Ever since before I entered junior high, giventhat many have said I am blessed because of having skills inMathematics-related kind of stuff, I became totally curious once I had heardnumerous different math terms and topics I had never heard and encounteredbefore in my grade school years from different people like my siblings – since theyare older than I. These terms include trigonometry, circular functions, algebra,matrix, vector, polynomial functions, conjugate, rationalize, integration andmany more.             Inmy junior high years, I admit that some of these terms and topics werechallenging for me, and had that difficulty that made me read all the lecturesthat had discussed again and again until I became satisfied with myunderstanding on that certain topic. That adventure, honestly, was so fun.

With that in mind, I truly hopedthat my journey would have had the same fun as before. That’s when before Ientered senior high school.             Calculus,such a simple word to hear yet a complex and a rational word indeed, they say.

My brothers had told me, even though this one is difficult, but if it is me, Ican just remove the dirt on my shoulders, figuratively. Knowing how hard thattopic is after hearing such reviews and feedbacks from different persons whohave undergone the “excruciating” years in studying calculus, I now botherresearching and finding helpful videos to make me have background knowledge on thesaid subject. One of the leading branches ofmathematics is calculus. It is a mathematical studyof continuous change, in the same sense in algebra’s and geometry’s; the studyof shapes, and the study of generalizations respectively. It has two major fields:one is differentialcalculus – it dealswith the rates of change and slopes of curves. It also studies thebehavior and rate on how different quantities change. And the second one is called integral calculus that deals with the accumulation ofquantities and also the areas between and under curves as well.

Even though thesaid fields are said to be polar to each other since integration is theopposite of differentiation, they are still linked and are related to eachother by the fundamentaltheorem of calculus. Both fields makeuse of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Theformal study of calculus had begun from the 17th century by well-known mathematiciansand scientists in the world, Isaac Newton and Gottfried Leibniz. The historyitself of the calculus didn’t begin with Newton’s and Leibniz’s findings buttheir calculuswas the culmination of centuries of work by other mathematicians andcontributors; it is possible that it has been at useas early as the Greek era since its elements have appeared in ancient Greece, then in Chinaand the Middle East, and still later again in medieval Europe and in India. Einstein’s andLeibniz’s Some of the ideas that had led to integral calculus were presentedand introduced in the ancient times. These ideas seemed to be that they werenot developed systematically and rigorously.

Though some of the formulas lackedmajor concepts and components and were simple to begin with, calculations ofvolume and area were introduced and could be found in the Egyptian Moscowpapyrus. From the periodof Greek mathematics, the method ofexhaustion was used by Eudoxus, which foreshadows the concept of thelimit, to calculate areas and volumes, eventually made Archimedes  develop this ideafurther, inventing heuristics which resemble the methods of integralcalculus. The method ofexhaustion was thendiscovered in China by Liu Hui and Zu Gengzhi independently.



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