Best books on Calculus

12192022, 11:49 PM
(This post was last modified: 12192022 11:52 PM by Matt Agajanian.)
Post: #1




Best books on Calculus
Hi all. I’m on the lookout for an excellent book which teaches Calculus at all levels.
To me, for starters, the Calculus Made Easy or other variations seem to be an improvement over the 'For Dummies' books. Frankly, the title is a little insulting. But, hey. Maybe the are better than I thought. You know what they say Don't judge a book by its cover? Any suggestions? 

12202022, 09:58 AM
(This post was last modified: 12202022 10:46 AM by carey.)
Post: #2




RE: Best books on Calculus
Matt,
Since you like Calculus Made Easy by Sylvanus Thompson (originally published in 1910), to find similar books, it may be helpful to consider what makes Thompson's book different from other calculus books. All calculus books agree on the rules of differentiation, but not on how to get there! It all boils down to deciding which terms to neglect. Thompson describes the differential dx as a "little bit of x." While a "little bit of x" can't be neglected, its square, cube, etc. can, so Thompson's approach is neglect of higher order (squared, cubed, etc.) terms. A modern book that employs the same approach as Thompson (neglect of higher order terms), but derived differently (from mathematical logic and Category Theory) is A Primer of Infinitesimal Analysis by J. L. Bell, 2nd edition. The alternative (more popular) approach for deciding which terms to neglect is to use limits. Limits allow neglect of dx's directly (i.e., without requiring higher order terms) but their rigorous definition (using deltas & epsilons) can be a turn off. A nice little book (written a decade before Thompson's) uses a brief and intuitive approach to limits and was the first Calculus book written by a woman in America. It is Calculus With Applications (An Introduction to the Mathematical Treatment of Science) by Ellen Hayes. For a full, traditional treatment of calculus that is old school, yet not overly stuffy, there is Differential and Integral Calculus by Harold Maile Bacon. 

12202022, 01:30 PM
Post: #3




RE: Best books on Calculus
Professor E McSquared's Calculus Primer?


12202022, 01:30 PM
Post: #4




RE: Best books on Calculus
The two best books to learn Calculus:
How to ace calculus the streetwise guide How to ace the rest of calculus By Adams, Thompson and Hass 

12202022, 03:57 PM
Post: #5




RE: Best books on Calculus
Paul's Online Notes  free online (and downloadable) notes
https://tutorial.math.lamar.edu/ Adrian Banner  Calculus Lifesaver https://press.princeton.edu/books/paperb...lifesaver 

12202022, 06:14 PM
Post: #6




RE: Best books on Calculus
Hello!
Just a curious question: How can I know which are the best ones without having read them all? Regards Max 

12202022, 08:22 PM
Post: #7




RE: Best books on Calculus
(12202022 06:14 PM)Maximilian Hohmann Wrote: Hello! Max, you're a veteran here; surely you know that "The best XXXXX is..." means "Of all the XXXXX that I've encountered, and still recall well enough to opine on, the one I personally like best is..." Which is pretty much the same as that means anywhere else... Bob Prosperi 

12202022, 08:43 PM
Post: #8




RE: Best books on Calculus
Hello!
(12202022 08:22 PM)rprosperi Wrote: Max, you're a veteran here... Don't tell me, last weekend I took a train in Switzerland and they only charged me the "elderly person" rate. The first time in my life I really felt a veteran :( (12202022 08:22 PM)rprosperi Wrote: ...surely you know that "The best XXXXX is..." means "Of all the XXXXX that I've encountered, and still recall well enough to opine on, the one I personally like best is..." So then for me it would be the books of the "Numerical Recipes" series. I have used them a lot back when I earned my living writing programs for engineering purposes. There are versions for FORTRAN, c, Python and maybe even BASIC, some of which can be found as free (but legal?) downloads on the internet. The algortitms are well explained and documented and can easily be adopted to other programming environments. Regards Max 

12202022, 10:52 PM
(This post was last modified: 12202022 10:53 PM by pier4r.)
Post: #9




RE: Best books on Calculus
Numerical recipes (old versions) are still available here http://numerical.recipes/oldverswitcher.html (one can get the single chapters as pdf going through them).
OT: For the usage of "best". In my internet experience, but could be that I am interpreting things wrong since decades, too many people really use best as in "the solution which is better than any others" (even future ones apparently). It should be really like what rprosperi said, but it is often distorted as really intending the "objective best". In that case, even reading all the books as Maximilian suggested, the best remains subjective. A bit like "I have a theory", that normally means "I have an hypothesis or a conjecture" and for this reason when one says "X is a scientific theory" people say "I don't believe it, I want a proof of it" (there is no belief in a theory, one either accepts or one doesn't; further a theory has enough evidence and thus it is taken as proven until a counterexample is found). All this also because the idea of a theory is distorted by the mixed meaning. Wikis are great, Contribute :) 

12212022, 11:05 AM
Post: #10




RE: Best books on Calculus
(12192022 11:49 PM)Matt Agajanian Wrote: Hi all. I’m on the lookout for an excellent book which teaches Calculus at all levels.That book arrive the next hours home: https://press.princeton.edu/books/hardco...athematics Will see if it deliver what the recommendations said. Dont know if it fullfill your requirements. (Euler or Legendre or.. any originals from author are interesting too). Or look at online data like https://mathworld.wolfram.com/Arithmetic...cMean.html HP71 4TH/ASM & Multimod, HP41CV/X & Nov64d, PILBOX, HPIL 821.62A & 64A & 66A, Deb11 64bPC & PI2 3 4 w/ ILPER, VIDEO80, V41 & EMU71, DM41X, HP75D 

12212022, 02:04 PM
Post: #11




RE: Best books on Calculus  
12212022, 05:12 PM
Post: #12




RE: Best books on Calculus
(12202022 08:43 PM)Maximilian Hohmann Wrote: Don't tell me, last weekend I took a train in Switzerland and they only charged me the "elderly person" rate. The first time in my life I really felt a veteran :( Like a korean person, teint your hair in black. you will look like 21 forever.. HP71 4TH/ASM & Multimod, HP41CV/X & Nov64d, PILBOX, HPIL 821.62A & 64A & 66A, Deb11 64bPC & PI2 3 4 w/ ILPER, VIDEO80, V41 & EMU71, DM41X, HP75D 

12212022, 06:31 PM
Post: #13




RE: Best books on Calculus
I got this book in high school, and thought it was really awesome. I honestly don't remember much from it now some 40+ years later, but it's one of the few books that involved programmable HP calculators in solving calculus problems.
https://www.amazon.com/CalculatorCalcul...0419129103 

12212022, 08:20 PM
Post: #14




RE: Best books on Calculus
(12212022 06:31 PM)bbergman Wrote: I got this book in high school, and thought it was really awesome. I honestly don't remember much from it now some 40+ years later, but it's one of the few books that involved programmable HP calculators in solving calculus problems. Here's an Internet Archive library link to the Calculator Calculus book by George McCarty cited above. A calculus supplement using the HP28S is also in the Internet Archive library. 

12212022, 10:43 PM
Post: #15




RE: Best books on Calculus
(12212022 08:20 PM)carey Wrote:(12212022 06:31 PM)bbergman Wrote: I got this book in high school, and thought it was really awesome. I honestly don't remember much from it now some 40+ years later, but it's one of the few books that involved programmable HP calculators in solving calculus problems. Actually found it on the HP Literature website: Calculator Calculator is here on this site 

12212022, 10:58 PM
Post: #16




RE: Best books on Calculus
(12202022 01:30 PM)KeithB Wrote: Professor E McSquared's Calculus Primer? I bouhgt that one some years ago. A good one for a primer. Saludos Saluti Cordialement Cumprimentos MfG BR + + + + + Luigi Vampa + Free42 '<3' I + + 

12222022, 12:09 AM
(This post was last modified: 12222022 12:10 AM by FLISZT.)
Post: #17




RE: Best books on Calculus
Hello,
Here is a list of books on calculus available on Eric Rechlin's website. (see the attachment) Bruno Sanyo CZ0124 ⋅ TI57 ⋅ HP15C ⋅ Canon X07 + XP140 Monitor Card ⋅ HP41CX ⋅ HP28S ⋅ HP50G ⋅ HP50G 

12232022, 04:27 PM
(This post was last modified: 12232022 05:57 PM by Jlouis.)
Post: #18




RE: Best books on Calculus
(12222022 12:09 AM)FLISZT Wrote: Hello, Thanks FLISZT, I wasn't aware the existence of calculus books in hpcalc. So many good things over there. We can't thanks Eric enough for hpcalc.org Edit: So many great books for the 28 and 48 that I wasn't aware! Happy Christmas to you all Cheers JL 

12232022, 04:52 PM
(This post was last modified: 12232022 06:06 PM by Jlouis.)
Post: #19




RE: Best books on Calculus
(12202022 03:57 PM)klesl Wrote: Paul's Online Notes  free online (and downloadable) notes Thanks for the link. There is even a complete solutions book for calculus I! I noticed when I tried to download the calculus II and III that it download the same calculus I. Does anyone know if there's only calculus I available or it's an error in the link? Anyway, as my son is just entering university and will have calculus lessons, and I have a book that I used in EE from some 40 years ago that is very yellowish and dusted, from Mounen Foulis (great book), so I'm trying some calculus books for him. So this thread is very handy. Edit: I gave my son my HP Prime G1 for his studies...and you know, now I have to buy a G2...you can't blame me, right? Cheers 

12232022, 11:09 PM
(This post was last modified: 12232022 11:15 PM by klesl.)
Post: #20




RE: Best books on Calculus
I didn't notice the 3 books were merged into 1 book.
The new Calculus book with 1375 pages (dated December 2022) includes Calculus I, Calculus II and Calculus III. It seems the Problems were also merged into 1 book. Having mentioned 3 books (dated March, July and August 2022) on my disc, the number of pages are: Calculus I  575 pages, chapters Review till Extras Calculus II  407 pages, chapters Integration Techniques till 3Dimensional Space Calculus III  312 pages chapters 3Dimensional Space till Surface Integrals totally 1294 pages, so the newer book has more pages The link for all 33 books leads to my Google Drive (the materials are free so I hope there are no problem with posting this books) Alg_Complete.pdf Alg_Complete_Assignment.pdf Alg_Complete_Problems.pdf Alg_Complete_Solutions.pdf Algebra_Cheat_Sheet.pdf Algebra_Cheat_Sheet_Reduced.pdf CalcI_Complete.pdf CalcI_Complete_Assignment.pdf CalcI_Complete_Problems.pdf CalcI_Complete_Solutions.pdf CalcII_Complete.pdf CalcII_Complete_Assignment.pdf CalcII_Complete_Problems.pdf CalcII_Complete_Solutions.pdf CalcIII_Complete.pdf CalcIII_Complete_Assignment.pdf CalcIII_Complete_Problems.pdf CalcIII_Complete_Solutions.pdf Calculus_Cheat_Sheet_All.pdf Calculus_Cheat_Sheet_All_Reduced.pdf Calculus_Cheat_Sheet_Derivatives.pdf Calculus_Cheat_Sheet_Derivatives_Reduced.pdf Calculus_Cheat_Sheet_Integrals.pdf Calculus_Cheat_Sheet_Integrals_Reduced.pdf Calculus_Cheat_Sheet_Limits.pdf Calculus_Cheat_Sheet_Limits_Reduced.pdf Common_Derivatives_Integrals.pdf Common_Derivatives_Integrals_Reduced.pdf ComplexNumbers.pdf DE_Complete.pdf Laplace_Table.pdf Trig_Cheat_Sheet.pdf Trig_Cheat_Sheet_Reduced.pdf Download 

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