Didactic and innovative, "Fundamentos para cálculo" [Foundations for calculus] addresses the mathematical transition between secondary and higher education. High school mathematics is often not enough either in terms of content or approach to succeed in math-related disciplines at university. Disciplines such as differential and integral calculus, statistics, physics, applied mathematics in chemistry and biology, among others, require a transitional approach focused on the fundamentals of calculus and analysis.
The fundamental concept of calculus and analysis is the function and their raw material is the number. Therefore, the book addresses primarily the concepts of number and function. They are explored theoretically and with assistance of the internet service called Wolfram|Alpha.
Wolfram|Alpha is the Google of mathematics, statistics and computing; the free math oracle; the quintessence of numerical, graphical and symbolic computation; the universal, free, numerical (exact and approximate), symbolic and graphical calculator; and beyond all that, it has a free-format command, plus the ultimate mathematical system with Mathematica as its underlying software. Wolfram|Alpha is a technological tool of great help in the learning process of mathematical concepts. Whenever possible, it is shown throughout the text how mathematics is operationalized by Wolfram|Alpha. Accordingly, a new stage of socialization of mathematics arises, called computational mathematics, resulting from the interaction between modern mathematical theory and numerical, graphical and symbolic computing systems.
The book contains no intimidating expressions such as “trivial”, “easy”, “obvious”, “immediate”, “clear”, since its proposal is to bring a didactic work, even if theoretically well structured.
Calculus and Analysis