Calculus, differntial and integral
The Differential and Integral Calculus "is the mathematics of change" (Larson, 1998 p.85). It is one of the most traditional disciplines in educational sciences at the university, and that has best preserved its original structure. It is important, and think why the fact that, even today, with the advent and spread of calculators, computers, modeling, among others, the backbone of the calculation is essentially the same since the time of its emergence as an efficient, to address problems of variation and area in the late seventeenth century.
In this study, we aim to show the origin and development of this discipline as important in the context of contemporary mathematics education. Through a literature review and the deductive method, we show that its origin dates back to Antiquity, its development occurs until the seventeenth century and its formalization in the nineteenth century.
[...] Much of what is now developed and taught in the field of Science and Technology, depends on computer use. This has become an indispensable tool for students, teachers and researchers. Issues that were desperately beyond the capabilities of mathematicians of previous eras recently been solved with the help of high-speed computers. If, as Kepler said, "the invention of logarithms doubled the life of an astronomer, the more the electronic computer expanded the careers of scientists and mathematicians" (Boyer p 456.). [...]
[...] A classic example is the geometry in Ancient Egypt. There geometry was associated with measurement of fields after the floods of the Nile River and construction of pyramids. The deductive period: It begins with the birth of Greek philosophy in the sixth century BC when the break occurs between the practical and the theoretical, between the concrete and the abstract. The strength of an idea happens to be on your way in Logic. A striking example of this period was Euclid of Alexandria, in 300 BC, who wrote his work, the Elements, from definitions, axioms and postulates, without the need for specific situations. [...]
[...] Brasilia: UNB v. BICUDO, Maria AV Research in Mathematics Education: concepts & prospects. Sao Paulo: UNESP BOYER, Carl B. History of mathematics. Sao Paulo: Edgard Blücher COLLETTE, Jean-Paul. History of Mathematical them ed. Mexico: Siglo XXI COURANT, Richard. What is mathematics? Rio de Janeiro: Modern Science EVSE, Howard. Introduction to the history of mathematics. Campinas: UNICAMP LARSON, Roland E. Calculation applications. [...]
[...] Initially the derivation and integration processes were studied separately. Only after the seventeenth century, it was possible to associate them through the call Fundamental Theorem of Calculus. Thus the problems of squares and tangents were unified by this theorem. As Baron (1985) has become an important and powerful tool in the study of more general problems by introducing also in the seventeenth century, a special notation and algorithms (or rules of calculations). Already in 1700, much of the calculation which is studied today in undergraduate courses was already established. [...]
[...] Applications made calculating an indispensable discipline for the scientific training of contemporary man. The knowledge acquired in a course of Differential and Integral Calculus enables us to analyze and solve a variety of problems. Know its history and its development is part of its reconstruction, while scientific knowledge and know its value for mathematics education today. REFERENCES ALMEIDA, Fernando José de. Education and Computers: Computers in school. São Paulo: Cortez BARON, Margaret E. history of mathematics Course: origins and development of calculus. [...]
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