Best books on Calculus

[Matt Agajanian]

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?

[carey]

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.

[KeithB]

Professor E McSquared's Calculus Primer?

[Jeff_Birt]

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

[klesl]

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

[Maximilian Hohmann]

Hello!

Just a curious question: How can I know which are the best ones without having read them all?

Regards
Max

[rprosperi]

(12-20-2022 06:14 PM)Maximilian Hohmann Wrote:  Hello!

Just a curious question: How can I know which are the best ones without having read them all?

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...

[Maximilian Hohmann]

Hello!

(12-20-2022 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 :-(

(12-20-2022 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

[pier4r]

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.

[floppy]

(12-19-2022 11:49 PM)Matt Agajanian Wrote:  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?

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

[KeithB]

(12-20-2022 06:14 PM)Maximilian Hohmann Wrote:  Hello!

Just a curious question: How can I know which are the best ones without having read them all?

Regards
Max

The ironic thing is that to judge the books you have to already know calculus so that you can evaluate how well they present the concepts!

[floppy]

(12-20-2022 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..

[bbergman]

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/Calculator-Calcul...0419129103

[carey]

(12-21-2022 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.

https://www.amazon.com/Calculator-Calcul...0419129103

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.

[Matt Agajanian]

(12-21-2022 08:20 PM)carey Wrote:  

(12-21-2022 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.

https://www.amazon.com/Calculator-Calcul...0419129103

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.

Actually found it on the HP Literature website:

Calculator Calculator is here on this site

[Luigi Vampa]

(12-20-2022 01:30 PM)KeithB Wrote:  Professor E McSquared's Calculus Primer?

I bouhgt that one some years ago. A good one for a primer.

[FLISZT]

Hello,

Here is a list of books on calculus available on Eric Rechlin's website.
(see the attachment)

[Jlouis]

(12-22-2022 12:09 AM)FLISZT Wrote:  Hello,

Here is a list of books on calculus available on Eric Rechlin's website.
(see the attachment)

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

[Jlouis]

(12-20-2022 03:57 PM)klesl Wrote:  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

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

[klesl]

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 3-Dimensional Space
Calculus III - 312 pages chapters 3-Dimensional 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

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