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Need suggestions for Math books

  1. Sep 14, 2013 #1
    The college I am currently in has started with Differential Calculus. Due to some reasons I haven't been able to attend the lectures. The current book assigned to us is of no help. The book only shows the solved problems on the topic with very less introduction and no geometrical meaning. I don't know to which area of mathematics the following topics belong and thus I am unable to search for any book.

    The following are already covered in the lectures:
    Asymptotes
    Curvature
    Curve Tracing
    Partial Differentiation
    Maxima and minima of functions with two variables
    Jacobians
    Envelopes

    The above topics were under the section "Differential Calculus" in the book I am assigned. In the next semester, I guess the instructor will begin with Integral Calculus. It would be great if anyone could suggest some books. Also, I heard my instructor talking about Polar coordinates. Please suggest a book for that too.

    Thanks!
     
  2. jcsd
  3. Sep 15, 2013 #2

    verty

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    You've got a mix of topics from one variable and multivariable calculus which is going to make it difficult to find the right book. Also I know that you like tough problems. So, I recommend these two instead:

    Problems in Calculus of One Variable - Maron
    Calculus of Several Variables (Problem Solvers) - Marder

    Both are older books from the 70's although Maron is in print in India, you can find it on ebay.in for example, but the second I could only find shipping from the UK or the USA, I don't know where you could find a paper version of it.

    Another option is to get the book Calculus, One and Several Variables - Salas, Etgen, Hille, you'll find it on ebay.in too.

    If you need better explanations for some things, look at MIT's stuff here and here, or the other versions they have, plus videos of course.

    I should mention that the Marder book may need you to know the one variable material but it definitely looks great to work though. In particular, it has Jacobians and envelopes listed in the contents.
     
    Last edited: Sep 15, 2013
  4. Sep 15, 2013 #3
    This time, I am not in search of any challenging problems in Engineering Calculus. I can't give much time to college studies at the moment, because of the same reasons that I could not attend the lectures. Its difficult to explain my current situation. Its not that I am trying to run away from studies, but the problem is, I have other subjects and topics to take care of.

    I should have checked the syllabus before making my post. The first semester syllabus also include the Integral Calculus. I will copy-paste the syllabus of both the semesters.

    Semester I:
    Semester II:
    As to my knowledge, different books will be assigned for both the semester. Ignoring the Physics part, any nice textbook would be of help.

    Also, does only Marder contains Jacobian and evelopes? I mean no other books deal with them? Can you suggest me some now?

    Thanks verty!
     
  5. Sep 15, 2013 #4

    verty

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    It would help to know exactly what you know already. Do you know one variable calculus? Do you know integration? Or is this the first course you are doing on calculus? I don't see limits or series in that semester 1, so I think you have done calculus before. How well do you know the one variable stuff?
     
  6. Sep 15, 2013 #5
    Yes, I have done calculus before. I very well know one variable stuff and I am good enough at it. I have already done a lot of challenging problems on one variable calculus. I do have some idea about Asymptotes and I have done a few basic exercises on Partial Differentiation and I think I know enough Partial Differentiation to clear my exams. I haven't done Maxima and Minima of two or more variables. I checked it out in the book I am currently assigned and it doesn't seem too difficult. Envelopes, Curvatures and Jacobians are entirely new to me.

    About integral calculus, I have done a lot of problems ranging from easiest to the most challenging ones in the past and I still remember a lot of stuff but I never dealt with Beta and Gamma functions, Rectification, Multiple integrals and Differentiation under the integral sign. I have done a few basic problems on Volume and surface of solids of revolution but I will start it from fresh.

    Does this help?

    PS: You can also have some idea about what I know from the practice sheets I sent you before.
     
  7. Sep 15, 2013 #6

    verty

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    Here's an option for you, the author is a professor at IIT Delhi so it should be good:

    http://justbooks.in/product/textbook-vector-calculus-0 [Broken]

    This is assuming you know the one variable material.
     
    Last edited by a moderator: May 6, 2017
  8. Sep 15, 2013 #7

    verty

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    Okay, I just saw your post above, it helps. Why not read chapters 2 and 3 in that Marder book, it'll cover that stuff that you mentioned. I think you are ready for it.

    Chapters 4 and 5 are integration but it stops a little early, rectification is just line and surface integrals so it'll cover that as well as multiple integrals, but there is more that it doesn't have. I'll look very quickly for something to cover the rest.
     
  9. Sep 15, 2013 #8
    Does all of the above mentioned topics belong to "Vector Calculus"? :confused:

    And don't worry that the book I look for should be by an Indian author. I personally prefer book by foreign authors, feel free to suggest any book. I will look if its available in my country. :)
     
    Last edited by a moderator: May 6, 2017
  10. Sep 15, 2013 #9

    verty

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    In that case, I'll recommend this book instead:

    Mathematical Methods in the Physical Sciences - Boas

    It'll cover what is missing and should also help with the ODE semester.

    About the other question, yes it is all vector calculus (well, asymptotes and envelopes are geometry) except the Beta and Gamma functions, I'm sure you could read about them online. I don't know what asymptotes is about, so I can't say anything about that.
     
  11. Sep 15, 2013 #10
    That should help, thanks a lot for your time verty! :smile:
     
  12. Sep 15, 2013 #11

    verty

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    Sorry, I forgot about curvature. Have a look here (http://ia801507.us.archive.org//33/items/DifferentialAndIntegralCalculus_109/ [Broken]), chapters 5 and 6 for asymptotes and curvature. These geometry topics are not in books I'm familiar with. The other thing is curve tracing which I guess is drawing curves but that should be easy.

    That Piskunov book is available but doesn't look too good, I would just look in those chapters.
     
    Last edited by a moderator: May 6, 2017
  13. Sep 15, 2013 #12
    Thank you again verty! :)

    Do you have some resources for Polar Coordinates?
     
    Last edited by a moderator: May 6, 2017
  14. Sep 15, 2013 #13

    verty

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    Yes, this is easy to answer. Problem set 8A here, do the parametric equations and then the polar coordinate stuff. The lecture notes and part A problems should be enough for you to understand it. There'll be a video too but I don't expect you will need it.

    Obviously I would normally recommend a book to learn all this stuff from but in your case, there isn't a lot of time.
     
  15. Sep 15, 2013 #14
    Thank you! :)
     
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