Analysis is a broader term for Calculus and the theorems behind it. It is studied both with real and complex numbers as real and complex analysis. Usually calculus just deals with the basic problems of differential calculus and integral calculus.
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The term calculus is a branch of mathematics. A synonym might be differentiation.The term calculus in medicine means a stone (kidney stone, gallstone).
There wasn't one single person involved in the creation of calculus. Many people had their contributions. Oftentimes, however, Sir Isaac Newton is given credit for "inventing" calculus. he also coined the term.
The ureters are the tubes in the human anatomy that conduct urine from the kidneys to the bladder. A calculus is a stone. Hence, a calculus of the ureter is a kidney stone that has formed in a ureter. Please see the link.
The term calculus comes directly from Latin. In Latin a calculus (noun) is a small stone used for counting, much like the beads on an abacus. One of the fundamental uses for modern calculus is integration, which is of course addition of infinitely small sections.
There are several meanings to the word 'calculus.' The plural for calculus is 'calculi.' There is no plural for the calculus we use in mathematics.