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Calculus Textbook Recommendation (for Chemist/Microbiologist)

  1. Jun 18, 2014 #1

    I am an undergraduate student majoring in the chemistry and microbiology. Summer vacation is truly a great time to teach myself some some subjects besides conducting the scientific research, and I am decided to self-study the calculus over this summer (I took the introductory calculus but the course was not too deep but focused only on the general problem-solving). I am planning to purchase some "deep, proof-based, and rigorous" calculus textbooks because I realized that physical chemistry, quantum mechanics, and physics (and chemistry itself) that I have to take later on really depend on the proof-based calculus. I am also thinking of purchasing one or two books from Spivak, Courant, Lang, or Apostol (I like to buy all of them but each costs a lot). What calculus textbook from above do you recommend to me? I am planning to finish the book by the end of the summer vacation. If you also know a calculus textbook that is dedicated to the chemistry, please let me share your information too.

    Have a wonderful day!
  2. jcsd
  3. Jun 18, 2014 #2
    How much calculus did you take and what textbook did you use in school?
  4. Jun 18, 2014 #3


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    Lang, you are likely to find cheap versions of it available because his books are very popular. Also I think you don't really need the FULL rigor of calculus for chemistry.
  5. Jun 18, 2014 #4
    I took the single-variable calculus course on the Fall; we used the book Stewart Calculus, which was okay book not not that deep and intuitive. Basically, the course was a computational calculus. I heard good reputation about the Lang, but I heard that it is not as good as Spivak or Apostol. In order to understand the derivations inside the physical chemistry and quantum mechanics, I think the full-rigor calculus is needed. However, please correct me if you think I am wrong on both Lang and mu opinion. Is there a good calculus textbook dedicated to the chemistry?
  6. Jun 18, 2014 #5


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  7. Jun 19, 2014 #6
    Thank you very much for the link, mathwonk! I think I will go with Spivak, as I did not like Courant and Apostol that much. However, I heard that Spivak only covers the single-variable, and he also left out the differential equations. Could you recommend a multi-variable calculus + differential equations textbook that I can study after Spivak?
  8. Jun 19, 2014 #7


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    Courant actually looks very similar to Spivak, it's almost like Spivak set out to write a book in the style of Courant. So I would make a serious attempt at doing all problems in Courant, this is going to be a very similar experience to any book of this sort (but Spivak surely has more challenging/interesting problems).
  9. Jun 19, 2014 #8
    OMG! I just looked at the Spivak's Calculus (4th edition), and the book was tough! Should I just stick to Lang's A First Course in Calculus/Stewart? Do you think Spivak will be helpful for the chemist or microbiologist?
  10. Jun 19, 2014 #9
    Spivak will be too rigorous for Chemistry. You won't need to know an awful lot of maths if you're just doing your first 4 years.
  11. Jun 19, 2014 #10
    I don't think full-rigor calculus is necessary. Its nice but not necessities. Book like Mary L Boas Mathematical Methods in The Physical Sciences or similar should cover everything you need to know.
  12. Jun 19, 2014 #11
    OP, take a look at this thread I made:


    I believe the problem is again with the Stewarts and similar types of computational books, which seem to have been watered down with each new edition. Intelligent students will want more - they will know something is missing. But they may not necessarily need or be ready for the rigor of Courant, Spivak, or Apostol. Their background may be insufficient for that level just now, but not insufficient for what I called in my thread linked above, "the intermediate" books category. These are calculus books by George Simmons, Serge Lang, etc. These from what I've seen, strike a good balance between application/computation and theory, proofs, etc. And I believe, if adequately prepared prior to university, anybody can use Simmons or Lang. But universities in the US (seeing as high school students are not very good at precalculus even), have to play to the lowest common denominator and thus use books like Stewart, Thomas, etc. If people are struggling with Stewart, how can they use a Lang or a Simmons, never mind Spivak, Apostol, Courant. If the US can somehow get its high school math curriculum in order, and better prepare students for calculus (maybe not even OFFER it in high school as one idea and instead better prepare them for calculus), then maybe, maybe they can offer books like Lang or Simmons. MIT uses Simmons for its regular, non-honors calculus and has for years. For their theory/honors (like Caltech), they use Apostol. But they assume students for those courses will have already been exposed to a good does of quality calculus in high school. And MIT and Caltech are the TOP schools in the US. They will attract the best of the best. The others? They need to keep it watered down unfortunately...
    Last edited: Jun 19, 2014
  13. Jun 19, 2014 #12
    I can't imagine High School without Calculus. Might as well then withdraw the math curriculum from HS.
  14. Jun 19, 2014 #13
    It's a sad state of affairs in the US. I wasn't original in my thought. I had heard that argument before being made. A thread on this forum here:


    Maybe the focus in fixing the system needs to be first in quality not quantity. Then focus on quantity if you want to catch up with the rest of the world.
  15. Jun 19, 2014 #14
    Wow. I'm shocked by this information. I assumed that Calculus was unilaterally a standard thing everywhere in the last (two) year(s) of high school. Actually I'm confused as hell about US maths education. What topics do they cover in HS?
  16. Jun 19, 2014 #15
    So the calculus level of Spivak or Lang is not required for the chemistry and biology?
  17. Jun 19, 2014 #16
    No, not at all.
  18. Jun 19, 2014 #17


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    According to Micromass, Lang is not that rigorous. And looking at Lang's second book, it looks pretty much like any other multivariable book so Lang may be a good middle ground between the usual books and books like Spivak.

    That said, you started off talking about proof-based course that will come later, so I still think Courant's volume 1 looks very good, you should give it a good go, I think it can work out. Spivak is as hard as nails, this is well known and is sort of why people choose it, so don't let that put you off other books that won't be quite the same.
  19. Jun 19, 2014 #18
    Thank you very much for the suggestion! Do you know the calculus textbooks related to the chemist? I looked at the Mathematical Methods for Physical Sciences by Boas, but the book mainly focuses on the physics, which is not my purpose. I searched the book and found the book called ""The Chemistry Maths Book" by Erich Steiner (in Amazon). DO you think this is a good book?
  20. Jun 19, 2014 #19
    Thank you very much for all the helpful information and suggestion! I made up my mind and I think I will spent the summer with Lang's A First Course in Calculus and Schaum's Calculus series. Do you think it is a good idea to read Spivak for deeper understanding (but not solving the problems in that book) after reading corresponding chapters in Lang?
  21. Jun 19, 2014 #20


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    I think you have found the books you wanted so now it is up to you. I think Spivak is for a later time when you know calculus and want to try to solve those challenging problems.
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