Re:Elementary Calculus: An Infinitesimal Approach (2000)
by hilbert42 on Thursday June 03, 2021 @08:40PM
(#27389182)
This is a nice gesture by H. Jerome Keisler, every bit helps to promote a math subject that frightens off so many.
That said, it's a shame the PDFs are in image format instead of text as it makes it more difficult to copy notes etc. from the text into one's workbooks. This would save the student time in taking notes.
Another minor criticism I have is that like many texts on mathematics it lacks both detail on the background to mathematical concepts and their applications. For example, the discussion of Eula's Formula on page 879 is somewhat incomplete. In some ways the Wiki page https://en.wikipedia.org/wiki/Euler%27s_formula does a better job in that it has a diagram of the 'Three-dimensional visualization of Euler's formula' (its application to circular polarization, etc.). Including this diagram and having some discussion about the significance of the relevance of the i, e and ᴨ in this famous relationship would have put the subject into better context.
(I recall the significance was lost on me when I first studied the subject for the same reasons. I think that many mathematicians don't realize that many of us ordinary mortals just don't think the same way they do, so including more visual descriptions and diagrams, typical applications and historical background do actually help one's understanding. However, I acknowledge that including this extra material makes textbooks larger and thus more expensive. Perhaps that's the penalty we have to pay.)
That said, it's a shame the PDFs are in image format instead of text as it makes it more difficult to copy notes etc. from the text into one's workbooks. This would save the student time in taking notes.
Another minor criticism I have is that like many texts on mathematics it lacks both detail on the background to mathematical concepts and their applications. For example, the discussion of Eula's Formula on page 879 is somewhat incomplete. In some ways the Wiki page https://en.wikipedia.org/wiki/Euler%27s_formula does a better job in that it has a diagram of the 'Three-dimensional visualization of Euler's formula' (its application to circular polarization, etc.). Including this diagram and having some discussion about the significance of the relevance of the i, e and ᴨ in this famous relationship would have put the subject into better context.
(I recall the significance was lost on me when I first studied the subject for the same reasons. I think that many mathematicians don't realize that many of us ordinary mortals just don't think the same way they do, so including more visual descriptions and diagrams, typical applications and historical background do actually help one's understanding. However, I acknowledge that including this extra material makes textbooks larger and thus more expensive. Perhaps that's the penalty we have to pay.)