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- #1

SepR

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Thank you.

- #2

bhobba

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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

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

Last edited:

- #3

DrClaude

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

- #4

alan2

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

- #5

wrobel

Science Advisor

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

- #6

bhobba

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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

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- #8

mathwonk

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

- #9

lurflurf

Homework Helper

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I have had the same temptation. Chemistry as well.At times I'm tempted to say that theoretical physics is applied representation theory of (symmetry) groups :-).

- #10

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From my own perspective, theoretical physics is scientific method applied to philosophical questions.At times I'm tempted to say that theoretical physics is applied representation theory of (symmetry) groups :-).

- #11

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