Infinite series

[devious_]

I'm interested in learning these. Does anyone have any resources? Books or links would do just fine. I'd also like to learn about infinite integrals.

[Damned charming :)]

It is a common topic. I can tell right away that the integrals \sum 1/n behaves in a similar fashion to \int 1/x the same with \sum 1/n^2 and and \int 1/x^2 . SOS mathematics seems to be a good site so here is a link their section on series- it is in the calculus section.

http://www.sosmath.com/calculus/series/convergence/convergence.html

[Ethereal]

I have a copy of Schaum's Outlines: Advanced Calculus by Murray R. Spiegel. It has chapters on infinite series and improper integrals, not to mention a lot of other calculus topics.

[devious_]

I have a copy of Schaum's Outlines: Advanced Calculus by Murray R. Spiegel. It has chapters on infinite series and improper integrals, not to mention a lot of other calculus topics.

That's what I'm looking for. Is the book any good?

[Ethereal]

That's what I'm looking for. Is the book any good?
I think so, since it has proofs of almost every result.

[devious_]

I think so, since it has proofs of almost every result.

But how's its style?

[Ethereal]

I think whether it suits you or not depends on whether you are interested in learning calculus for yourself rather than because you need a textbook supplement. Since I haven't taken any course specialising in calculus, and haven't been taught it in-depth yet, I found the book tremendously useful simply because it endeavours to prove just about every formula it uses. It's your call, though. Couldn't you look through the book in your local library to see if it's any good?

[devious_]

We don't have local libraries here. :frown:

I'm doing this purely out of interest, and I'm not going to have any sort of teaching. Basically, I don't want a book that's too concise, and from your description this book appears to be the opposite. I guess I'll give it a go, then!

Thanks. :biggrin:

[Ethereal]

We don't have local libraries here. :frown:That's odd.

Basically, I don't want a book that's too concise, and from your description this book appears to be the opposite. I guess I'll give it a go, then!Actually, it is quite concise, given that it was meant to be an outline. There are times when the book attempts to prove some theorem, but doesn't quite elaborate enough on what exactly it is doing. But I guess this could be due to that fact that maybe I'm too stupid to know what exactly it's doing.

[devious_]

Hmm... If it's concise, maybe I'd better look for another one.

Thanks anyway.

[Ethereal]

I would actually recommend it. The fact that it attempts to be concise should not put off anyone. Those who write textbooks often have a choice of either explaining the concepts very clearly, which would take up a lot of space (hence the high cost), or being concise. Having said that, I find that this textbook, which as I said earlier, proves just about every formula it uses strikes a balance between clarity and coverage. Here are the chapters of the book:

Numbers
Functions, Limits and Continuity
Sequences
Derivatives
Integrals
Partial Derivatives
Vectors
Application of Partial Derivatives
Multiple Integrals
Line Integrals, Surface Integrals and Integral Theorems
Infinite Series
Improper Integrals
Gamma and Beta Functions
Fourier Series
Fourier Integrals
Elliptic Integrals
Functions of a Complex Variable

Having said that, of course you could always set out to find a book which attempts to cover that many topics, but there might be a trade-off: lesser proofs given, or you might end up with a very thick and costly textbook. Of course, if cost is no object, then you could always go look for a better textbook.

[devious_]

I'm going to give it a try.

Thanks. :smile:

[devious_]

I gave Schaum's Outline of Advanced Calculus another look and decided it wouldn't be suitable, as I want to teach myself the material. (It was too concise.)

Anyway, I've been looking for alternatives in the same price range. I liked How to Ace the Rest of Calculus, and will be getting it. However, it doesn't cover everything I'm looking for. Here's a list of topics (from Ethereal's last post) I'd like to learn:

Functions, Limits and Continuity (I skipped Limits & Continuity when I started learning Calculus :shy:)
Line Integrals, Surface Integrals and Integral Theorems
Functions of a Complex Variable

I'd be grateful if anyone could recommend some books that cover these topics. Though please bear in mind that I want to use them for self-teaching, and that I'm on a limited budget.

Thanks.