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Good calculus book

J

JJChicken

Diamond Member
Can you smart ATOTers recommend a good college-level calculus book that covers Bsc/Msc level of differentiation/integration? I'd prefer a book that provides rigorous proofs from first principles as opposed to a quick summary of important results?

e-beers for all 🙂
 
American stores seem to have different editions with different covers, but I'm pretty sure this is the same as the book I used, which is excellent and has a ton of worked examples at all levels.
http://www.amazon.com/Calculus-Early...4&sr=1-2-spell

Will take you through single and multi variate calculus.

Edit- yes I've confirmed that's the new edition of the book I have. They changed the title slightly.
 
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I have a book similar to the one above. I'll let you know in like 3 terms how good it is... (After I've taken Calc I, II, and III with it)
 
Calculus Early Trancendentals by Stewart. 6th edition. Took Calc 1,2 & 3 with it & its very good.
 
Barack Obama said:
Can you smart ATOTers recommend a good college-level calculus book that covers Bsc/Msc level of differentiation/integration? I'd prefer a book that provides rigorous proofs from first principles as opposed to a quick summary of important results?

e-beers for all 🙂
Click to expand...

I don't know if these will be specific enough for you but here's lots of calc videos from a solid instructor that might be beneficial.
 
In my classes we used single variable Calculus by Stewart(for calc I and II) and Calculus by Stewart (for calc III).

Diffeq I used A First Course in Differential Equations with Modeling Applications (Eighth
Edition), by Dennis Zill


They were okay, but I'm sure there has to be much better.


Looking at the others books needed at the university I go to.
Advanced Calc here uses Introduction to Analysis (Fifth Edition) by Edward Gaughan
and Diffeq II uses Fundamentals of Differential Equations and Boundary Value Problems
(Fourth Edition), by Nagle, Saff, and Snider
I However don't know the quality of those books.
 
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If you are serious about learning real proofs don't listen to anyone who recommends Stewart. No offense to them, but they simply don't have a clue what they are talking about.

Royden is a decent standard. Rudin is also used a lot of places and there are others, but if you haven't read a real math book before (and no offense to the many people hawking mainstream math books, but books like Stewart are not real math books) it might be a tough read. Of the "standard" books for rigorous courses, Royden is generally thought of as the easiest read. MIT has some stuff up on open courseware too. It's the calculus with theory, not the ordinary calc. 😉 Here are some lecture notes derived from the ones I used at my alma mater for good measure.

Going it alone with a real math book for the first time is a little - er - bold. It is a foreign language. Much more so than the mainstream textbooks designed for the bulk of the student body. Then again, you might not actually be looking for a real proof book after all - despite how you worded your request. If you are really just looking for a reintroduction to calc, Stewart might do you just fine. 99% of people will certainly find it much more readable! 😀
 
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nonlnear said:
If you are serious about learning real proofs don't listen to anyone who recommends Stewart. No offense to them, but they simply don't have a clue what they are talking about.

Royden is a decent standard. Rudin is also used a lot of places and there are others, but if you haven't read a real math book before (and no offense to the many people hawking mainstream math books, but books like Stewart are not real math books) it might be a tough read. Of the "standard" books for rigorous courses, Royden is generally thought of as the easiest read. MIT has some stuff up on open courseware too. It's the calculus with theory, not the ordinary calc. 😉 Here are some lecture notes derived from the ones I used at my alma mater for good measure.

Going it alone with a real math book for the first time is a little - er - bold. It is a foreign language. Much more so than the mainstream textbooks designed for the bulk of the student body. Then again, you might not actually be looking for a real proof book after all - despite how you worded your request. If you are really just looking for a reintroduction to calc, Stewart might do you just fine. 99% of people will certainly find it much more readable! 😀
Click to expand...
Recommending these books to someone who doesn't even own a calculus text yet? Fail. Sorry dude, that's just wrong. These books will not introduce you to university level calculus. You don't not want to try to tackle books on analysis unless you already have a background in calc.
 
Barack Obama said:
Can you smart ATOTers recommend a good college-level calculus book that covers Bsc/Msc level of differentiation/integration? I'd prefer a book that provides rigorous proofs from first principles as opposed to a quick summary of important results?

e-beers for all 🙂
Click to expand...
Rigorous proofs? You don't want rigorous proofs. You want the dumbed down version. Trust me.
 
GodlessAstronomer said:
Recommending these books to someone who doesn't even own a calculus text yet? Fail. Sorry dude, that's just wrong. These books will not introduce you to university level calculus. You don't not want to try to tackle books on analysis unless you already have a background in calc.
Click to expand...
Hey he asked for rigorous proofs from first principles, and a book that straddles the graduate level. I answered his question. I gave the caveat at the end because I suspect they aren't really what he's looking for either. OTOH on the off chance that really is what he's looking for then my post was the only informative one in the thread so far.
 
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Ok. I have some book by Larson, Hostetler, and edwards called Calculus: Early Transcendental functions. It's the fourth edition

ISBN-10: 0-618-60624-6
ISBN-13: 978-0-618-60624-5

Yep.
 
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