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Calculus textbooks, Single or Multi-variable?

  1. Sep 15, 2008 #1
    I am looking for a good book to go over the basics of Calculus again, currently I am looking at my schools library and have found this one called:

    Essential Calculus: Early Transcendentals by, James Stewart.

    My goal is to over the year probably finish this book or if possible even before and then move on to some high advanced maths, ex. Differential Calculus, Linear Algebra...

    Now I would like to know if I should review with just single variable calculus or review and study multi-variable as well. I have actually had no training, nor did I ever learn Calculus with Multi-variables.

    I was also wondering how the author Spivak is when it comes to some of the above mentioned topics? Is there any good book written by him which could also help me out? Thanks.
  2. jcsd
  3. Sep 15, 2008 #2
    I forgot to add this, but I am in a science program. So for me I wish to try and understand how to use the theorems and formulas of Calculus and advanced math in applying it to the sciences. I am taking Chemistry and some simple Biology courses, strangely math is not required. People I know and some friends from upper years have recommended that I try to teach myself if anything some of the more advanced maths so as to get a better understanding of the chemical principles.

    Hope this information helps in some way.
    Sorry I just noticed the EDIT button now when I was trying to add this information. My final question is actually about the advanced topics in mathematics. When it comes to differential equations, Linear Algebra and such - that is the topics covered and used most by advanced theoretical chemistry (I guess in a way atomic Physics), what topics are most crucial for review from basic Calculus?

    Thanks again.
    Last edited: Sep 15, 2008
  4. Sep 15, 2008 #3
    I recommend these two Calculus Books. I have the first book but the second I don't but plan on getting it later when I have more $Bling$. :yuck:

    Calculus, Early Transcendentals, 7th Edition - By C. Henry Edwards

    University Calculus: Elements with Early Transcendentals - By Joel Hass, Maurice D. Weir
    Last edited by a moderator: Apr 23, 2017
  5. Sep 15, 2008 #4
    James Stewart is dumbed down calculus. That is, it has very little theory. Its a good for a calculus introduction though. James Stewart Calculus (the single and multivariable volume) has everything an undergraduate chemist will need and more. If you already did single variable calculus, you should move on to multi-variables as most of the concepts will be reviewed in a more general setting. If you insist on single-variable calculus, a book with some theory I reccommend is Salas and Etgen Calculus. Its just like Stewart, but it gives the theory.

    If you want to understand upper division science courses, I strongly suggest you study differential equations from a book like Boyce and DiPrima. You only need to know single variable calc to study this. If you want to get into quantum mechanics and atomic physics you will definately need linear algebra. You don't need any calculus for it, so I suggest you begin to study linear algebra as soon as possible.

    Lastly, Spivak is pure theory. It won't make you understand science courses better. What it will do is explain how and why calculus works. Its more of a "Intro to analysis text", and as such is extremely difficult. Such a book is of more use to mathematicians. While I loved Spivak's books, I am somewhat confused as to where they belong in a math curriculum. Both calculus and calculus on manifolds don't cover enough to be complete calculus texts (notably critical point applications). They are too difficult as first exposures to the subjects, yet too elementary to be real analysis books. To me, they are sort of summer reading before you begin junior real analysis courses and after you've done your lower division maths). I do not suggest you learn calculus from them as a first exposure, unless you are in a pure math program and you have the time to devote to such a course.
  6. Sep 16, 2008 #5

    Thanks for the great answer. I would like to do some multi-variable Calculus so I will look into the other textbook you recommended. As for Linear Algebra - thanks for telling me that I do not need a full knowledge of Calculus as I would have left it off much later than earlier.

    Also, I just wanted to confirm with you about this, so does upper year chemistry such as Quantum Mechanics rely at all on multi-variable Calculus or it primarily uses Linear algebra and differential math?
    Last edited: Sep 16, 2008
  7. Sep 16, 2008 #6
    No problem.

    Quantum Mechanics uses a lot of differential equations and linear algebra. There is a little bit of multivariable calculus, but its mainly the first two. You'd be wise to have all of it down before you start any kind of quantum chemistry.

    Again, just get Stewart's book and do his multivariable sections (skip his crappy introductions to differential equations). Also, you might want to do linear algebra before differential equations. So do linear this term, and diffy next term. Differential equations uses a little bit of partial derivatives as well, so this will also give you time to bring multivar up to speed.
  8. Sep 16, 2008 #7
    I personally fnd Stewart's treatment of multi-variable calculus to be confusing and badly treated. For differential equations I would recommend Polking, Boggess, Arnold (that's one book by three authors).
  9. Sep 16, 2008 #8
    Oh I see, alright I will take that into consideration for sure.
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