Elementary calculus
by H. Jerome Keisler · first published 1971
69% recommend31% neutral
Why HN recommends it
Teaches calculus using infinitesimals rather than limits, treating dx as a term from the start. It is more intuitive and clearer than epsilon-delta, suiting learners who struggled with limit-based courses.
Summarised by Claude from recommending comments
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I loathed limit-based calculus in High School and College. Later I read Elementary Calculus: An Infinitesimal Approach http://www.math.wisc.edu/~keisler/calc.html and it all came clear in a fraction of the pages. It's infuriating that most math curricula won't drop those old, bloated, overly…
on “What are the 'real numbers', really?” ↗…through Calculus Made Easy, I found it curious that the text begins with “On Different Degrees of Smallness” and the limit is mentioned qualitatively but not used formally. It reminds me of the preface to Elementary Calculus [1] [2] an excellent text that I discovered years after learning the subject using the limit: > The calculus was originally developed using the intuitive concept of an infinitesimal, or an infinitely…
on “Calculus Made Easy (1914) [pdf]” ↗I don't have a complete answer for you, but I linked to this book a few days ago. It's pretty good. http://www.math.wisc.edu/~keisler/calc.html Elementary Calculus: An Infinitesimal Approach for a mathematically rigorous course in infinitesimal calculus. I think it is much more intuitive than typical limit calculus.
on “Ask HN: Independent Math Study” ↗Another recommendation - Keisler's Elementary Calculus: An Infinitesimal Approach http://www.math.wisc.edu/~keisler/calc.html (pulled from this old slashdot thread) http://books.slashdot.org/story/04/03/04/028253/Five-Free-Ca...
on “Calculus Revisited - a complete self-study calculus course from MIT OCW” ↗…with infinitesimals (also called "nonstandard analysis") implemented on the machine. If you like the approach, a more general and rigorous investigation can be had by reading H. Jerome Keisler's book Elementary Calculus, which is freely available online in the 2nd edition here: http://www.math.wisc.edu/~keisler/calc.html The third edition is now in print. I've been studying calculus with it off-and-on for a while…
on “Exact numeric nth derivatives” ↗Other Calculus book worth mention is "Elementary Calculus: An Infinitesimal Approach", by Jerome Keisler. One thing that makes learning Calculus harder than necessary is the clumsy epsilon and delta formalism, that became sort of a COBOL for Calculus. This is…
on “Calculus for Seven Year Olds [pdf]” ↗For a truly non-standard, very good Calculus book, I recommend Elementary Calculus: An Infinitesimal Approach, by Jerome Keisler. It's available for free at https://people.math.wisc.edu/~keisler/calc.html
on “A non-standard book list for software developers” ↗For the sciences that depend on higher maths, a Calculus book worth mention is "Elementary Calculus: An Infinitesimal Approach", by Jerome Keisler. One thing that makes learning Calculus harder than necessary is the clumsy epsilon and delta formalism, that became sort of the COBOL of Calculus teaching.…
on “Ask HN: Which books do you consider real gems in your field of work/study?” ↗"Elementary Calculus: An Infinitesimal Approach", by Jerome Keisler. Learning calculus is made harder than necessary by the legacy of clumsy epsilon and delta formalism. This formalism is not the intuitive approach Newton…
on “The dirty secret of mathematics: We make it up as we go along (2018)” ↗…Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus. It can be freely downloaded at https://people.math.wisc.edu/~hkeisler/calc.html Relevant…
on “Calculus Made Easy by Silvanus P. Thompson (1910)” ↗> i've stumbled a few years ago on a math book that described the original concept of "infinitesimals" and how a whole different way of doing calculus exists. Was this book "Elementary Calculus: An Infinitesimal Approach", by Keisler? It's an awesome book. It's free to download at https://people.math.wisc.edu/~hkeisler/calc.html
on “On Leibniz Notation” ↗Nice, I didn't know about this book. Did you try the Keisler book too, "Elementary Calculus: An Infinitesimal Approach"? See https://people.math.wisc.edu/~hkeisler/calc.html
on “Multiplicative Infinitesimals” ↗I recommend Elementary Calculus: An Infinitesimal Approach to those interested in calculus. It treats dx as a term from the start, and matches my (and I suspect most people's) intuition of the subject much better than epsilon-delta.…
on “Does mathematics have a place in higher education?” ↗Completely agree with you here, just want to add that if anyone is looking for a rigorous approach to infinitesimal calculus, check out this book: https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infini... And more generally, look in to "non-standard analysis": https://en.wikipedia.org/wiki/Non-standard_analysis
on “An Interactive Guide To The Fourier Transform” ↗Depends what you're looking for. Full Frontal Calculus[0], Intuitive Infinitesimal Calculus[1], and Elementary Calculus[2] are all textbooks on the calculus sequence using an infinitesimal pov. The basic approach is to extend the Real numbers to include infinitesimals (greater than zero but smaller than every positive…
on “Simplifying and Refactoring Introductory Calculus” ↗