Can you recommend a decent math book for me?

[MrNerd]

I'm almost done with the book I've been reading(Exploring Black Holes by Taylor and Wheeler), and I've heard people list off last names of people for books. I was wondering if there are any recommendations for someone who completed math classes up to Calculus I. It can't be expensive, like $40+, or preferably easily available at a typical library. I appreciate any recommendations.

 

[mathwonk]

try this:

Introduction to Calculus and Analysis. Volume I (only)
Courant, Richard & John, Fritz
Bookseller: Boards & Wraps
(Baltimore, MD, U.S.A.)

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Book Description: Interscience Publishers, USA, 1965. Cloth. Book Condition: Good. Dust Jacket Condition: Fair. Textblock is unmarked. Very small squiggle on first free end page. Binding is tight. Grey boards are clean. Spine is lightly bumped. Gold dust jacket has shelf wear and soil. Spine is scuffed. Hardcover. Bookseller Inventory # 024339

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[MrNerd]

Sorry, this was an accidental double post.

 

[MrNerd]

I appreciate the thought Mathwonk, but it states above that I have completed math up to Calculus I. It does look like you did a very detailed recommendation, though, and I applaud that.

 

[G01]

I appreciate the thought Mathwonk, but it states above that I have completed math up to Calculus I. It does look like you did a very detailed recommendation, though, and I applaud that.

Have you really covered all of the material in this book in a one semester Calculus 1 course?

A brief skim of the contents of the book on Amazon shows that vol. 1 of this text covers differentiation and integration, infinite sequences and series, methods of integration, numerical methods, trigonometric and hyperbolic functions and applications of all of the above to physics. Usually this material is introduced throughout both Calculus 1 and 2. I agree with mathwonk that this would be a great book for someone interested in physics and math who has just finished Calc 1.

(Also: This is just the first volume of the book! There is more advanced material in the second volume. For the price, I don't think it can be beat.)

 

[MrNerd]

Have you really covered all of the material in this book in a one semester Calculus 1 course?

A brief skim of the contents of the book on Amazon shows that vol. 1 of this text covers differentiation and integration, infinite sequences and series, methods of integration, numerical methods, trigonometric and hyperbolic functions and applications of all of the above to physics. Usually this material is introduced throughout both Calculus 1 and 2. I agree with mathwonk that this would be a great book for someone interested in physics and math who has just finished Calc 1.

(Also: This is just the first volume of the book! There is more advanced material in the second volume. For the price, I don't think it can be beat.)

When I said Calculus I, it was technically AP Calculus AB. With what you say, I suppose I should give it a chance, then. Hyperbolic functions were never covered in the calculus class I took. All I know about them is they're curvy, used by MC Escher in a picture, and involve e^x. I could probably use some more on series/sequences, too.

 

[MrNerd]

Alright, I've checked out the book on Amazon as well, and it looks pretty good, getting excellent reviews. Does anyone know if the answers(or at least something like the odd numbered problem answers) are in the back of the book? This isn't going to be for school, so it would be nice if I could check my answers in the back. It's really irritating if a book gives you a problem and no way to see if you did it right, leaving you to have to ask other people if you're right or wrong.

 

[Number Nine]

Alright, I've checked out the book on Amazon as well, and it looks pretty good, getting excellent reviews. Does anyone know if the answers(or at least something like the odd numbered problem answers) are in the back of the book? This isn't going to be for school, so it would be nice if I could check my answers in the back. It's really irritating if a book gives you a problem and no way to see if you did it right, leaving you to have to ask other people if you're right or wrong.

Courant is not a book in which you plug numbers into formulas and check your work at the end of the book. You took AP calculus, which means you learned about a few algorithmic methods to calculate derivatives and a few integrals but you didn't learn anything about what calculus is or how it was developed. Courant will help you with that. You already know how to do differentiation (a bit), this book will teach you about differentiation. It is not beneath you; it's a trillion times more thorough and informative that whatever you learned in AP. That said, I don't think volume I has any answers in the back of the book (I don't have my copy near me at the moment). It's a non-issue anyway, since there are different ways to prove any given theorem.

Note: You may want to pick up an introductory book on mathematical proofs (e.g. How to prove it).

 

[MrNerd]

Ah, that does sound more informative. If I can gather up the money, I think I'll get it.