Any good book about mathematics?

[JasonRox]

I am looking to learn more about Calculus.

I have done High School Calculus.

I understand how to find the derivative, or definite integral(anti-derivative), in the following:

Quotient Rule
Chain Rule
Product Rule
Logs (10)
Trigonometry

I understand how to apply them, and there functions. (Maxima/Minima, Optimization)

I know about finding the area under the curves.

I need a textbook, or book with details, that will take me to the next level.

If possible, maybe list what the book includes.

Also, I am looking for a good book on Geometry. Any book that will allow me to study Non-Euclidean Geometry, Differential Geometry, and Tensors. They can be separate books of course.

Just to make things clear, I would like to learn Relativity. It sounds far-fetched, but if you so happen to know the best way, inform me. I'm not looking for the quickest way really; I am looking for the path in which I will understand and know what I am doing, and know what the numbers are telling me.

I learn quickly independently, so I recommend books that pick up the paste. This isn't to go fast, but merely so I don't get bored. I'm the type of person who enjoys it when the book leaves a few things out, and you somehow figure it out doing questions. If I don't figure it out, I simply look it up in another book.

THANKS!

 

[fourier jr]

I am looking to learn more about Calculus.

I have done High School Calculus.

I understand how to find the derivative, or definite integral(anti-derivative), in the following:

Quotient Rule
Chain Rule
Product Rule
Logs (10)
Trigonometry

I understand how to apply them, and there functions. (Maxima/Minima, Optimization)

I know about finding the area under the curves.

I need a textbook, or book with details, that will take me to the next level.

If possible, maybe list what the book includes.

I really like Morris Kline's "Calculus: An Intuitive & Physical Approach". Another good one is the one by Michael Spivak, but I think it would seem really rigorous to someone in 1st year, but since you've already seen a bunch of calculus, maybe it won't be so scary. Kline's books includes the following: derivatives & related theorems (like product rule, etc), integrals (& related theorems for this too like int by parts, etc), the geometrical significance of the derivative & maxima/minima, trig functions & inverse trig functions, log/exp functions, polar coordinates. I think Kline's would be better for someone who hasn't seen calculus very much because it isn't as rigorous as Spivak's. Spivak's includes: derivatives & integrals with all the related theorems, infinite sequences & series (not included in Kline's). I find that the problems are a lot harder in this book; some of them are pretty long, even the ones where you just have to find a derivative, and he gives theorems to prove in the problems also. Since you want to go fast, maybe you should check out Spivak's, but if it's too fast, try Kline's.

Also, I am looking for a good book on Geometry. Any book that will allow me to study Non-Euclidean Geometry, Differential Geometry, and Tensors. They can be separate books of course.

I think the one by Howard Eves is the standard Euclidean geometry book. After that one, do Coxeter's 'Geometry Revisited'. As for Non-Euclidean, I was given some course notes that derived everything in Non-Euclidean from special relativity, and I don't know of any book that does it that way. The prof said it's works out to be the fastest way to do non-Euclidean that he knows of.

 

[recon]

I'm in about the same situation as Jason. Does anyone know where I can get math e-books. I currently have no access to a library.

 

[robphy]

These may be interesting

http://ocw.mit.edu/OcwWeb/Mathematics/18-013ACalculus-with-ApplicationsFall2001/Readings/index.htm

http://archives.math.utk.edu/visual.calculus/

http://www.math.temple.edu/~cow/

 

[yifan]

Have you tried the Cambridge reading list?
I think it is quite nice, bothe the 'readable maths' part and the 'history of maths' part.