Thomas Calculus 11th Ed: Thorough & Easy to Follow

[HeLiXe]

Just wanted to recommend this book. I am using it to supplement my calculus I w/analytic geometry class, and I find it very thorough and easy to follow. I'm using the 11th ed. ISBN: 9780321185587, but I understand that there is also a 12th ed.

 

[Settia]

Thomas' book is a classic. I never used the new editions. The edition I used was the second. I second your recommendation. =)

 

[HeLiXe]

Thanks Settia :) My professor told me that calculus hasn't changed for hundreds of years, so I think the second edition would be just as good as the twelfth! It's really a great book. I think my calc class covers 1/5 of what is covered in Thomas' book.

 

[Compaq]

I own both the eleventh and twelfth editions, and I think it's a great book so far. I'm using it in my Calculus 1 course at the uni, first year.

 

[thrill3rnit3]

Thomas' book is a classic. I never used the new editions. The edition I used was the second. I second your recommendation. =)

I have both the 2nd edition and the 4th edition (which I first learned calculus from).

Both are classics, but I would recommend the 4th edition, which I think is the best one out of all of them.

 

[n-dimensions]

I'm using the 9th edition of Thomas for a distance learning course. It's a good, sturdy presentation. I'm reading Richard Courant's Calculus and Analysis Vol.I concurrently because I plan on studying higher math down the road and I want to get my feet wet with some more rigor.

That's not to say that Thomas' book is dumbed down. It takes thought and effort. But it's so straightforward that sometimes I feel like it doesn't challenge me to develop the concepts on my own. Anyway, I like using the two books together. In that way I can choose the appropriate level of difficulty depending on how readily my brain is absorbing a given topic.

 

[mathwonk]

There may be a huge difference in different editions of thomas. i prefer the oldest ones over the newest ones, but some intermediate ones were nice too. I also liked the hardback 9th edition by finney and thomas, blue cover with a lighthouse on it. but the currently offered 9th edition paperback on amazon seems to be a different book. there are zillions of editions of thomas on abebooks for as little as one dollar. i would definitely avoid university calculus by hass weir and thomas. but in the end whichever one you can learn from is the right one for you. I second the approach in post 6.

 

[brocks]

There may be a huge difference in different editions of thomas.

Can you elaborate on this? I always hear that new editions are just a scam to get more money out of students; e.g. "they just rearrange the problem numbers, but the text hasn't changed much at all in the last 20 years, except maybe a few nods toward CAS systems."

The "scam" question aside, what would make a newer edition actually worse to learn from than an older edition? I am especially interested in this as it relates to someone who is reading the text outside of a formal classroom environment (like me). Thank you.

 

[Naty1]

I still refer to my third edition of Thomas...it's fine...always has been always will be...

Which edition is "easier to learn from" is likely more in the eyes of the reader than the text itself...

Having said that, it can be helpful to use two texts...to sometimes get a different flavor, a different perspective, on concepts that may puzzle at first...especially when you are learning on your own. Another good trick: explain what you think you have learned in your own words...that will promptly tell you if you really learned it. I tutored some peers during college and I usually learned as much explaining things to them as they did...

 

[mathwonk]

well in the case of thomas, the book has been considered the standard for over 40-50 years. In that amount of time however Thomas has actually died and students have changed in their level of or lack of preparation. Thus recent editions are completely different from older ones. I.e. it is impossible to recognize that the 9th and the 2nd editions are the same book and in fact they are not even by the same person. Because the Thomas name was a guarantee of high sales, the publishers just hired other people to completely rewrite the book, and these totally different books were published with Thomas' name tacked on cynically. E.g. people like the posters in posts 2,5 above are innocently recommending in good faith, books they apparently do not realize have almost no resemblance to the one you are asking about. I heard the same thing on my first job. People who had learned from the original Thomas, always swore it was the best book to adopt, even though they had not read the versions we were adopting. As preparation for my job, I read Thomas' 1st or 2nd edition, then arrived to find we were using a very different edition. Still in those days it did resemble the original in some essential ways. Now I admit I am often much too hard on decent books, especially when I am forced to teach from them, but if you are interested in my scathing review of a recent edition you can read it on amazon.

 

[mathwonk]

well in the case of thomas, the book has been considered the standard for over 40-50 years. In that amount of time however Thomas has actually died and students have changed in their level of, or lack of, preparation. Thus recent editions are completely different from older ones. I.e. it is impossible to recognize that the 9th and the 2nd editions are the same book and in fact they are not even by the same person.

Because the Thomas name was a guarantee of high sales, the publishers just hired other people to completely rewrite the book, and these totally different books were published with Thomas' name tacked on cynically. E.g. well meaning people like the posters in posts 2,5 above are innocently recommending in good faith, books they apparently do not realize have almost no resemblance to the one you are asking about. I heard the same thing on my first job. People who had learned from the original Thomas, always swore it was the best book to adopt, even though they had not read the versions we were adopting. As preparation for my job, I read Thomas' 1st or 2nd edition, then arrived to find we were using a very different edition. Still in those days it did resemble the original in some essential ways.

Now I admit I am often much too hard on decent books, especially when I am frustrated because I am forced to teach from them, but if you are interested in my scathing review of a recent edition you can read it on amazon. The 9th edition, blue cover, lighthouse, however, although totally different from the original Thomas, was very clearly written, and i liked it.

By the 10th edition however, I had completely become disillusioned with it. They are continually dumbed down, to accommodate weaker and weaker students. In the 9th edition a I recall, most proofs of derivative laws were put in the back, but it seemed ok to me to just give a few to get the idea. Then in the 10th as I recall, ALL proofs of these laws were banished to the back of the book. This was the last straw that broke my patience.

So basically the newer versions are giving you less and less information, and challenging you less and less.

 

[mathwonk]

Here is one example I noted of how the new "University calculus" by "Thomas et al", (published after Thomas' death), differs mathematically from the original versions: (reproduced from a comment to my amazon review)

In the original book by Thomas himself, the section on centers of mass is followed by their application to computing work, since the work done by moving a mass is equal to that done by moving only its center of mass. This is an analog of the beautiful and classic theorem of Pappus for calculating volumes using only the motion of the centroid. In the current book, these applications and even the theorem of Pappus itself are omitted, rendering the section on centers of mass completely unmotivated, just another topic to be memorized without any idea of why it is important.

Obviously an average student especially will be able to calculate work more easily knowing that the center of mass of a cone is 1/4 of the way up from the base, as archimedes knew, than trying to do an integral. Indeed Thomas himself says practicing engineers often work just this way. If you want a book for average students from which they may actually learn something, try the books i recommended for them, thomas's own book, stewart 2nd edition, or thomas and finney 9th edition, not this one. Thomas original book by the way is available used for one dollar, and even one cent!

As one positive aspect of this book, I am finding that although the explanations are poor, the exercises are pretty reasonable, being well chosen to be accessible by an average student, and not as tedious to work out, nor downright undoable as they are in some competitors. So if a reader just works as many problems as possible, he may benefit. Of course many make no sense in practice, such as triple integrals which serve only to calculate the volume of a tetrahedron that is more easily done other ways, but they are workable.

 

[mathwonk]

Note also how many different "co authors" these books have had over the past few years: Hass, Weir, Giordano, Finney. And there now seem to be more than one "Thomas": calculus, with the existence of both the "University Calculus" with his name tacked on, written after his death, and the other "Thomas": calculus now up to at least the 12th edition. But the authors Has, Weir, of University calculus, are also among the authors of the other ":Thomas calculus" as well. This is a book that has deteriorated far from its original form.

Nonetheless, you are a student learning calculus, not a professor grown weary of teaching it like me. If the book speaks to you, then use it for all it is worth. Every book has some value. Since I already know the subject, I am picking on flaws I see. Since students do not know the subject, there will be many points they can learn from.

But in general, for math books the first edition is almost always to be preferred. The fact that the subject does not change, means later editions are usually changed for cynical reasons to sell more copies rather than to improve them. A typical change is to include more trivial problems and take out more challenging topics.

 

[n-dimensions]

Interesting Mathwonk. In fact the 9th Edition that I'm working from is the blue hardcover one with the lighthouse. The layout has a sturdy feel to it - kind of a middle road between an older approach and the abominable glossy magazine-layout of comtemporary texts. The presentation seems more than adequate. It feels 'dependable'. It's a very solid text in my opinion. I've browsed through a dozen or so Calculus texts and none struck the balance that this one does.

Incidentally, the Courant and John book I'm supplementing with is pretty phenomenal. He was a gifted expositor. I certainly get bogged down sometimes and have to skip some stuff (which he encourages in the preface), but 80-90% of it is within reach. It feels *good* to have to work a bit harder.

 

[HeLiXe]

Note also how many different "co authors" these books have had over the past few years: Hass, Weir, Giordano, Finney. And there now seem to be more than one "Thomas": calculus, with the existence of both the "University Calculus" with his name tacked on, written after his death, and the other "Thomas": calculus now up to at least the 12th edition. But the authors Has, Weir, of University calculus, are also among the authors of the other ":Thomas calculus" as well. This is a book that has deteriorated far from its original form.

Nonetheless, you are a student learning calculus, not a professor grown weary of teaching it like me. If the book speaks to you, then use it for all it is worth. Every book has some value. Since I already know the subject, I am picking on flaws I see. Since students do not know the subject, there will be many points they can learn from.

But in general, for math books the first edition is almost always to be preferred. The fact that the subject does not change, means later editions are usually changed for cynical reasons to sell more copies rather than to improve them. A typical change is to include more trivial problems and take out more challenging topics.

Thanks Settia :) My professor told me that calculus hasn't changed for hundreds of years, so I think the second edition would be just as good as the twelfth! It's really a great book. I think my calc class covers 1/5 of what is covered in Thomas' book.

^^I hope I didn't cause a row with this! When I wrote this I hadn't considered that the older texts would have been better or that the newer would have been worse, I am far from the level of expertise to draw such a conclusion. At the time, I asked my professor which book I could use to supplement the class and she told me that calc hasn't changed in hundreds of years so they should all be good. I was going off this premise as naive as it sounds and recommended the edition I was using in good faith because I found it really useful and it contained a lot more information than what was being taught in my class. I'm using the 11th edition.

I'm going into calcIII next semester and based on your suggestion as a passionate professor, I'll try my best to get my hands on a copy of the first edition.

 

[brocks]

I greatly appreciate your very informative reply.

 

[n-dimensions]

^^ At the time, I asked my professor which book I could use to supplement the class and she told me that calc hasn't changed in hundreds of years so they should all be good.

Wow, that was a pretty flippant answer by your professor. The definition of a Limit, which founds Calculus, wasn't even around until the mid-19th century. So Calculus has probably been firmly founded for a little over 100 years, but not at all 'hundreds of years'. Mathwonk would be able to set the record straight here.

Next time you see your prof you should tell her that, based on your studies of one of those good old books she OK'd you're not going to worry about limits anymore, infinitesimals get the job done well enough for you and the Bernoulli brothers. Sure, you won't be able to define a derivative. But what's a derivative anyway? You mean a 'fluxion'?

 

[HeLiXe]

Next time you see your prof you should tell her that, based on your studies of one of those good old books she OK'd you're not going to worry about limits anymore, infinitesimals get the job done well enough for you and the Bernoulli brothers. Sure, you won't be able to define a derivative. But what's a derivative anyway? You mean a 'fluxion'?

LOL! What's worse is that I just brainlessly accepted what she said -_- Algebra's been around much longer and all textbooks are definitely not the same. Anyways I did search through a few books to see which one was better for me before getting one, and I found this one very easy to follow.

Thanks for the info on the general age of calculus, I am now interested in the history behind the subject, so I'll definitely be doing more research where that is concerned :)

 

[Sankaku]

I think it is quite possible "a hundred years" was said, while "hundreds of years" was heard.

...not going to worry about limits anymore, infinitesimals get the job done well enough for you ...

Ironically, non-standard analysis (using infinitesimals) is one of the areas of Calculus put on a rigorous foundation in the last 100 years.

http://en.wikipedia.org/wiki/Nonstandard_analysis

 

[HeLiXe]

I think it is quite possible "a hundred years" was said, while "hundreds of years" was heard.

>_>
"hundreds of years" was read, we converse by e-mail :) Still have it and it still says it lol

 

[mathwonk]

I am not an historical expert but have read a few old sources. It is easy to have arguments about when calculus started, since people have different opinions as to what should be called calculus. Some people claim Archimedes started integral calculus , others disagree.

There is one feature of integral calculus that he did seem to know, and that is the cavalieri principle, or volumes by slicing. He did know that two figures all of whose parallel slices have the same area, must also have the same volume. So if you think of integral calculus as the method of computing volumes and areas as a sort of limiting process based on dividing them up into slices, then he knew that, but without a modern definition of limit.

But if you think calculus means the fundamental theorem, whereby not only do the areas of slices determine the volume, but that there is a technique of going from formulas for those slice areas to a formula for that volume by antidifferentiation, then that is the part that occurred in the last few hundred years.

If you think calculus stems from Newton's time, that still makes it hundreds of years old. But if you think calculus only began when Riemann, Weierstrass and the other nineteenth century mathematicians started giving precise definitions, then is less than 200 years old I guess. But be aware that Newton for instance already proved that the area undera curve made sense, i.e. the Riemann integral does exist, for all monotone functions, well before Riemann even defined his integral.

Fermat also had a good grasp on tangent lines and computing derivatives as linear approximations in the 1600's.

So computations of areas, volumes, and tangent lines, preceded by hundreds of years, in some cases over a thousand years, the date when those computations were made precise by giving them clear definitions and rigorous proofs. So by calculus do you mean the techniques themselves and their use in computations, or the development of logical foundations for those computations?

Of course we are likely to mean by calculus whatever we learned in class, but that may be rather different from what a more experienced mathematician means by that term. Most people say that Newton was an inventor or creator of the calculus. I myself give Archimedes a lot of credit. So I would tend to agree that calculus in the broader sense has existed for hundreds of years.

 

[gmax137]

I picked up a used copy of "Calculus and Analytic Geometry" by George Thomas (4th Ed, 1968) - is this the same book you are talking about in this thread? Also, when you say "Courant" what's the title of that one?

Thanks!

 

[HeLiXe]

Yes gmax137 I believe so...I was searching for the first edition yesterday and found that it was titled "Calculus and Analytic Geometry" the latest editions are called "Thomas' Calculus."

Thanks for the info mathwonk :)

 

[mathwonk]

you are welcome, I think I had the third (alternate) edition. It was sort of red and blue, old fashioned looking. thick and square like a brick, not as large pages as todays books.here is an original addison wesley photo, of the old cover.https://www.amazon.com/dp/B000H1IIDI/?tag=pfamazon01-20

 

[n-dimensions]

I picked up a used copy of "Calculus and Analytic Geometry" by George Thomas (4th Ed, 1968) - is this the same book you are talking about in this thread? Also, when you say "Courant" what's the title of that one?

Thanks!

The Courant book is actually by Richard Courant and Fritz John, 'Introduction to Calculus and Analysis I'. While I think it's fantastic, it might or might not be for you depending on your goals. What I find interesting about the book is that, rather than turning Calculus into 'Analysis lite', i.e. stripping Calculus of its physical origins and applications, Courant develops the subject in a very 'mathematical' way, but always after first giving a substantial intuitive presentation. In this way you get some rigor without being made to feel inadequate and dumbfounded by an excessively streamlined and abstract treatment.

I think each of us has to find our way. There are probably brigher students than me who would skip Courant and jump into Apostol or Spivak, but I've looked at those books and I'd rather set goals that I can achieve with reasonable, rather than extreme effort at this point. And Courant is not a cakewalk by any means. If I wasn't using Thomas alongside it, I'd be wasting a lot of time trying to fill in some of Courant's gaps too.

If you can get a copy of his 'What is Mathematics?', you'll get a sense of his teaching style. That book is roughly equivalent in terms of difficulty. It's cheap on Amazon, and though I haven't been all the way through it, what I have studied is beautiful and very, very well presented. He has a knack for finding the sweet spot of difficulty between the trivial and the excruciating.

 

[mathwonk]

wonderful post n dimensions. there was actually a courant calculus written alone, but it is so famous that it costs an obscene amount of money. the second rewrite by fritz john, is very faithful to the original and maybe even better, but is not as famous, so is much cheaper, and a fantastic bargain at under $50. I used it for my honors calc class a few years back.

 

[n-dimensions]

Thanks. That's cool that you taught from the book. I'm currently enrolled in a distance learning class, but it basically amounts to structured self-study. I'm in my early 30's, in the past year I've developed a hunger to know some math (as in, a solid undergraduate pure math level of exposure).

There's a good chance I'll end up taking some upper-level courses at the local university down the road so it's good to know I'm handling honors-level material ok so far. I'd say my abilities have a negative slope on the bell curve but are far from exceptional. I'm relatively stronger at thinking laterally or globally rather than computationally.

 

[mathwonk]

it is so rewarding that you appreciate the advice we suggest. of course we are not always right, but our advice is sincere and reflects years of experience.

in spite of our passionate advice, please decide ultimately in favor of what works for you. sometimes students err by accepting the advice of others over their own judgment.

it makes sense to start with our suggestions, but modify them as you gain experience. good luck and best wishes.

 

[Locrianz]

I am currently finishing reading thoma's calculus 12th edition and i will warn you about one thing. The first half of the book is fine, proofs are presented and its pretty clear presentation style. But the more you read on the worse it gets, the stuff on multivariable calculus just becomes a bunch of formulas and you just plug in numbers, the excercises are not challenging at all and it just becomes unbearably dull. No motivation, no proofs, no justification, just number plugging.
If you are doing first year calculus it is fine but i would not recommend it by any means for multivariable calculus.

 

[asimzb]

Is the Thomas Calculus better than Stewart Calculus?

I see Stewart is more popular at amazon.com. what you guys say from your personal preference?

 

[Locrianz]

They are probably equally bad, get a book that actually explains things as opposed to assuming you can't understand anything. Courant, spivak and apostol seem to be always recomended although i only own spivak.

 

[danR]

Wow, that was a pretty flippant answer by your professor. The definition of a Limit, which founds Calculus, wasn't even around until the mid-19th century. So Calculus has probably been firmly founded for a little over 100 years, but not at all 'hundreds of years'. Mathwonk would be able to set the record straight here.

Next time you see your prof you should tell her that, based on your studies of one of those good old books she OK'd you're not going to worry about limits anymore, infinitesimals get the job done well enough for you and the Bernoulli brothers. Sure, you won't be able to define a derivative. But what's a derivative anyway? You mean a 'fluxion'?

The Dedekind cut put calculus into the pedagogical dark ages.

 

[danR]

I think it is quite possible "a hundred years" was said, while "hundreds of years" was heard.


Ironically, non-standard analysis (using infinitesimals) is one of the areas of Calculus put on a rigorous foundation in the last 100 years.

http://en.wikipedia.org/wiki/Nonstandard_analysis

Non-standard analysis did not put calculus on a rigorous footing, I think you mean the quasi-infinitesimals of the hyperreals, which I understand Gödel proved did not involve a contradiction over the field axioms.

 

[danR]

Just wanted to recommend this book. I am using it to supplement my calculus I w/analytic geometry class, and I find it very thorough and easy to follow. I'm using the 11th ed. ISBN: 9780321185587, but I understand that there is also a 12th ed.

1) Textbooks are an obsolete evil. Thomas' is no less evil than the rest of them.

2) Replace limits with Robinson's hyperreals, and soon students will be doing physics like a bunch of Richard Feynmans.

 

[Locrianz]

1) Textbooks are an obsolete evil. Thomas' is no less evil than the rest of them.

2) Replace limits with Robinson's hyperreals, and soon students will be doing physics like a bunch of Richard Feynmans.

But is that not more difficult? Understanding hyperreals etc, would you not need good grounding in logic to understand that stuff in depth whereas limits are pretty easy once u get the idea.

 

[HeLiXe]

1) Textbooks are an obsolete evil.

Evil is good...obsolete is better Actually I have been quite spoiled by prof Burger's lectures on Thinkwell, but the calculus goes straight to my head and I have difficulty communicating what I am doing with others, this is why I reference the evil and obsolete :) I am actually going to take calculus III in a classroom setting because of this. I also need to focus more on proofs.

 

[bcrowell]

But is that not more difficult? Understanding hyperreals etc, would you not need good grounding in logic to understand that stuff in depth whereas limits are pretty easy once u get the idea.

In my opinion, calculus is easier with infinitesimals than without. Scientists and engineers never stopped using infinitesimals even when they were out of style with mathematicians ca. 1890-1960. ideally it helps to be fluent in thinking with both approaches, limits and infinitesimals. There happens to be a good freshman calc book that uses infinitesimals and is free online: Keisler, Elementary Calculus: An Infinitesimal Approach, http://www.math.wisc.edu/~keisler/calc.html

 

[Locrianz]

In my opinion, calculus is easier with infinitesimals than without. Scientists and engineers never stopped using infinitesimals even when they were out of style with mathematicians ca. 1890-1960. ideally it helps to be fluent in thinking with both approaches, limits and infinitesimals. There happens to be a good freshman calc book that uses infinitesimals and is free online: Keisler, Elementary Calculus: An Infinitesimal Approach, http://www.math.wisc.edu/~keisler/calc.html

Yes I've read parts of it, it was probably better than thomas calculus,but not that great and i can see how infinitesimals might make more intuitive sense to nonmathematicians. As you said its probably good to know both approaches.

 

[Sankaku]

Non-standard analysis did not put calculus on a rigorous footing...

That is not what I said. I said that non-standard analysis was put on a rigorous footing.

 

[james1234]

Thomas Calc is definitely one of the best texts out there but for those starting out I would also highly recommend "Early Transcendentals Single Variable" by howard anton. Its perhaps a little more accessible and all though in some regards may lack the rigor of Thomas it is a brilliant textbook!

 

[HeLiXe]

Thanks James :)

 

[trujafar]

Hello

Could I ask which is better (Thomas' Calculus or Calculus : A Complete Course (Adams)). mathwonk says that there seems to be a lot of difference between the editions of Thomas' Calculus, and I need some guidance. I had created a topic but no one had replied:
https://www.physicsforums.com/showthread.php?t=535203

 

[brocks]

Hello

Could I ask which is better (Thomas' Calculus or Calculus : A Complete Course (Adams)). mathwonk says that there seems to be a lot of difference between the editions of Thomas' Calculus, and I need some guidance. I had created a topic but no one had replied:
https://www.physicsforums.com/showthread.php?t=535203

All of the popular freshman calc texts cover about the same material at about the same level, so IMO it's just a matter of preference for whose writing style you like. Professional mathematicians like mathwonk favor books with more rigor, but IMO there is enough rigor for the average student in any of the popular texts, if you will just work through all the proofs until you can do them on your own, and attempt the high-numbered problems in each section. I think the average student will do better with a text that provides more motivation and diagrams, than one that is more rigorous but more terse. If you need to learn analysis, you can always take an analysis class later.

If you can't look at a library copy or something to see whose style you like best, your next best bet is to read the reviews on Amazon and see what average people, as opposed to gifted professionals, think about them. Note that almost every book, good or bad, will have some glowing reviews from the author's friends, and some terrible reviews from students who flunked the course, so try not to take too small a sample.

 

[flyingpig]

I have three books with me

Mccallum, Stewart, and Thomas

Thomas >> Mccallum & Stewart combine.

It's rich, beautifully colored diagrams, straight to the point, and very detailed.

 

[trujafar]

I had a look at both at the library, and I like the fact that Thomas' Calculus is in color, makes it a lot more interesting to read, even though Calculus: A Complete Course was more straight to the point with clearer explanations.
I've asked, and I'm allowed to borrow Thomas' Calculus 9th edition from the library.
Thanks for the advice.