[Calculus] Lost and what book to Use Next

[numbersloth]

Hello!

I have used Stewart's Calculus for the last year of Calculus and we made it through Taylor and MacLaurin Series. Next year we will be continuing. Since I really enjoyed calculus and I'm thinking of studying math/physics/computer science in college, I was looking for a good textbook to review calculus so far yet not feel boring. I was reading through Kline's Calculus: An Intuitive and Physical Approach, but it felt too easy and not even as rigorous as Stewart's, which I know is mainly an application based book. I read online that both Apostol and Spivak provide a rigorous review of calculus and will allow me to try my hand at proofs.

Which book will feel less like a review and more exciting to do even though I've learned quite a bit of calculus already? I was so bored reading through Kline and I want something hard but accessible (I'm a smart kid but I wasn't doing calculus in the womb or anything like that...).

Thanks

Edit: Just want to mention that I have no idea what happened to my title

 

[verty]

It sounds like you know calculus. So what I recommend is trying the problems here, there are not a lot of them and they are very good. There are lecture notes and videos in case you get stuck.

For review, that is what I recommend. Or if you want a book, try https://www.amazon.com/dp/0137363311/?tag=pfamazon01-20 or one of their newer editions to get many problems.

Now, you asked about Spivak and Apostol. Apostol will surely not be exciting enough for you. Spivak will be but it is really a book about theorems and proofs. If that is what you want and you want to be challenged, try it. You can also look at https://archive.org/details/DifferentialIntegralCalculusVolI which is available online. I must admit, this one looks pretty good to me. Thank you to Mathwonk for this one. It is slightly less accessible but don't be frightened by it, read carefully and do all the questions, it would suffice as well.

Or, you could learn most of this from almost any real analysis book, if that is something you are interested in.

 

[micromass]

If you want something very interesting and exciting then you should go for https://www.amazon.com/dp/0387770313/?tag=pfamazon01-20 It's one of the best math books I've come across. It's not terribly difficult too, but it gives a very nice perspective on math.

 

[numbersloth]

It sounds like you know calculus. So what I recommend is trying the problems here, there are not a lot of them and they are very good. There are lecture notes and videos in case you get stuck.

But there are no solutions online...? I always like to have solutions so I don't think I'm doing the right thing the whole time and meanwhile I'm completely wrong.

 

[verty]

But there are no solutions online...? I always like to have solutions so I don't think I'm doing the right thing the whole time and meanwhile I'm completely wrong.

Personally, I think answers are a hindrance to learning. If you can't answer a question, go back to the notes/readings. I always like to say, for any homework problem there is a very similar example that you have already seen. Go back to it, study it. In this case, the examples are in the lecture notes and additional reading notes. The information is there, you just need to find it. That is so much better than looking at an answer.

 

[numbersloth]

Personally, I think answers are a hindrance to learning. If you can't answer a question, go back to the notes/readings. I always like to say, for any homework problem there is a very similar example that you have already seen. Go back to it, study it. In this case, the examples are in the lecture notes and additional reading notes. The information is there, you just need to find it. That is so much better than looking at an answer.

But what if I feel sure that I am right, thus I don't look back over the lecture notes, and pick up bad habits? I agree that answers can cripple creativity and learning, but I also feel like they are necessary when someone is learning on their own.

 

[micromass]

But what if I feel sure that I am right, thus I don't look back over the lecture notes, and pick up bad habits? I agree that answers can cripple creativity and learning, but I also feel like they are necessary when someone is learning on their own.

You can always ask on the forums whether you did it right.

 

[matineesuxxx]

Another really good one is Calculus by Michael Spivak. Very in depth, very rigorous; much more so than the Stewart text.