Thomas Calculus 11th Ed: Thorough & Easy to Follow

[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.