Let's analyze the historical aspects of the calculation

carlos84 (72)in #philosophy • 6 years ago (edited)

Some of the fundamental ideas of the calculus go back to the ancient Greek mathematicians of the time of Archimedes (287-212 a.C.) as well as to the works of the first years of the XVII century made by René Descartes (1596-1650). Pierre de Fermat (1601-1665), John Wallis (1606-1703) and Isaac Barrow (1630-1677). However, the invention of the calculus is attributed to Sir Isaac Newton (1642-1727) and Gottfried Wilhelm Leibniz (1646-1716) because they initiated the generalization and unification of these mathematical concepts. Likewise, other mathematicians of the seventeenth and eighteenth centuries intervened in the development of calculus, some of them were: Jakob Bernoulli (1654-1705), Johann Bernoulli (1667-1748), Leonhard Euler (1707-1783) and Joseph L. LaGrange (1736-1813). However, it was not until the nineteenth century that the foundations of the notions and calculation processes were established by mathematicians such as Bernhard Bolzano (1781-1848). Augustin L. Cauchy (1789-1857), Karl Weierstrass (1815-1897) and Richard Dedekin (1831-1916).

[Textual quotation]: Calculation book. Author: Louis Leithold. 7th edition. Pág .: xxvi.

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Analysis of the textual quotation:

We can verify chronologically that the first indications of the calculus go back to pre-Jesus Christ times, and when I say the first indications it is why we did not have with certainty how to give a solution to the problem of the tangent line to the curve at a given point, however, it was mathematicians such as Archimedes, Pythagoras, among others who gave answers to the calculation of the areas of some known geometric figures, although the calculation of many of these areas only limited to squares, triangles, circles, rhombuses, among others, the problem began to arise when it was necessary to perform the calculation of areas of curved figures, it is at this point of inflection that a before and after in the history of the infinitesimal calculation began to exist.

It was not then almost seventeen centuries later that we began to see concrete results on topics that at that time were enigmatic, as was the case of the tangent line for curved sections, and the problem of calculating areas for curved figures, these were problems that then they would translate into what we now know in our universities as Derived from a function of real variable e integral of a function of real variable.

All the advances especially in Engineering and that apply the infinitesimal calculus in their applications in science and technology, we owe it to a great extent to the contributions that all the mathematicians and philosophers of antiquity to which I refer in the textual quote of the historical aspects of the calculation.

Chronologically speaking we must separate three historical moments of the calculation:

First efforts to solve the problems of the tangent line at a point to the curve: were the years 287 BC where very good contributions were given especially in geometry, so much so that many of those contributions are used and are relevance in the actuality, with all this it is possible to be demonstrated that these knowledge of the oldest mathematics were bases and fundamental pillar for the discovery that a priori did Leibniz and Newton on the infinitesimal calculus.

Transitory period between the mathematics of antiquity and calculation: With all the existing contributions until then, it was not enough with the contribution of the Euclidean Geometry, it was of paramount importance to develop certain knowledge in algebra and analytical geometry, It was in this transitional journey that many contributions of mathematicians and philosophers took place, such as René Descartes, Pierre de Fermat, John Wallis, Isaac Barrow. All this took place between the years 1600 and 1700, giving a century of hard effort and contribution until we reached the century where the foundations of the infinitesimal calculus will be laid.

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Period where the solid foundations of the calculation were laid: Having well prepared the ground and only needed to cultivate and lay the foundations, it was by means of the physical problems that were had in antiquity with respect to the increase of the position with respect to time (Variation of velocity), if there were two points in the trajectory of a moving object, graphically we could calculate the slope of the line joining the two points and obtain the average velocity of the object. The problem arose when you wanted to calculate the speed in a moment of time, since for a moment of time there was only a single point, then you began to think about the theory of an approximation to that point, starting from another that was approaching him (this is what we know today as the limit of a function of real variable). It was Isaac Newton and Gottfried Leibniz who discovered, initiated and generalized each one with their works and investigations separately everything that we nowadays know as calculus, which includes the theory of limit, derivative and integration of real variable functions. However, you can not attribute all this contribution only to the two of them, since it is true that they laid the foundations for the calculation, but mathematicians such as Bernhard Bolzano and Augustin L. Cauchy among others are those who polished all the material and gave it shape as we know it today, they established the foundations of the notions and processes of calculation as we now study them in our universities.

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Conclusion

The importance of studying, analyzing and evaluating the historical events of the calculation lies in being able to understand all the efforts that humanity has made so that today we have such precious knowledge, and how we are all of us as institutions to provide university-level education to serve of spokespersons so that these aspects are known in sources of intellectual production, in science and education. Many times we have the tools in our hands with which we can survive and have a decent life, but we do not know of all the sacrifices that were made in order to reach this point of balance.

Today we can teach these theories with a complete order of ideas, where they can be applied in science, technology, medicine and engineering without having to think about the problems that afflicted the ancient world and mathematicians of centuries ago, without a doubt Although we do not have these historical figures today to express our most precious gratitude, at least there are media such as this where the corresponding tributes that dignify those works can be rendered.

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