# Calculus Best Calculus book for self-study - Choosing between 3

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1. Jun 9, 2015

### christian0710

So I'm trying to choose between 3 calculus books for self-study and would love some suggestions or comments on the books i posted: I really like when a book is clear and has relavant expamples (also for exercises) without skipping too many steps, however I do also like history or understanding of where things came from but i might want to get a second book for that.

Calculus and Analytic Geometry (9th Edition) - Georg B Thommas
Calculus with analytical Geometry - George Simmons 1995
Calculus early transcendentals - Anton howard.

2. Jun 9, 2015

### MidgetDwarf

An older edition of simmons can be found for 5 dollars. That Thomas book sucks. Anton tends to be too wordy and some explanations unclear.

The superior book, would be, Thomas Calculus with analytic geometry 3rd ed. The Thomas book out now is not the same as the older edition. It is a different book.

Simmon's and Thomas Calculus with analytic geometry 3rd ed complement each other nicely.

3. Jun 9, 2015

### verty

There should be a rule, no comparing of textbooks. It's unfair to the authors because the difference between two books may be miniscule and there is no reason why everyone should buy one or the other. You should choose on price and ask, is this book good enough? That's how the market is supposed to work after all. The invisible hand effect only works when people choose cheap and sufficient because that causes the trickle down.

Sorry for the rant but I don't think it is fair to compare them. I can speak for the first two, they are certainly both good enough for you to learn calculus just fine. I don't know the third one.

PS. That Thomas book does not suck. Note he didn't say it was the alternate edition.

4. Jun 9, 2015

### micromass

Staff Emeritus
I'm going to suggest a fourth book: Keisler's calculus. https://www.math.wisc.edu/~keisler/calc.html (free)
This book takes the historical approach with infinitesimals, and I find it to be perfect for self-study. Everything found in a usual textbook can be found here, but this book delivers some extra bits. If you're planning to do physics or any kind of geometry, then this book is almost mandatory.

5. Jun 9, 2015

### MidgetDwarf

It does suck compared to the older editions of Thomas Calculus with Analytical Geometry. Thomas was the standard calculus book in use, however, Thomas died and in order for the publisher to keep sales (iit was a big seller), authors were added and new editions published. If you compare a 6 ed or was it 7th ed and up to an earlier version of Thoma(3rd), it is a completely different textbook.

Yes, the 9th edition of Thomas was the last decent version of Thomas (mmuch better than Stewart by miles), however it is inferior to the 3rd ed.

And there should be no rule against comparing textbooks. I consider physics forum as a place of enlightenment. it has led to find information I would have otherwise not found, and differnt ways of thinking about material. Authors should be held accountable for the books they publish. It is great to compare books. Who wants to spend 80 dollars and up on a stinker of a textbook, when a hidden 5 dollar gem explains the material better?

I am aware that one textbook may work for you but not me, and vise versa. So consumer discretion is advised. The reason I recommended both Thomas 3rd ed and Simmons purchased together are:

Simmons gives an informal, yet intuitive understanding of calculus. It has a great explanation on the rules of differentian, proofs of these rules are easy to follow, explains factorial briefly in a paragraph (mmost students I knew struggled with equations with factorials), and minama/maxx problems, related rates, and differential s.

However, one big flaw of Simmons is no epsilon/ddelta explanation of a limit, curve sketching is rather weak, relationship between logs and inverse can be explained better.

Thomas on the other hand. Explains these sections better. Geometric explanations are really clear, and easy to follow. Most derivations are easy to follow. Explains logs extremely well. Integration techniques are explained excellently.

Thomas can be hard to read for the Section on parametric equations (ffor a first time exposure).

List goes on and on. Both books strengthen each others pros and flaws.

The appendix in Simmons is a gem.

6. Jun 9, 2015

### verty

Point 1, being inferior is not the same as sucking. You said it sucked. Point 2, inferior is relative to need or purpose. It fulfills the purpose perfectly well if the purpose is to learn calculus. The 9th edition is all about applications. That doesn't make it inferior. In fact, it can mean higher marks for students who use that book, and still a perfectly functional understanding. I haven't seen the 3rd edition but I'll bet you it doesn't rate the related rate concept very highly. How do I know that, because you just said it's a different book. If it's a different book, they shouldn't really be compared, now should they?

Both those first two books are very cheap, eg $15 on ebay. We aren't talking about$80 books.

There you go, you just made my point. The consumer should exercise discretion by having a choice and choosing. That's all I'm saying, okay? If all those books are sufficiently good to meet his needs, I think we should refrain from picking out the one we would choose. If you don't believe they do, and it seems you think that book sucks, then of course you may then say that. But it doesn't and you should realise that (or at least consider that an applied book can be good).

Last edited: Jun 9, 2015
7. Jun 9, 2015

### MidgetDwarf

Not entirely, here you playing politician and twisting my words, I believe, this is based on the fact that I disagreed with your post in regarding Thomas. Rather immature behavior. I never made the argument that applied books are not good. Why spend months reading a book that is trash/ watered down, when one can use thone months learning from a book that is supperior.

I also mention that the 9th ed is better than the Stewarts and the Larsons.

If you have not seen the third edition why comment? That's like saying George Orwell 1984, is way better than Jack London's The Iron Heel. When said person did not even read Londons book. It is inferior and does suck compared to the 3rd edition. The txt lacks clarity and insight that 3rd edition is known to have. Tolstoy wrote about this effect in his work," Shakespeare and the Drama." How people will say something is great because everyone agrees so, or howpeople comment on matters that they have no experience with. You can learn something by reading this literary work.

However, you made a statement of how theRe should be a rule on this website, that should not allow people to compare books with other books. So if a person asked about a txtbook costing 200 hundred, members would be only allowed to say good/bad. A member who offered a better txtbook would be in violation of such rule.

Maybe I was not clear. Here is an example. For linear algebra, ussually a second reading, people recommend Friedberge, Axler, Shilov, or the other book I forget. All are good books, however readers will find one easier to use than the other. However in the case of the Thomas versions, 9th should not even be used in the same sentence as the 3rd.

8. Jun 10, 2015

### christian0710

Thank you so much for your detailed explanation! I've also looked at tHomas 4th edition and it looks very good and i can get it cheep , would you still say 3rd edition is better?

9. Jun 10, 2015

### christian0710

Thank you very much, So i guess I'm going to get that to, It looks really good :D

10. Jun 10, 2015

### MidgetDwarf

I would say the third. The 4th introduced a different formating. Diagrams, text, and even sections are thrown into a single page, this in turn, makes the book hard to follow. Not sure, if this is a deal breaker, but it is for me. I dislike when too much is going on in one page. The third edition can be found for 8 dollars shipped for part 1, and 18 shipped with part 1 n 2. This is a book that you will keep on your book shelf as a reference, the higher cost imo is justifiable.

11. Jun 10, 2015

### MidgetDwarf

That book is also good. However, it can get tricky ie limits vs infinitesimal. Solid book.

12. Jun 10, 2015

### micromass

Staff Emeritus
Yes, it is tricky because it teaches two very different approaches to calculus (yes, it teaches the traditional approach too). But I think it is a good thing to get acquainted with both approaches. The traditional approach is widely used, but isn't really good for intuition. The infinitesimal approach is still used in physics and geometry. So seeing both ways is beneficial.

13. Jun 10, 2015

### christian0710

Than you so much! I'll get te third: Is this the correct 3rd version of the book?
http://www.amazon.co.uk/Calculus-An...99&sr=8-1&keywords=george+thomas+calculus+3rd

14. Jun 10, 2015

### christian0710

I'm also interested in a good calculus book thats all about problem solving:
a "this i how you do X,YZ" problem solving book with bunch of organized examples.
This is not to i can set my brain on autopilot mode, but more so i have it as a reference when reading physics
and I'm faced with different ways do integrate or differentiate functions. I know there are many
different techniques that can be Applied for differentials and integration and i know I will forget this, so having a good reference book with examples would be great.

I've considered Anton Howard for that matter, but don't know if there is a better alternative.

15. Jun 10, 2015

### verty

I wasn't comparing them, I was arguing for the 9th edition (not the alternate edition) on its own merits. By the way, the Amazon reviews are superlative.

Tolstoy did not write clearly. For example, in War and Peace Anna Scherer sends out invitations for her dinner party:

So the footman had red clothes. It seems utterly irrelevant when one reads that. Why does it matter that he was dressed in red? But this was in St Petersburg which is very far north and snow-covered most of the time. This red-clothed footman delivering invitations would have stood out, people would have noticed. This was meant to be decadent, meant to show off. If you were someone who received one of these invitations, you were important. Tolstoy doesn't convey this meaning, he says they were dressed in red. One reads past it and doesn't think twice.

And look at this passage:

The meaning, Genoa and Lucca have fallen to Napoleon and he is about to march across Europe. Anna Scherer thinks Russia should prepare to meet the threat. She is a woman and is arguing politics, why? Because the threat is imminent. Did you get that from the passage? No, she seems like a screaming banshee. He didn't convey the meaning.

16. Jun 10, 2015

### MidgetDwarf

Yeah you recommended that book a while ago. I wish I could a physical copy. It actually makes more sense using infinitesimals.

17. Jun 10, 2015

### MidgetDwarf

I dislike Anton ' s text. He sometimes omits crucial steps (his linear algebra book is the greatest offender). He is too verbose, and often he words passages unclearly. Simmon's has very good sections on "word problems". Tells you that alot of these problems in a certain section are solved by similarity. I wish Stewart would have told me that, when I was first learning optimization/related rstes.

And yes your link is correct. I am kind of envious of you, you can staedtler tradition really cheaply and noris. I wished the states sold these in stores.

18. Jun 10, 2015

### christian0710

Yea sometimes it's amazing at what prize you can get old gems like this :D
I know i keep asking you about books and i get the impression that just like me, you like to read a more than one good books on the same subject?
I've looked at even another book, and if you know it, let me know what you think. I might also get this, if not I'll let you know about it whe I'm done going through all these old treasures :D
https://www.amazon.com/Mathematics-...p/0486409163/ref=cm_cr_pr_product_top?ie=UTF8

Last edited by a moderator: May 7, 2017
19. Jun 10, 2015

### SuperDaniel

Hello Christian,

Despite I am not a mathematician, I want to suggest you your first choice, Calculus and Analytic Geometry by George B. Thomas, but despite you mentioned, the 9th edition, I prefer the editions when Professor Thomas was still alive. We don't have to forget that Calculus has 400 years old, so, an edition from the 50s works perfect. In addition to this, you can find it a very cheap copy on Amazon. For instance:

https://www.amazon.com/gp/product/B004HLVL88/ref=olp_product_details?ie=UTF8&me=

Good luck,

D.

Last edited by a moderator: May 7, 2017
20. Jun 16, 2015

### bacte2013

Hello christian0710,

I understand you want to choose one from those three textbooks you mentioned, but I strongly recommend Serge Lang's A First Course in Calculus. That book has a very clear writing, and it provides both insights and technical details of single-variable calculus. Plus, Lang's book is not much chatty, and it gets to the essential points in a quick manner. The price of a book should not be a big problem since it is relatively cheap. Only problems with Lang's books are that it contains relatively fewer problem sets than other books and that it has some unconventional terms (particularly the curve sketching) but they should not a major problem. If you would like to stick with books you mentioned, Simmons would be my recommendation.