A new approach to calculus based on an old idea of Descartes

What is it about?

Traditionally, calculus has been introduced via the deep and difficult notion of limits, even in case of the simplest polynomials. Here we describe a new and different approach based on simple high school algebra that greatly simplifies the discussion of all algebraic functions. Furthermore, this approach naturally leads to consider deeper analytic concepts and techniques involving limits only when they become indispensable, such as when discussing exponential and trigonometric functions.

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Why is it important?

This approach should help to make calculus more accessible to the majority of today's diverse student population. It emphasizes motivation and guides the reader from simple familiar algebra to deep analysis concepts such as completeness and limits. A book that implements this approach has recently been published: "What is Calculus? From Simple Algebra to Deep Analysis", World Scientific Publ. 2015