Which books for Calculus AND Linear Algebra

[Elementalnature]

I wanted to go through Calculus and then Linear Algebra following either of two paths:

a) Keisler's Infinitesmal approach>>>Nitecki Deconstructing Calculus>>>Nitecki Calculus in 3D>>>Freidberg's Linear Algebra

OR

b) Simmons Calculus with analytic geometry>>>Apostol Vol 1>>>>Apostol Vol 2>>>>Shilov's Linear Algebra

The first path (a), follows micromass's self-study article but the problem I have with it is that it is almost impossible to find any reviews on both of Nitecki's books.

I have a pretty good level of Mathematical Maturity from my studies in Mechanical Engineering but never studied Maths in a systematic way and had terrible teachers. Therefore I want to change that by following a regime using a sequence of books. I've grown to realize that I think more like a mathematician/philosopher so I like the idea of proofs which I did rudimentarily while in high school.

If it helps I'd like the linear Algebra and Calculus I learn to be relevant for a graduate course in Computer Vision. Although I still want to gain the full benefit of a rigorous mathematical approach to Calculus and Linear Algebra, not an engineering approach.
I considered using Lang's intro Calculus and Linear Algebra books in place of Simmons for Calculus and also as an additional book for learning Linear Algebra. If you have opinions on this, I would like to hear them too.

 

[dRic2]

I have a pretty good level of Mathematical Maturity from my studies in Mechanical Engineering but never studied Maths in a systematic way and had terrible teachers. Therefore I want to change that by following a regime using a sequence of books. I've grown to realize that I think more like a mathematician/philosopher so I like the idea of proofs which I did rudimentarily while in high school.

Same for me. At the beginning it was fun and useful, but then I abandoned the project

Btw here on PF, someone once suggested me Spivak's "Calculus". It is really good and since you have te same interest I had, I can assure you it is a book worth reading (or at least consulting... you know, 600 or more pages... ). From what I have understood is more or less on the same level of Apostol, but it is "smoother" (?). Anyway I don't know the other books so I can't really say what you should do, but if you can download Spivak's book you can check if you like it.

 

[mathwonk]

you cannot go wrong with either choice. in the first place the mere fact that micromass rcommended those books is in itself a positive review and one by someone you know is very reliable. as a second one i will say that i was very positively impressed by the only book i have read by nitecki, his DE book.

in the second choice of course i rcommend anything by apostol and simmons.

 

[Humanlimits]

Maybe someone else can comment on this, but as far as I know, Apostol teaches linear algebra as you go. So, a dedicated text after Apostol might not totally be necessary. If Apostol teaches enough linear algebra and you have enough mathematical maturity, you're time could be best spent on really understanding Apostol and not worrying about other books.

 

[mathwonk]

i suspect this is right. any time spent on reading and studying just apostol is extremely well spent.

here is another great book (assuming you know one variable calculus) that may be cheaper today;

https://www.amazon.com/dp/013112367X/?tag=pfamazon01-20