#CALCULUS OF INFINITESIMALS PDF#

I am not experienced enough with more advanced calculus and mathematics in general to see through to whether this formulation will or will not have undesirable side effects later on, and am interested in responses from those who are. Scanning through the book, it appears at a glance that about the same amount of room usually spent on limits is spent on discourse over manipulations using infinite and infinitesimal numbers, so in light of this it doesn't look like this approach will necessarily yield less work to be done. In general does this seem to be a good idea to you? I admittedly find it more intuitive, however it does seem notably less rigorous than the limit formulation, even with the formal hyperreal system. I'm wondering what the general opinion held here is regarding this formulation of calculus. Where dx is an infinitesimal number, and the function st(x) extracts the standard (purely real) part from a hyperreal number x. So, for example, the derivative is defined with In the theory of limits the term infinitesimal is sometimes applied to any sequence whose limit is zero. The book develops calculus using the hyperreal number system, which contains infinitesimal numbers and infinite numbers. In the engineer’s practical treatment of the differential calculus, an infinitesimal is a number so small that its square and all higher powers can be neglected.

#CALCULUS OF INFINITESIMALS PDF#

I recently stumbled across this page which contains a link to a PDF document of the book 'Elementary Calculus: An Approach Using Infinitesimals'.

In a sense, you can think of them as quantities of the form. These are quantities so small that they are smaller than any positive real number. It is based on the concept of infinitesimal quantities, or just infinitesimals, for short.

The traditional approach to developing calculus is of course with limits using the epsilon-delta definition. Today, this intuitive method is called infinitesimal calculus.

Calculus of infinitesimals