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Calculus books used at top universities

  1. May 26, 2014 #1
    Hello, I only post this here, since I can't post in the learning materials section of this page.

    I am going to begin studying physics in Europe in autumn. I know that I will learn a lot but I want to be really good and learn in the most efficient way. In order to achieve this I will have to use the best learning material. I know that physics is not mathematics but being able to calculate the consequences of a theory is crucial. As a consequence, being good at mathematics is a must. Right now my math is at high school level but I want to improve.

    Now I've got some questions:
    1. Which topic of math shall I begin with?
    2. Which calculus books are used at the top-physics-universities like MIT, Harvard, CalTech,...? I assume that they probably use the best learning material.
    3. Which book is the best calculus book? (Right know I read Calculus by Spivak, but I don't know if it is the best calculus book for physicists.)
    4. Which mechanics books are used at the top-physics-universities like MIT, Harvard, CalTech,...?
    5. Which books are good for studying mechanics?

    It would be very cool if you answered questions 2 and 4 since I think it is quite good if you use the same learning material as the best universities.

    P.S.: Please excuse my English but I am no native English Speaker.
  2. jcsd
  3. May 26, 2014 #2


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    I don't know what books the top schools pick, books change all the time. I do know that both of these have been used at MIT (well not this Matrix Version but the standard version). These should be very efficient. I'll give links to amazon.co.uk in case that helps.

    Calculus 6/e, Early Transcendentals Matrix Version - Edwards & Penney - more than a year's worth of college math, covers calculus (single and multi), differential equations, linear algebra.

    An Introduction to Mechanics - Kleppner & Kolenkow - uses calculus throughout, very efficient
  4. May 26, 2014 #3
    Top schools use pretty much the same books as other universities. You can head over to the Textbooks section of this forum to find textbooks that satisfy your needs, though. Other than that, MIT does post the syllabus for their courses:

  5. May 26, 2014 #4


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    If you want to know what textbooks or other learning materials are used at various universities, check out their websites. Many professors post syllabi and textbooks used for their courses online now. A lot of assignments like HW problems, projects, or even exams sometimes find their way online as well.
  6. May 27, 2014 #5


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    I'll give you a brief list of mechanics texts:

    Harvard - Introduction to Classical Mechanics by David Morin: very difficult; used by honors physics students.
    MIT - Kleppner and Kolenkow - An Introduction to Mechanics; the book I bought for self-study; used by honors physics students. It's not as hard as Morin's but still my favorite introductory mechanics text. It's quite difficult when compared with Young and Freedman or Halliday Resnick.
    Caltech - Frautschi, et al., The Mechanical Universe, Advanced Edition
    Last edited: May 27, 2014
  7. Jun 1, 2014 #6
    If you want a NICE book, that actually explains how to use calculus, and wants the reader to really learn it, rather than to represent and boast how much the author knows about the subject I recommend this beauty:

    Calculus Made Easy by Silvanus P. Thompson
  8. Jun 7, 2014 #7
    Cambridge University recommend Calculus by Spivak/Apostol, then Rudin, but they seem to prefer Burkill for some reason.
  9. Aug 11, 2014 #8
    It depends. It can vary year to year and school to school and even for the same year at the same school they may use different books for different levels (biologists/etc. track vs. math&physics track vs. honors).

    I can say that my honors sequence at Tufts used Apostol Vol. I for honors Calc I/II in the fall and Vector Calculus" Marsden&Tromba then for honors Calc III in the spring.

    I'm not sure. My honors calc sequence was really incredible and very interesting, but I can't say it was particularly in the style of what many physics guys seem to prefer (although I ended up being a physics guy myself), especially not for the first semester using Apostol. But I loved how it started from the very lowest levels (far below calculus) and built everything up proof by proof. The first semester was particularly amazing (of course the particular professor may have played a major role as well, I had it with one of the school's most beloved professors). At the end of the day, you won't be necessarily be quite so careful and so 'mathy' with much of the math as you use it in physics though.

    Again it depends, perhaps: Fowles&Cassiday, Morin, Kleppner,Alonso&Finn, Feynman Lectures although maybe more typically just something like University Physics Young&Freedman&Ford (derived from Sears&Zemansky&Young) unless it is Caltech/MIT/honors section.

    The top 200 or so schools generally grab from the same basic pool of books for the most part, other than special honors sections perhaps or perhaps at a few of the top highly tech oriented schools.

    If you want a better overall idea, I'd suggest you go to the websites of a whole bunch of the schools and check the individual course pages. In many cases you should be able to find out what they are using.
    Last edited: Aug 11, 2014
  10. Aug 11, 2014 #9
    The book that seems to be ideal for science students ,because the( well-known )author doesn't draw a line between applied and pure math is Calculus with applications by Peter lax and Maria terrell,it's free avaible online for students from Cornell.
  11. Aug 14, 2014 #10
    Sorry for this: The level of education at European universities is far beyond of what is typical in the U.S., even at top schools. In the courses on theoretical physics in Germany, starting in the first or second semester, students learn what would be considered graduate level at American universities. Walter Rudin's Principles of Mathematical Analysis is an elegant and concise book. Books used at German universities (like Amann/Escher oder Königsberger) are, however, more general, broader, deeper and give you more concepts. You can find on YouTube recordings of lectures given at Yale, MIT or CalTech, perhaps by the best profs in the world, but their lectures are left in the dust by what is standard in Europe.

    BTW: Best mechanics books: For theory, consider Arnold's "Mathematical Methods of Classical Mechanics" and Thirring's "Classical Dynamical Systems", for practise consider Landau/Lifshitz (really hard examples with solutions!). Marsden/Ratiu also appears to be very interesting (for theory), but I just got a snapshot yet.
    Last edited: Aug 14, 2014
  12. Apr 29, 2015 #11
    From my experience, the best books on Calculus are in order,
    James Stewart, Soo Tan, followed by Thomas' Calculus and Howard Anton. The first 2 are excellent in that the proofs are presented well with no need to read in between.
    I would mention Robert Minton, then Robert Adams'&Essex book as good reference books.
    The point is to understand the material and I would not recommend stuff like Spivak, Lang, Apostol or any other old school books as they might even discourage you as they are a bit cumbersome and to most people overwhelming.
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