Teaching Calculus With Infinitesimals

This short book is about teaching differential and integral calculus, but instead following the traditional approach, with limits being defined with epsilon and delta, the author provides a simpler way by presenting all the definitions using infinitesimals, as is defined in Nonstandard Analysis. With this approach, the concepts are simpler to understand and the theorems easily proved. The public of this book is anyone interested in calculus, thus students of science, engineering, economics, etc. After a short introduction to Nonstandard Analysis, the author explains in a simple way, but with rigorous techniques, the fundamental notions like convergence of sequences, derivatives, integrals and series.

Autorentext

Ricardo Almeida received his Bachelor and Master degrees in Mathematics fromUniversity of Oporto, Portugal, and Ph.D. degree in Mathematics from University of Aveiro, Portugal. He is currently Assistant Professor in the University of Aveiro. His research interests include fractional calculus, calculus of variations and optimal control theory.