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Partial differential equations?

  1. May 30, 2014 #1
    Any books that are easy to understand on partial differential equations?
    I just came back from barnes and noble. I briefly looked at the book on partial differential equations, but it is confusing for me because it jumps to topics about partial differentiation that I didn't learn.

    The only experience in partial differentiation is:
    -partial derivatives
    -differentials

    That's about it. Not very much. So is there a book on it that covers the basics and moves onto other related topics with great explanation? I'm not very good at english, but it is the language I read.
     
  2. jcsd
  3. May 30, 2014 #2
    Oh, I forgot. I haven't learned partial differential equations yet. Not even the basic methods of solution. I really don't know much about it, so any books about partial differential equations for beginners is great.
     
    Last edited: May 30, 2014
  4. May 30, 2014 #3
    what about the book: mathematical methods in science and engineering by S. Selcuk Bayin, published by Wiley.
    Or you can find other books about mathematical physics.
     
  5. May 31, 2014 #4

    SteamKing

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    Well, what about ordinary differential equations? Have you studied those yet?
     
  6. May 31, 2014 #5

    HallsofIvy

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    And it would help if you said what "topics about partial differentiation" the book showed that you hadn't learned. Do you know the "chain rule" for partial derivatives?
     
  7. May 31, 2014 #6
    If you want an entry level introduction, I would suggest Asmar's Partial Differential Equations (it's the book we used for the PDE course I took) and a PDF of the solutions is offered. It briefly introduces the basics of differential equations and assumes little knowledge of DE. It introduces many integration techniques like Laplace and z-transforms and applies a lot of Fourier analysis into methods of finding solutions.

    Personally, I don't believe I would of done as well in the course unless I took a course in ordinary differential equations (which you haven't specified). Many ODE require a lot of practice to understand and PDE add more layers to extracting the solutions. In addition, I'm not a mathematician so take my recommendation with a grain of salt.
     
  8. May 31, 2014 #7
    yes I have studied ordinary differential equations
     
  9. May 31, 2014 #8
    @Hallsoflvy I know the chain rule for partial derivatives
     
  10. May 31, 2014 #9

    micromass

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    Last edited by a moderator: May 6, 2017
  11. May 31, 2014 #10
    @micromass I'm asking books for self study. Any other books or suggestions?
     
  12. Jun 1, 2014 #11

    verty

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    Here are some cheap books, I don't know PDE's myself so I'll just comment on what type of books they seem to be.

    https://www.amazon.com/Partial-Diff...1603792&sr=1-12&keywords=partial+differential

    This one looks pretty decent, it seems well organized and has the style I prefer which is to speak using the math. The other style is to try to explain first and use math later, but this can mean that one has more difficulty solving the problems.

    It does have the character of needing one to think about what is being said, what does it mean, why is it relevant. I think the answers are there to be found but it needs some thought as one goes through it. But it seems like the author tries hard to be clear, so it shouldn't be a problem.

    https://www.amazon.com/Partial-Diff...01603792&sr=1-7&keywords=partial+differential

    This one reads more like a graduate book in the sense that not a lot is explained; claims are presented and one is expected to convince oneself that they are true. If you're the type of learner who likes to get it accurately and quickly, this would be good. But for each page you would need to look at each claim, decide why it is true, what is the import, write notes or summaries to allow you to reinforce that knowledge.

    That said, the math used looks accessible so it won't be difficult from that point of view. So more initiative and diligence required but it looks good to me. For example, no reviewer had anything bad to say about it.

    https://www.amazon.com/Introduction...1603792&sr=1-10&keywords=partial+differential

    This one looks more mathy in the sense of following a logical progression and using words like "suppose", "then" and "hence". One reviewer calls it intermediate level but is any PDE book going to be at the beginner level? If you prefer a proof book then this is a cheap option although consider that it seems to progress quite slowly.

    https://www.amazon.com/First-Course...1608239&sr=1-17&keywords=partial+differential

    This older book seems to focus on methods of solving PDE's. Sometimes it is nice when first learning a subject to get a quick view of the practical side of things. It can help when learning theory to be able to say, oh yes, this is the theory of so-and-so which I have seen before. And this book is very cheap. So I think there is no beginner book but this is one way to try to fill in that beginning void.

    -----------------------------------------------------

    Just to say again, treat these as face-value reviews.
     
    Last edited by a moderator: May 6, 2017
  13. Jun 1, 2014 #12

    jasonRF

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    The easiest, friendliest book on PDEs that I know of is the book by Farlow:
    https://www.amazon.com/Differential...eywords=farlow+partial+differential+equations

    It describes what the equations mean and the basic methods of solution. It is NOT deep, but it is easier than every other PDE book I own or have looked at (Weinberger, Strauss, Zachmanaglou & Thoe, Haberman, Carrier and Pearson, ...). See if your library, or even Barnes and Noble has it in stock so you can flip through it to see if it is what you are looking for. If it is too easy, then some of the other suggestions may be better for you.

    The book by Nearing is also worth a look - the chapters I have read are very good, but I haven't looked at the PDE chapter:
    http://www.physics.miami.edu/~nearing/mathmethods/


    Good luck!

    jason
     
    Last edited by a moderator: May 6, 2017
  14. Jun 1, 2014 #13
    Well, the books look nice, book I looked at the preview. They jump ahead to heat equations or something like that, and jumping to those equations really confuses me.

    I only learned partial derivatives and the chain rule related to partial differential equations.
     
  15. Jun 1, 2014 #14
    I second that one
     
    Last edited by a moderator: May 6, 2017
  16. Jun 1, 2014 #15

    jasonRF

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    Perhaps you can give us more details on what exactly you want to learn. The field of Partial Differential Equations is essentially the study of equations such as the heat equation, the wave equation, etc. Perhaps you are looking to learn something different? Perhaps you just want to learn more about multivariable calculus?
     
  17. Jun 1, 2014 #16
    @jasonRF I don't need the applications at all at least for now. I just want to learn how to solve partial differential equations similar to ordinary differential equations. For example, you use various methods to get the general solution.
     
  18. Jun 1, 2014 #17

    jasonRF

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    I think we need more information from you. In my experience, books that satisfy this:
    Will usually
    So I must be misunderstanding what you are looking for. What is it about the heat equation that confuses you? Have you really tried reading the simpler books (especially Farlow)?

    jason
     
  19. Jun 1, 2014 #18
    @jason No, its that I haven't learned the heat equation. I also haven't learned the other equations that are used for applications.

    I will see farlow's book if it is understandable. I am not very good with reading comprehension.
     
  20. Jun 2, 2014 #19

    jasonRF

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    Well, either you will learn about these equations from the applications side first (eg in physics, engineering, chemistry, etc.) or you will learn about them from the mathematics side first (from a PDE book). I am not aware of another option here, although you seem to be looking for one.

    Fortunately, most (or perhaps all?) intro PDE books spend a number of pages deriving some of the equations, discussing what they mean and how they model reality, etc., before jumping into methods of solution. For example, Farlow spends ~30 pages on the heat equation before showing the first method of solution, and also helps the reader interpret what the derived solutions actually mean.

    Finally, there are many different styles of learning. If self-study from books doesn't work well for you, perhaps it makes sense for you to look for online videos from PDE courses?

    jason
     
  21. Jun 2, 2014 #20
    After a first course in differential equations, I think the three books by RV Churchill and JW Brown (Complex Variable and Applications, Fourier Series and Boundary Value Problems, Operational Mathematics) and its Schaum's Outline accompaniment by M Spiegel (Complex Variable, Fourier Series, Laplace Transforms) will make a nice follow up. The Schaum's Outlines is particularly suitable for self study.

    For PDE, if you want something deeper than Farlow, I recommend RB Guenther & JW Lee, F John, and J Kevorkian. These three texts complement each other nicely.
     
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