Using Apostol as my first calculus book?

[Franco_Carr14]

Hello, I'm currently learning pre calculus from various sources. I'm preparing myself to hopefully be able to learn calculus which I feel is an essential tool for Physics. I've just purchased Apostol's Calculus Vol.1. Enough research for great introductory calculus textbooks brought me to Apostol. But recently I've discovered another great book that is talked about in this forum, Thomas Calculus 3rd e. My question is, is it a good idea to use Apostol calculus without any exposure to former calculus material, other than precalculus material? Will the rigor of Apostol benefit me as it will expand my comfort zone? Or should I first use Thomas Calculus 3rd e. to be able to learn the most from Apostol's? Thank you..

 

[MidgetDwarf]

I would suggest working from Thomas 3rd ed and buying 2 other books. How to Prove it and Naive Set Theory. Then after working out of thomas and completing the equivalent of calculus 2. Work on Apostol. Just my opinion.

 

[Franco_Carr14]

I would suggest working from Thomas 3rd ed and buying 2 other books. How to Prove it and Naive Set Theory. Then after working out of thomas and completing the equivalent of calculus 2. Work on Apostol. Just my opinion.

Thats a great suggestion! Also can you please provide a link for the Naive Set Theory book you were referring to. Thank you so much for the help!

 

[bacte2013]

"Naive Set Theory" by Paul Halmos. Incredibly fascinating book on the set theory. This is the book you want to start to learn the set theory before jumping into well-regarded texts like Jech. Also regarding to the proof-teaching book Mr. MidgetDwarf mentioned, "How to Prove It", I actually recommend "Mathematical Proofs" by Chartrand.

 

[MidgetDwarf]

"Naive Set Theory" by Paul Halmos. Incredibly fascinating book on the set theory. This is the book you want to start to learn the set theory before jumping into well-regarded texts like Jech. Also regarding to the proof-teaching book Mr. MidgetDwarf mentioned, "How to Prove It", I actually recommend "Mathematical Proofs" by Chartrand.

It I crazy. I have been reading the Chartrand book and didn't even know it. I have an older ed green book. It reads like a conventional textbook compared to how to prove it. How to prove it is more talkative.

 

[micromass]

Hello, I'm currently learning pre calculus from various sources. I'm preparing myself to hopefully be able to learn calculus which I feel is an essential tool for Physics. I've just purchased Apostol's Calculus Vol.1. Enough research for great introductory calculus textbooks brought me to Apostol. But recently I've discovered another great book that is talked about in this forum, Thomas Calculus 3rd e. My question is, is it a good idea to use Apostol calculus without any exposure to former calculus material, other than precalculus material? Will the rigor of Apostol benefit me as it will expand my comfort zone? Or should I first use Thomas Calculus 3rd e. to be able to learn the most from Apostol's? Thank you..

No, doing Apostol as very first calculus book is not a good idea. Don't get me wrong, Apostol is an absolutely beautiful book that you must work through. But without experience, it is just too difficult.
I'm not really fond of Thomas as a calculus book but apparently many people like it. For a first book, I like to recommend the free and nonstandard book by Keisler: https://www.math.wisc.edu/~keisler/calc.html

 

[bacte2013]

Before reading Apostol, how about "A First Course in Calculus" by Serge Lang? The book is relatively straightforward and clear, which you can finish by month or so. "Principles of Mathematics" and "Fundamentals of Freshman mathematics" by Allendoerfer/Oakley also offer very intuitive treatment of the integration and differentiation.

 

[bacte2013]

It I crazy. I have been reading the Chartrand book and didn't even know it. I have an older ed green book. It reads like a conventional textbook compared to how to prove it. How to prove it is more talkative.

I prefer Chartrand over Velleman. Although Velleman is more fun to read, I think Chartrand's book is very instructional and offering many insightful advice about proofs and reasoning behind the proofs and logical steps. His chapters on the linear algebra, group theory, and ring theory were good preparation before advancing into Artin and Hoffman/Kunze.