2 ms·
I find the logically sound version of the infinitesimals approach to be much more difficult to understand than the approach using limits. For example, you have
by stiff 13y ago
I find the logically sound version of the infinitesimals approach to be much more difficult to understand than the approach using limits. For example, you have to introduce hyperreals to make it work (most common approach):
http://en.wikipedia.org/wiki/Hyperreal_number http://en.wikipedia.org/wiki/Hyperreal_number
- abecedarius 13y agoThe book I linked to uses http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis (a quite different approach). I haven't studied nonstandard analysis.
- nopinsight 13y agoHow would you explain the continued popularity of 103-year-old "Calculus Made Easy" then? The method used in the book might not be rigorous enough to solve all calculus problems but it jives well with a large number of people. Most of them could get a better intuitive understanding of Calculus. (We should of course conduct a rigorous study comparing the effects of using different approaches to teach Introductory Calculus.) Then those who need to use the limits approach for other courses could use the intuition to learn it faster. In addition, they would understand Calculus from two different angles and could select the more suitable approach for each problem. http://en.m.wikipedia.org/wiki/Calculus_Made_Easy http://en.m.wikipedia.org/wiki/Calculus_Made_Easy