Smirnov's "Course of Higher Mathematics"

[SepR]

Hi, I recently have rekindled my love for mathematics while in University for Political Science. I have reviewed all of my old pre cal books, but now I want to start learning Calculus eventually on to more difficult things like PDEs and things of that nature. I like having a series of textbooks that I can just go through without worrying about missing some material / learning between different books. Since Smirnov has both the beautiful old Soviet style writing about mathematics and the I believe 6 volumes teaching you everything even Linear Algebra I thought it would be the best thing to purchase. I downloaded the PDF of the books but looking at my laptop screen destroys my eyes and I would rather have the physical copy. I couldn't find any copies online with a non ridiculous price that has been up for many months even years. I was wondering if anybody on here has volumes I could buy. I could spend around $250 dollars for the series if need be.

Thank you.

 

[bhobba]

I can't help you with Smirnoff but over the years have thought about the best way to learn proper, rather than intuitive calculus, and here is my take, just for you to think about.

Actually calculus at the intuitive level is not hard at all - I personally believe it could be taught to 14 year old's in a combined calculus pre-calc course - but that's just me. The book I like for an easy intuitive introduction is:
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20

After that since you want a doing it approach altogether in one book Boaz's classic is good:
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

Finally to bring it altogether, in a rigorous presentation (except differential equations which Boaz covers well) the following by Hubbard is the best book I have ever seen:
http://matrixeditions.com/5thUnifiedApproach.html
Although to ease your way into the above a modern treatment of single variable analysis may help::
https://www.amazon.com/dp/0691125333/?tag=pfamazon01-20

But it must be said Hubbrad is used after a basic course on Calculus at Cornell for Honors students so you likely can get away without a book like MacCluer - although personally I would do MacCluer first as I am a easy steps often type guy. I would do it after Quick Calculus.

With that background you are pretty much ready for anything - mathematically speaking.

Note to keep cost down you can always buy used - I get a lot of books that way, although for me the above were so useful I got them new (except MacCluer - I already had other more advanced books like Apostle - but in your case I think MacCluer is better after something like Quick Calculus).

Thanks
Bill

 

[DrClaude]

Actually calculus at the intuitive level is not hard at all - I personally believe it could be taught to 14 year old's in a combined calculus pre-calc course - but that's just me. The book I like for an easy intuitive introduction is:
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20

A math book by physicists? Welcome to the dark side, Bill

 

[alan2]

What is your purpose in learning calculus? That makes a big difference.

 

[wrobel]

I have never thought that Smirnov exists not only in Russian. Good text indeed.

 

[bhobba]

A math book by physicists? Welcome to the dark side, Bill

While I love analysis you would need rocks in your head to start that way. Simply by considering infinitesimally small numbers to be so close to zero you can FAPP neglect it and the inverse of an infinitesimally small number as an infinitely large number that is again FAPP infinite you can present calculus in a concise and intuitive manner. Mathematicians (and by training I am one of those) will IMHO often start out more formal than needed - physicists IMHO understand the need to start simple from my observation. Of course after that a book on analysis will help with later studies as well as answer questions from students that actually think.

I was once a mathematician of the puerile variety (sorry I mean pure) but over time outgrew it (with the occasional biting comment from my professors) and understand now any decent mathematician/physicist needs to do both applied and pure.

Math books for a pure/applied background is something I have thought a lot about and what I wrote is what I came up with.

Thanks
Bill

 

[vanhees71]

I know Smirnov's books in German translation. It's in some parts a bit outdated in the notation (particularly in vector analysis, but contentwise excellent. Of particular value for my studies was volume III/1 which covers linear algebra including the representation theory of groups. The latter subject you usually don't find in such a comprehensible form for physicists, and for me it's THE key for understanding why the theories of physics look as they look. At times I'm tempted to say that theoretical physics is applied representation theory of (symmetry) groups :-).

 

[mathwonk]

always look on abebooks for used books:

https://www.abebooks.com/servlet/Se...ts&an=smirnov&tn=higher+mathematics&kn=&isbn=

 

[lurflurf]

At times I'm tempted to say that theoretical physics is applied representation theory of (symmetry) groups :-).

I have had the same temptation. Chemistry as well.

 

[Demystifier]

At times I'm tempted to say that theoretical physics is applied representation theory of (symmetry) groups :-).

From my own perspective, theoretical physics is scientific method applied to philosophical questions.

 

[vanhees71]

Theoretical physics is a scientific method applied to order scientific results rather than philosophy, which is "unreasonably ineffective" for science