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Calculus books to understand physics

  1. Dec 25, 2014 #1
    Good morning Everybody and Merry Christmas,
    Could someone advise me a book they had in the past from which they learned calculus for physics?
    I am looking for a difficulty level so that I could understand in classical mechanics electromagnetism. I would like to know how to solve every possible equation in this part of physics and if possible that this book starts from the beggining of calculus(step by step).
    Thank you for your time and I wish you all happy holidays.
    p.s. the equations in the picture show the math I would like to learn

    Attached Files:

  2. jcsd
  3. Dec 25, 2014 #2


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    For this you need vector calculus. I've just given a lecture on it for our freshmen (in Frankfurt they really teach vector calculus in the 1st semester, which is pretty tough on the students). Among many German books, I liked

    D.E. Bourne, P.C. Kendall, Vector Analysis and Cartesian Tensors, 3rd edition, Springer-Science and Business Media (1992)

    Also the volume in the Schaum's outlines series is very good (with tons of solved problems):

    M. R. Spiegel, Vector analysis and an introduction to tensor analysis, Schaum's Outline Series, McGraw Hill (1959)

    If you need a quick introduction by an outstanding physicist, I recommend

    A. Sommerfeld, Lectures on Theoretical Physics, Vol. II (Mechanics of Deformable Bodies), Academic Press (1950)

    which has a chapter on vector calculus, including the important Helmholtz fundamental theorem of vector calculus.
  4. Dec 25, 2014 #3


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    Of course vanhees71 is correct that vector calculus is what you need to learn. I second the recommendation of the schaum's outline of vector analysis if you already know calculus.

    Have you learned basic calculus yet? Your desire for a book that starts at the beginning of calculus seems to indicate hat you haven't. Many calculus books cover through basic vector calculus. I learned from Thomas and Finney 7th edition


    which was fine for me, and suitable for a beginner. Used copies can be found for a dollar plus shipping. Any vector calculus I learned beyond that I mostly learned from electromagnetics textbooks.

    Last edited by a moderator: May 7, 2017
  5. Dec 25, 2014 #4


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    To get to this point you need to start with just introductory calculus. You can't realistically just jump into vector calculus without understanding the basics of calculus first. It sounds like you haven't gotten through the basics yet. The calculus in most of these equations is covered mostly in calculus III. To really get to that point though, you need to have a solid understanding of calculus I (limits and differentiation), and calculus II (integration and infinite series).
  6. Dec 25, 2014 #5
    I would recommend an older version of thomas with analytic geometry 3rd and an older version of stewart calculus. I would use thomas as the primary and stewart as the secondary. If u find some of the explanations in thomas difficult the ones in stewart may be easier. Buying stewart calculus will also serve as a workbook of problems. Should not be more than 20 dollars combined, maybe less if you look around.

    Thomas 3rd edition explanation of the epsilon delta is not that coherent compared to the one in stewart. Stewart does not explain the theorem of pappus early enough that it can't be any help solving work problems. Thomas explains the many integration techniques thoroughly, however the explanation of the chain rule is quite tricky as it relies on knowing what a parametric equation is. The proofs in thomas are quite clear except for the chain rule for the above reason I mentioned.

    Gl on your education. After learning some calculus, maybe pick up elementary linear by paul shields (strongly recommended by mathwonk).
  7. Dec 26, 2014 #6
    I have learned basic calculus,but I mostly learn it by parts from the internet so I miss on a lot of parts,that is why I want a book from the exact beggining with every single detail.
    Thank you for helping me
    Last edited by a moderator: May 7, 2017
  8. Dec 26, 2014 #7
    If you read the replies we have given answers. There is a difference between knowing something and having an idea. One cannot learn mathematics properly without doing programs and reading a book.
  9. Dec 28, 2014 #8
    I agree but actually you can. I learned 80% of physics and its math just on MIT online courses,and red some autobiographies on some of the finest physicist.All of them(Kaku,Hawking,some French guys) advise that the best way to study something without anyones help(in the 21st century)is over the internet.
    I know what will you answear,I am missing out on this 20%,but that is why I am here.Thank you :)
    p.s.this is where I study: youtube.com/user/MIT/featured
    Last edited: Dec 28, 2014
  10. Dec 28, 2014 #9
    Yes but it shouldn't be used as a crutch 90% of the time when a person gets stuck. The youtube videos and lectures are quite nice but if a person turns to google after every 5 min they are confronted with a difficult problem, then their brain is not given the chance to critically think. Getting stuck is crucial to test whether you understand something or not. Watching solely videos hampers the critically thinking process. After a while our textbooks are not going to have problems or diagrams (for the most part). What are you going to do? Turn to PatrickGMT for a nonexistent mathematical video which covers a graduate level topic? Good luck.

    Richard P. Feynman also talked about the joy of figuring things out. How are you going to figure things if you are letting online videos dictate you're thinking?

    I'll give you an example. On one of my cal 2 test our teacher put a problem. Find the area of the polar curve of an Arch. Spiral from thetha greater than or equal to zero. Guess what only 3 people in the class got it correct because we bothered to understand the material behind integration/polar/improper integration.

    I have seen this many times when students watch videos and memorize how to solve things. You through them a trick problem and they complain the test was too hard.

    Do as you like.
  11. Dec 28, 2014 #10


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    Autobiographies and qualitative descriptions of some of the great physicists of history doesn't really add up to "learning physics" in any real sense. A Brief History of Time is a fun book to read, but it doesn't teach you a whole lot about physics in anything resembling a practical way. If your idea of "all the great physicists" is Kaku, Hawking, and some French guys...then you have a great deal to learn about physics.

    The best way to study something without external help is likely the internet. But that doesn't make the internet alone a comprehensive tool to teach physics. There are textbooks that have become classics because they're just -good-. No YouTube video is ever going to cover it all. You say you've learned "80% of physics and its math just on online courses." If you're yet to even learn vector calculus, you have not yet learned anywhere near 80% of physics. YouTube videos are great, but they cover introductory material. You aren't going to find those same videos for graduate level material or cutting edge areas of research.
  12. Dec 29, 2014 #11
    Advanced Calculus Demystified is, in my experience, a wonderful book on that subject for getting into it. After I finished that, I used the Shaum's Outlines book "Vector analysis with introduction to tensor analysis".

    Having read some of your other replies here, I feel very strongly that I need to say that a "conceptual" introduction to math and physics is not nearly enough to prepare you to solve math and physics problems. You cannot learn without solving problems and putting in the effort.
    Last edited: Dec 29, 2014
  13. Dec 29, 2014 #12
    I do not know which results have given your aquantances from the knowledge of the internet,but I can assure you that I have had great results in my physics competitions,if there would not have been for the internet lectures that I have seen I would not have gained the knowledge that I have.But like I said,that is why I am here searching for books :)
  14. Dec 29, 2014 #13
    I am sorry if I can not express myself in the correct way,what i intended with "all the great physicists" and autobiographies I ment:I do not know the exact word in english,but it would mean their life work,do you honestly belive that I would be introduced by some book made for children?I do not mean to be rude,but if you want to help me,advise me as you can,if not I would prefer that you would not judge the ways I study becouse that is not the topic,if you want to continue the conversation,you can e-mail me on this mail: nprodanov313@gmail.com
    p.s.The main reason I study and watch lectures on the internet is becouse I can not afford that much books,and I live in a country where my libraries do not apriciate the knowledge of physics
  15. Dec 29, 2014 #14
    I have seen that book somwhere already,I think on a book-fair,just pitty it was in german(can not understeand physics + german lol)
    Thank you though :D
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