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  1. Introduction
  2. The importance of differential and integral calculus
  3. Calculating differential and integral
  4. Conclusion

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. [...]

[...] CALCULATING DIFFERENTIAL AND INTEGRAL The applications of differential and integral calculus are present in most measurable phenomena. This implies that its use extends from physics to economics and management. The calculation is words of Latin origin: "calculus, and in ancient Rome was a small stone or pebble used for counting and play, and the Latin verb calculare came to mean 'figure', 'computing', 'calculate'" (SIMMONS p.70). Currently, the word indicates a calculation method or system methods to resolve certain types of quantitative problems, such as the calculation of probabilities, logical calculus, the calculus of finite differences vector calculation, calculation of resíduas and so forth. [...]

[...] Rio de Janeiro: LTC p. LEVY, P. The intelligence technologies: the future of thought in the computer age. São Paulo: Editora MACHADO, Nilson J. Mathematics and education: allegories, technologies and related topics. São Paulo: Cortez Epistemology and didactic:. The concepts of knowledge and intelligence and the teaching practice. São Paulo: Cortez SIMMENS, George F. Calculation with analytic geometry. New York: McGraw-Hill STRUIK, Dirk J. História concisa da Matemática. [...]

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