Best Calculus book for self-study

[Bassir]

I'm currently in high school and would like to get a better understanding of Physics as well as Calculus, as I have no experience with either precalculus or calculus, and I really want to self study it.

What books do you recommend for learning calculus on your own?

 

[stewartcs]

I'm currently in high school and would like to get a better understanding of Physics as well as Calculus, as I have no experience with either precalculus or calculus, and I really want to self study it.

What books do you recommend for learning calculus on your own?

I would recommend studying Precalculus/Trigonometry before attempting Calculus.

However, I am a fan of James Stewart's Calculus books.

CS

 

[Bassir]

I would recommend studying Precalculus/Trigonometry before attempting Calculus.

However, I am a fan of James Stewart's Calculus books.

CS

I'm currently taking trigonometry.

Do you have any books you can recommend for learning precalculus all the way up to calculus?

 

[DarrenM]

Trigonometry is Precalculus; or rather, it's part of it. Precalculus is part algebra and part trigonometry. For example, Georgia Tech's Precalculus course description says:

Analytic geometry, the function concept, polynomials, exponential, logarithms, trigonometric functions, mathematical induction, the theory of equations.

They use Precalculus,7th edition by Larson, Hostetler, Houghton-Mifflin. I can't speak to that, as I'm not familiar with the book. I used Stewart's Precalculus: Mathematics for Calculus, 5th edition, and I liked it quite a bit. I should point out that this is the same Stewart mentioned by stewartcs.

 

[Bassir]

Trigonometry is Precalculus; or rather, it's part of it. Precalculus is part algebra and part trigonometry. For example, Georgia Tech's Precalculus course description says:



They use Precalculus,7th edition by Larson, Hostetler, Houghton-Mifflin. I can't speak to that, as I'm not familiar with the book. I used Stewart's Precalculus: Mathematics for Calculus, 5th edition, and I liked it quite a bit. I should point out that this is the same Stewart mentioned by stewartcs.

Would 4th edition be adequate?

 

[DarrenM]

Yea, snagging old editions of textbooks can be a pretty cost-effective way of getting your hands on them. An old edition would probably suffice; just be aware that an older edition may have a few more errors than the most recent version. That's not a big deal, though. You'll just have to strike a balance between being determined enough not to give up when you encounter a tough problem and smart enough to realize that the book itself may be wrong.

 

[Bassir]

Also, does anyone have any recommendations for introductory physics textbooks with very minimal math skills, considering I've no exposure to calculus?

Something not too advanced, just high school AP physics/college freshman physics.

 

[Feldoh]

Halliday and Resnick fundamentals of physics.

 

[Bassir]

After being exposed to precalculus, what textbook do you recommend for learning calculus?

Calculus by James Stewert?

 

[Sankaku]

Stewart's Calculus is ok - the 5th edition can be found for very cheap. However, there are other books that may be a little better.

I like Swokowski for a good general book but I hear that Kline's book and Gootman's book are also popular for people new to the subject.

Once you have the basics, look for Spivak.

 

[DarrenM]

Yes, I like Stewart's Calculus quite a bit, but that may be because I'm comparing it to the book I've had to use. It's called University Calculus and it's a weird derivative of Thomas' book. Frankly, I'm not fond of it.

I have heard, but not seen for myself, that Spivak's book is very good. I haven't been able to find even an old edition that wasn't still a bit pricey.

 

[DanP]

From the series "Dover books on mathematics"

"Essential Calculus with applications" , Silverman
"Advanced calculus", WidderCant go wrong with them , even if you may have to look to a video lecture or two for some issues and explanations. (For example the analysis of trig functions is omitted )The price is excellent, ~25 USD for both, compare this with the price of today popular textbooks.

 

[qspeechc]

I am not familiar with Stewarts precalculus books, and I don'y know any such books I can recommend. However, I was forced to learn calculus with Stewart's book. In short, I hated it. Ok, you will learn everything you need to know about calculus from this book, so in that respect it is worth getting. I'm not singling out Stewart's book here, I think most calculus books at that level are mediocre.

I could write an essay on why I think Stewart and many other calc books are not worth your time or money. But I won't bore you. Let me instead present a list of books I think are worth your time, and they won't break the bank either. Btw, as others have said, you pre-calculus needs to be good before you start calculus. Here's the promised list (you need to do single-variable calculus before multi-variable calculus):

Calculus Made Easy by Thompson. Don't let the title or the price fool you. Calculus is really a simple subject, as Thompson skillfully shows here. It's so cheap, you should definitely get this book. The 2nd edition is the best. Only covers single-variable calculus.

A First Course in Calculus by Serge Lang. Ok, it's Lang, but don't be scared. To the point and well written. Only covers single-variable calculus. Can find it used for a good price.

Calculus of Several Variables by Serge Lang. The follow-up to the above book. This one covers multi-variable calculus. You can also find cheap copies of this one.

Vector Calculus by Marsden and Tromba. Multi-variable calculus book. A very difficult book if you have no background in proofs, but the best vector calculus book I have read. You might want to try the other calculus books by Marsden, but I've never read them.

Div, Grad, Curl and All That by Schey. Vector calculus book, very intuitive, and actually explains the things in vector calculus, which surprisingly, is rare in calculus books, e.g. Stewart. I strongly recommend this one.

Calculus by Gilbert Strang. The book is available for free online (it's legal):
http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm
I haven't myself read this book but:
1) It's written by Strang, so it's probably good (it has good reviews on amazon.com).
2) It covers both single- and multi- variable calculus, but it's not too long (Stewart is over 1100 pages!).
3) It's free!

**********************************
In short, I recommend:
Thompson, Schey, Strang.

 

[n!kofeyn]

Spivak's calculus is absolutely wonderful. You really shouldn't learn calculus from Stewart unless you have to, i.e. a course requiring you to use it. It is the same standard textbook that is 1000+ pages and has endless exercises that don't do anything but teach you computation and worthless applications. Plus, Spivak starts off by teaching you about the real numbers and precalculus. It is highly recommended. Some might say it is analysis book or too difficult (it's a thorough calculus text), but if you can get through the first 70 pages or so (the introductory precalculus material), then you'll be fine for the rest of the book. The payoff is huge if you learn calculus from this text.

 

[jgens]

I'll second n!kofeyn's recommendation. Spivak's Calculus is a great book and he presents the material in a way that's easy to understand. The problems in Spivak's calculus text are also considerably more difficult than those in Stewart's calculus text (I felt I was wasting my time by working the problems in Stewart's text whereas Spivak's problems are challenging and engaging).

 

[Bassir]

Wait, Spitvak's Calculus has precalclus in it?

Does that mean Precalclus by Stewert is unnecessary if I decide to go with Spitvak?

 

[Sankaku]

Wait, Spitvak's Calculus has precalclus in it?

Not in the way that you think. Spivak builds your understanding of Calculus from the ground up, but you still need a very good grasp of precalculus topics to have any chance of understanding Spivak.

It is a great book, but everyone here recommending it probably learned basic calc from a different book and then found Spivak (just a guess!). It is super for deeper understanding, but I stand by my suggestion that it probably isn't the text for a first time calc student unless you are very strong at grasping new math topics.

Buy a copy of the 3rd edition (cheaper) and see for yourself. It is worth owning anyway...

 

[n!kofeyn]

Wait, Spitvak's Calculus has precalclus in it?

Does that mean Precalclus by Stewert is unnecessary if I decide to go with Spitvak?

I should clarify. I didn't mean that it would be enough to completely teach you precalculus. I meant that if you are at a level at which you can understand or get through the first 70 pages, then there isn't much reason to go and find another precalculus book, especially since you've had trigonometry. But if you find yourself hesitant or not comfortable with the material in that section of Spivak, then go find a precalculus book at your local library. I don't know of any precalculus books that stand out, but others might. In my opinion, a precalculus book won't be an investment. You'll learn it and never look back, but your calculus text will always be a great reference. You can use any library's interlibrary loan to basically get any book you want that your library doesn't, so get Spivak and find a precalculus book, and then you could make a better judgement where you should start.

There isn't any reason someone can't learn calculus for the first time with Spivak. That's why it's there and such a good book. Stewart and the like (i.e. any book that makes endless editions, multiple types of editions, interactive CDs, etc. just to make publishers and the authors money) teach computational and boring calculus. Don't shy away from learning calculus the right way. Learn precalculus by any method you choose and then go for it. You could just go for Spivak and find that it really didn't matter that you haven't a formal precalculus class, or you could find that you need to step back and learn it. You don't lose either way.

Final thought, I wish I had learned calculus first from Spivak and not Stewart.

 

[qspeechc]

If you're going to use Spivak, and it is an excellent book, maybe you want to learn how to do proofs first. I recommend How to Read and Do Proofs by Solow, or How to Prove It by Velleman, whatever you can get cheapest.

 

[FantasyQueen]

I personally love the Barron's EZ series and I'd recommend it for anyone who has had no previous experiences with the subject (general information often covered in elementary school will be required). They have a book entitled EZ Calculus, but it is best understandable if you read the books Barrons EZ Precalculus and Barrons EZ Algebra.
If the Barrons EZ series is not working for you, you can always give Calculus for Dummies a try. I'm currently in the eighth grade and I am learning calculus very easily with the Barrons EZ series.
Good luck with learning calculus! I admire your motivation to learn calculus at this age.

 

[osnarf]

I am going to cast my vote with Spivak. I am also definitely going to second reading a book on proofing and logic first, though.

Spivak was my first experience to proofing, and the first quarter of the book made me want to throw the book across the room, until i got the hang of having to prove things (especially things that seem like they're just obvious). It turned out all right in the end: it's doable, just not recommended. I imagine it would be a lot easier to first learn to proof, then learn calculus, instead of learning both at the same time.

If you have had trig and algebra, you are capable of doing Spivak. He really does go from the ground up.
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Edit: This thread is over a year old?

 

[Ashuron]

I must say Apostol's treatment is very thorough..
He build the knowledge from the foundation..

Some of the elementary analysis textbooks also good for learning logic and proof..
Books like Analysis from Steven R. Lay or Elementary Analysis by Kenneth A. Ross are really accessible..

 

[Caramon]

Hands down:
"Calculus: Graphical, Numerical, Algebraic" Published by Pearson Education in 2003. The authors are Ross L. Finney, Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. It is a revision of the Finney Thomas Demana Waits, "Calculus", published by Addison Wesley.

 

[eumyang]

Hands down:
"Calculus: Graphical, Numerical, Algebraic" Published by Pearson Education in 2003. The authors are Ross L. Finney, Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. It is a revision of the Finney Thomas Demana Waits, "Calculus", published by Addison Wesley.

"Hands down"? Are you kidding?? Sorry, I'm going to have to disagree here. This book is VERY poor in my opinion. It is rather lacking in explanations. The material presented is low-level, avoiding even remotely complicated reasoning. A colleague of mine currently teaches the 3rd edition (2007) and she does not like it.

(There is also a Precalculus book by 3 of the same authors, of which I am currently using in my Precalculus class. It's also quite lacking, topics are often presented out of order, and the examples are either too hard or too easy.)

 

[Caramon]

When I used it in High School I finished AP Calculus with 100% and got a 5 on the AP exam. I thought the textbook was great and there are proofs in the back and lots of interesting application questions.

 

[osnarf]

I got a 5 on the ap exam too. And then I read spivak's book and realized that I had only thought I understood it before. Will be starting apostol's soon, I hear that is great as well.

 

[aortizmena]

If you really want to learn calculus, you shoud first learn logic and how to do proofs. Then read and work on any of these authors calculus books by Spivak, Apostol or Courant for a deep formal approach (depending on which one you like the most, you can't go wrong with this ones). And maybe (just maybe) work on the exercices on Thomas to learn how to procede when confronted with easy problems.