Any good book about mathematics?

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For someone looking to advance their understanding of calculus, Morris Kline's "Calculus: An Intuitive & Physical Approach" is recommended for its accessible style, while Michael Spivak's book offers a more rigorous approach with challenging problems. Both texts cover essential topics such as derivatives, integrals, and their applications, but Kline's may be better suited for those less familiar with calculus. For geometry, Howard Eves' standard Euclidean geometry book and Coxeter's "Geometry Revisited" are suggested, along with a note that course materials on Non-Euclidean geometry derived from special relativity may provide a unique perspective. Additionally, resources for accessing math e-books are shared for those without library access.
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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!
 
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JasonRox said:
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.
 
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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.
 
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/
 
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Have you tried the Cambridge reading list?
I think it is quite nice, bothe the 'readable maths' part and the 'history of maths' part. :smile:
 
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