Calculus Calculus by Michael Spivak

Greg Bernhardt

• Author: Spivak
• Title: Calculus
• Amazon Link: http://www.amazon.com/Calculus-4th-M...alculus+Spivak
• Prerequisities: High-school mathematics

Table of Contents:

micromass

This is a wonderful and exciting book. I feel that this is one of the few books that any math major should read. It mainly covers single-variable calculus and it does so very rigorously. Make no mistake about it, the book is rigorous and quite hard. The exercises tend to be very challenging. As such, I would consider the book more an introduction to real analysis than an actual calculus book. If you wish to read this book, I would recommend that you had some experience with calculus already and preferably an experience with proofs too.

Astrum

I second this.

It's a great book, although if I had used this as my first calculus book.... I probably would have been pretty discouraged.

I don't really like how he never used Leibniz notation, but that's not a huge deal.

MarneMath

I used this for my first Calculus book. Extremely difficult, but it really gives you a feel if you'll enjoy a mathematics major or not. Very friendly and easy to read book. As Micromass said, this book isn't so much an intro to calculus book, but an intro to real analysis. Although, it is at a level less than most real analysis books. I'll say you should use this book if you have taken calculus course and want to review it from a more rigorous view, but don't want to get bogged down with very many new terms and abstract views.

jbunniii

Probably the best rigorous calculus book for most students. The main alternative would be Apostol volume 1. Spivak's exposition is more conversational and his proofs are somewhat more detailed than Apostol's. Also, Spivak has more interesting exercises, and many of them are quite challenging. Both books are excellent, however.

You would have to be quite a strong student to be able to handle Spivak as your first exposure to calculus, but most people (in the US, at least) will have already taken a computational calculus course in high school anyway, so this isn't really an issue. With that background, you already know what calculus is used for, and how to calculate things, so with Spivak you can focus on why and when those calculations are valid, and how to prove it.

Likewise, most people have a tough time with Rudin's Principles of Mathematical Analysis if it is their first exposure to real analysis. If you have read and worked your way through Spivak, you will have a much easier time with Rudin. You will already understand epsilon-delta proofs and will know many of the theorems, so you will be able to focus on the new material such as topology, and marvel at how clean and efficient Rudin's proofs can be: "wow, Spivak took 20 somewhat grungy lines to prove this, and Rudin did it in only 3 beautiful ones!"

Sankaku

Yes! I think people recommending it to beginners are looking back in time after doing a "normal" calculus course and then finding Spivak. They think how much they like Spivak's insights but forget about the fact that they already understand the mundane parts of the subject.

My mantra in mathematics is: "Preparation trumps everything." Despite how well-written and conversational Spivak is, you would need to be very well prepared to use it as a first text.

mathwonk

yes. some perspective: as a young college student knowing no calculus, i had all A's in high school math, 800 on math SAT test, had been on the school math team that retired the state contest trophy, and had won several individual state and mid - state math contest titles. i had difficulty gaining admission to, and struggled in, the college course for which then courant, and now spivak, was used as a text.

middleCmusic

Would this be the appropriate place to ask a question about a specific problem from Spivak? (Not doing it for homework - just self-study)

Jorriss

http://physicsforums.com/forumdisplay.php?f=156 Here would be more appropriate.

middleCmusic

Thanks.