is also known as "Newton's Calculus," or "Leibniz’s Calculus" depending on who you ask. Mathematics majors tend to refer to The Calculus as "Leibniz’s Calculus" and physics majors tend to refer to The Calculus as "Newton's Calculus.”
Any Given Major: "I need help with my calculus homework."
Physics Major: "Are you referring to 'Newton's Calculus?'"
Math Major: "I think you mean 'Leibniz's Calculus'"
Physics Major: “No, I mean ‘Newton’s Calculus,’ because Newton slapped Leibniz around like a step-child at Wal*Mart.”
Math Major: sob sob
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