A good math review book...

BioCore

So I just started my Physics class over the summer about a week ago. For the first time, it is a course that uses Calculus a lot and so it will be a bit different for me although I do not think it will be too much of a difference.

My current knowledge though of Calculus is very small and only extends to power series with limited knowledge. Seeing as my professor started using vectors, but with Calculus explanation has left me a bit dazed, so to speak.

Basically I would like a textbook that can help me somewhat review rather quickly and then teach myself some of the more advanced Calculus topics that are generally used within Calculus based Physics courses. Also I would like to further my knowledge of Physics then a bit so I guess I would need to study more advanced Calculus topics and thus would like to know what people would recommend there.

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A Bit of background:
I am a student at the University of Toronto, studying Biotechnology and hope to do a Masters in Biotechnology and then move into industry. Who knows maybe even try and make a start-up later in life as I have thought of this also.

Currently I am really interested in BioChemistry since it is the basics of Biotechnology. But I have also started having some greater interest in Physics and specifically its' uses in Biophysics. So I would like to teach myself some Biophysics later on.
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Thus after reading this somewhat long post, what textbook would you all recommend that I use to review and expand my current Calculus knowledge?

BTW,
A book I was thinking of using is called:
"Single variable calculus : early transcendentals 5th ed." by Stewart, James
or would "Multivariable Calculus" by the same author be better?

Thank you for the help.

mgiddy911

this book will have a lot more than you need but is an overall good math reference:

Mathematical Methods in Physical Science - Boas

BioCore

Thank you for the advice mgiddy. I just had a look at the textbook as I am luckily in the library at this time - it is quite a thick book as you mentioned. But I am not sure if I would be able to learn from it as easily although I am not sure.

Maybe if I give some more information about myself it will help.
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Basically I took advanced Functions and Intro Calculus in my last year of high school and then took Calculus for Bio majors in University. This was my last course in mathematics.

Although I did achieve good solid marks in High School I did notice that in University I had lacked a lot in some of the knowledge and I particularly blame my lack of interest or enthusiasm which was something that was brought on by the courses at High school. They usually do not try to connect math to the many uses in other subjects.

Anyways, as I started Physics I noticed I would have to get a stronger understanding of its roots (so to say). Specifically its' language which brought me back to Calculus. So I would like a book that could explain to me the concepts and that would allow me to study some more advanced topic like Differential Equations and I believe it is called Linear Algebra, while at the same time allowing me to easily study Quantum Mechanics later on as well.
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I hope that shed some light on my concerns.

mgiddy911

Are you planning to take those other math classes you mentioned? or do you just want to self study them.
You may find studying QM very hard without proper math requisite. Self study may not give you enough knowledge to succeed.

mathwonk

40 years ago or so, when i was a student, a prof at maybe mit wrote a book on vector analysis for physics students called maybe "div, grad, curl, and all that". you might look at it, after you get your basic calc back. i myself have not used it and only perused it briefly in a store years ago, so cannot remember enough to evaluate or describe it, but i have heard some other people recommend it.

Since there exist so many hundreds of calc books out there, i suggest you go to a university library and sit down in the calc book section and look at lots of them until you find one that speaks to you, i.e. that you can learn from right on the spot by reading it.

then keep reading it in the library as long as you can. when you get up you will know if you want to study from it.

even then if it gets less useful, just go back and with your new improved knowledge, read some more and pick another one or more and try those.

but just start reading and WORKING EXERCISES, or else your reading will be for nought.