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-Mathematical historian Morris Kline considers Calculus, after geometry, to be the greatest creation in all of mathematics.
-Its invention is generally attributed mainly to two 17th-century mathematicians, the English Isaac Newton (1642-1727) and the German Gottfried Wilhelm Leibniz (1646-1716).
-However, this is an absurd and excessive simplification of the facts.
-Actually Calculation, as we know it today, is the product of a long evolution in which these two characters certainly played a decisive role.
-In very general terms, Calculation came to solve and unify the problems of calculating areas and volumes, the trail of tangents to curves.
-Pretty much, we can say that Calculus began since ancient times with the Greeks tackled different mathematical problems. In particular, they were interested in solving two classic problems: one was area calculation and the other was tangent plot.
-Various were the Hellenic characters who made great contributions to it, among them, the most famous being Archimedes (287 a. C. - 212 a. C) of Ciracuse, whose work is not only considered as the culmination of the contributions of the Greeks, but also remains the subject of admiration and study today.
-It was until the first half of the 17th century, when renewed interest in these problems and several mathematicians from different parts of Europe such as Bonaventura Cavalieri (1598-1647), John Wallis (1616-1703), Pierre de Fermat (1601-1665), Gilles de Robe Rval (1602-1675) and Isaac Barrow (1630-1677), achieved advances that paved the way for the play by Leibniz and Newton.
-In the 18th century, called The Century of Mathematical Analysis, the consolidation of Calculus and its applications to natural sciences, particularly Mechanics was given.
-By the end of the 18th century, some mathematicians had detected various limitations and incongruencies on the bases on which differential and integral calculus had been developed until then.
-The works of Jean D’Alembert (1717-1783) on the vibrating rope and by Joseph Fourier (1768-1830) on Analytical Theory of Heat, 1807, referred to the need to consider wider classes of functions, such as rep functions stentables as power series the Lagrange way.
-At that time, the need to clarify the properties of continuity and integration of functions, as well as the convergence conditions for function series emerges.
-It was until the nineteenth century, with the construction of the system of real numbers, the general concept of real function and the concept of limit to a function; when the fundamental foundations upon which actu rests were established mind the Calculation.
-Some of the noteworthy personnel who made great contributions to that regard were Augustin Louis Cauchy (1789-1857), Bernhard F. Riemann (1826-1866), Karl Weierstrass (1815-1897), Richard Dedekind (1831-1916), among others.
-Based on the previous historical review, we can conclude that:
-Most concepts of Computation have required a long evolutionary process spanning several centuries. This is why we cannot expect students nowadays to be able to grasp the concepts covered in Calculus courses immediately within a short period of time, as they are usually said courses. But yes we can gradually develop in students the maturity necessary to achieve that goal.
-It is true that the big names in the creation of calculus are, of course, Isaac Newton and Leibniz. However, Descartes, Fermat, Cavalieri, Pascal, Roverbal, Barrow and at least a dozen more well-known mathematicians made significant contributions before them. However, neither Newton nor Leibniz could formulate the basics of Calculus correctly.
-It is a significant fact that the logical fundamentals of the numerical system, algebra, and analysis were not developed until the late 19th century. In other words, over the centuries when the most important branches of mathematics were built, like Calculus, there was no logical development for most of them. Great men's intuition seems to prevail over their logic.
-What can we deduc from the history of Calculation?. Morris Kline responds:
-"It seems clear that the concepts that had the greatest intuitive meaning were first accepted and used: all the numbers, fractions, and geometric concepts." The less intuitive numbers, irrational numbers, negative numbers, complex numbers, the use of letters as general coefficients, and the concepts of computation took many centuries to create or to accept.
-Furthermore, when they were accepted it was not logic that induced mathematicians to it, but arguments by analogy, the physical meaning of some concepts, and the obtaining of correct scientific results. In other words, it was intuitive evidence that induced mathematicians to accept them.
-Logic has always come long after invention, and evidently it has been harder to come by. Thus, the history of mathematics suggests, though not to prove it, that logical approach is more difficult. "
-Therefore, within an environment where intuition is promoted, students could develop skills to deeply understand concepts of Calculus.
-Therefore, it is important that we as teachers, have at least a basic knowledge of the history of mathematics, of the subject or subjects we teach, to achieve that students are not only aware of history facts icos but also to develop intuition and finally achieve one better understanding of the concepts.