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Calculus is a branch of mathematics that deals with continuous change, the accumulation of quantities and the rate at which these quantities change with respect to time.

It is also known as infinitesimal calculus because it involves infinitesimal quantities ( values close to zero but not absolutely zero)

Two key terms we might come across in calculus are the derivative and integral.

The derivative is a measure of the rate of change of a function, while the integral is a measure of the area bound by a curve

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This controversy between Sir Isaac Newton and Gottfried Wilhelm Leibniz broke out when there was a dispute between the two on which of them was the founder of calculus.

The truth was that both of them independently developed calculus in the late 17th century. However, Newton's work on calculus, which he referred to as "method of fluxions", was created around 1665-1666, but he didn't publish it at that time because he preferred to keep his manuscripts confidential.

Leibniz, on the other hand, began making great strides toward the development of calculus around the 1670s and published his first paper on differential calculus in 1684 and his second on integral calculus in the year 1686. Because Leibniz published his findings on calculus before Newton did, his manuscripts became widely known to many people before those of Sir Isaac Newton.

This brought about suspicions and accusations of plagiarism from both parties, with Sir Isaac Newton's supporters affirming that Leibniz had stolen the ideas of Newton, while Leibniz's followers believed they had no right to say that because Leibniz published his ideas first. This resulted in an all-out feud between the English (who were on Newton's) side and mathematicians from the European continent

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The truth of the matter was that the contributions of both Leibniz and Newton led to the development of Calculus as a whole. But they're individual contributions led to the branches of calculus that we know today: differential and integral calculus.

Leibniz brought about the dx, dy and the ∫ notation we use today, so the invention of differential calculus is accredited to his name.

Newton's ideas on the other hand, mainly involved finding the areas under curves through his method of fluxions. He was also able to discover the fundamental theorem of calculus and how it could be used to solve real-life problems.

So in conclusion, Leibniz's investigations led to the development of differential calculus, while those of Isaac Newton led to Integral Calculus

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Studying Calculus as an IBDP student has a variety of advantages that it gives to the student, even beyond the scope of the IBDP. These include:

1. The enhancement in the critical and analytical thinking skills of students.

2. It gives students the necessary tools to solve complex problems in many fields such as engineering, physics and computer science

3. It serves as the basis for many advanced math programs and concepts, even at the university level. Meaning students become abreast with any calculus concepts they come across at the university level.

4. The study of calculus at IB opens up a great number of high-paying career opportunities in the real world because the analytical skills calculus equips students with are highly valued by many employers

5. Top-notch selective universities such as the Ivy League schools value IB Math AA HL calculus students because it depicts that they can handle tough quantitative work

6. It helps the student to visualise the links calculus has with certain topics in other subjects, such as physics, chemistry, computer science and economics.

7. Mastering complex ideas and principles from calculus gives you the confidence that you are capable of handling complex ideas that are even beyond the field of math.

8. Calculus can be used in the real world to model the rate at which things such as population growth increase with time

9. In a more general sense, Calculus lets students better understand the world from their perspective

10. Lastly, every unspoken bit of the universe deals with a bit of calculus. So studying calculus as a student lets you know about the union calculus has with the world we find ourselves in

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In conclusion, studying calculus as an IBDP student is a great opportunity to have because it opens a wide range of doors for you. So I would personally encourage students out they to give out their all when they get the opportunity to study calculus because it is basically the language of the universe.