Infinitesimal calculus: A blunder in mathematics?

This article reveals the fact that considerable study time invested into acquisition of proficiency in infinitesimal calculus leaves behind only the ability to tackle problems of order four or less. Today's problems reaching into orders of thousands are being handled by clever computer-based algorithms seldom addressed in high school or college. Yet, the calculus teaching will persist as long as physics and some other natural science teachers start their lectures with a differential equation. An alternative method, preparing high school students for serious problem-solving abilities, is presented with examples. References provided, many published by this author, do apply the method to a broad range of natural sciences.