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Calculus Is A First Course In Calculus a good book for a beginner?

  1. May 31, 2015 #1
    I am going to purchase a calculus textbook named "A First Course in Calculus" By Serge Lang, is this a good book for a beginner? I mean, complete beginner? This is my first time being exposed to Calculus.

    Also, if this is not a beginner friendly book, is there any different textbooks that I can purchase to self teach myself calculus ?
  2. jcsd
  3. May 31, 2015 #2
    Yes, it should be good for a complete beginner. He doesn't even assume you know trig and logarithms (although I do recommend you know them before reading).
  4. Jun 1, 2015 #3


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    I also like Lang's book. However it has Lang's special take on textbook writing. It explains very clearly the ideas, and steps of arguments. But as I recall it is a bit short on routine exercises, and there is very little repetition. We learn not just by hearing or seeing but also by doing, and hence one should probably augment Lang's clear explanations by some tiresome sets of exercises which give one practice at computing what he has explained. But it has been many years since I saw his book. Maybe it has been expanded. At the time I thought, wow this is so clear and brief, why is it not more popular? So be aware that while people who know the subject well, llike micromass and I, think it is as clear as can be, some beginners think it is too terse.

    OK I have looked a bit online and it seems the book with that title today is 2 or 3 times as long as the one from 1964 with that same title. Perhaps they have combined his earlier books, first course and second course, and maybe more into one book. The earlier book was about 250 pages and this one is well over 600 pages and has several variables calc in it as well as one variable. Still it is quite possible it does not have a huge number of exercises, so I would look at it and try reading and learmning something from it.

    If you arte just buying this book used say, check which edition you are getting,a s they cost about the same, and the 5th edition seems to have maybe twice as many pages and as much more content.

    Lang can give some of the clearest explanations you can find anywhere. He can also skip completely over things you may well want to know, and give far fewer examples than needed to master a subject, especially in his famous algebra book, which also has been expanded by many pages from the1960's edition I have.
    Last edited: Jun 1, 2015
  5. Jun 1, 2015 #4


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    here is the original first course in calculus, indeed 260 pages, and all of differentiation and integration in under 200 pages, with the rest on infinite series. In the current 5th edition, pretty much the same material occupies twice as many pages. so you are not really getting the succinct intro he originally wrote. But maybe the new version is more user friendly? without the shortcomings in terms of practice problems i worried about?


    A remark about Lang's books in general. He had no shame at all at publishing exactly the same material multiple times under several different titles, so if you bought all of Lang's books you would pay several times for the same stuff. He is the only mathematics author I know of to do that. There are also different editions with the same title that contain very different material as in this case. His later books on differential manifolds or abelian functions also may be twice as long as his earlier books of the same title, depending on which edition you get. On the other hand he published the same discussion of advanced calculus under several different titles. Thus it makes sense to glance at a copy of the book you buy to see whether it really contains material different from that in another of his books you own.

    Another book I rather liked, was: Lectures on freshman calculus, by Cruse and Granberg:


    But at those prices you should look at a library copy first to see how you like it. The standard calculus book for a long time was the one by George B Thomas, before his co authiors began to change it. Not as sophisticated as Lang, and more engineering oriented, but very solid. Here are some early editions:


    Again check it out in a library.
    Last edited by a moderator: May 7, 2017
  6. Jun 2, 2015 #5


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    I'm currently working through this book over summer break in my free time. I've completed the whole calculus sequence and a course in differential equations already though, so it's not my first exposure to calculus. I'm finding it to be very beneficial as an alternative exposure to calculus though. There are some different approaches and different explanations than what I saw in my calculus courses, which is of course always a good thing.
  7. Jun 2, 2015 #6
    I prefer simmons to lang to be honest. Courant and hardy are better alternatives to lang. The recommendation of thomas is a solid choice. Make sure you get the 3rd ed or maybe 2nd. 4th ed has nasty formatting. Makes it hard on the eyes.
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