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There might be some genuine errors, but the fact that you could manipulate differentials algebraically (a la Leibniz or Euler) is a big deal. A big deal that w

• earthicus 8y ago
  You don't need nonstandard analysis to make differentials concrete - Cauchy showed us how to model them with ordinary variables, and this method is taught in standard undergrad textbooks like Stewart. The issue i was bringing up is that the early use of differentials does not correspond to this. The algebraic models of differentials presented in Cauchy or Robinson's nonstandard analysis is not the same thing as the algebraic models used in Euler. The book i suggested uses differentials from beginning to end, but uses the modern, correct form that doesn't lead one to wrong answers when manipulated with standard algebraic rules. There is absolutely no reason to go back in time and inflict this confusion on yourself by intentionally unlearning the hard-won right answer. Although I should point out that Archimedes correctly understood how to compare different orders of infinitesimals in his book 'On Spirals' (via tangents), circa 200 BCE! Wow!!!