Thomas Calculus 11th Ed: Thorough & Easy to Follow

[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.