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I'm looking for an easy to read undergraduate book on partial differential equations, ideally something that is not much harder than a multivariable calculus/ordinary differential equations book.

I am preparing for a course which is using the text by Walter Strauss, but I found this text a bit difficult to read. Specifically, I found that many of the derivations were missing steps that were not obvious to me or provided little justification for the manipulations. When I searched for introductory books however the Strauss book seems to be recommended.

Google seems to recommend, among others:

  • Partial Differential Equations for Scientists and Engineers by Farlow
  • Introduction to Partial Differential Equations by Peter Olver

I have ruled out:

  • Partial Differential Equations: An Introduction by Walter Strauss
  • An Introduction to Partial Differential Equations by Michael Renardy
  • Partial Differential Equations by Fritz John
  • Partial Differential Equations by Lawrence C Evans

My background is having read A First Course in Differential Equations with Modelling Applications by Dennis Zill. Would I be better off reading the extended version of this book (Differential Equations with Boundary Value Problems)? I was a little bit hesitant because I was not sure how relevant the book is to PDEs. The chapters I have not read are Fourier Series, Boundary Value Problems in Rectangular Coordinates, Boundary Value Problems in Other Coordinate Systems, Integral Transforms and Numerical Solutions of Partial Differential Equations.

EDIT: I ended up finishing about half the book, which is everything covered in my course, Chapters 1 through 7.

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  • $\begingroup$ The book by L C Evans was used as a textbook when I took PDE $\endgroup$
    – P. J.
    Feb 16 '21 at 12:22
  • $\begingroup$ I think you would benefit greatly by reading the chapters in the extended version of Zill. You would get a nice overview of the subject, and everything you learned would be relevant to the course you're going to take. I've never looked at Zill, but I'm sure it's fine. $\endgroup$
    – B. Goddard
    Feb 16 '21 at 12:26
  • $\begingroup$ I think B. Goddard is right, but also perhaps you should be given some encouragement to stick with Strauss. A book that leaves some steps out trains you to figure those steps out yourself. And it is guaranteed to help with your future class. I'll also mention that there's a solution manual if you look hard enough... $\endgroup$ Feb 16 '21 at 12:38
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    $\begingroup$ It's Fritz John, not John Fritz. That's a good book, but it's more advanced than Strauss. Generally speaking, you can rule out any book mentioned here: mathoverflow.net/questions/72318/…. But you might get some useful suggestions here instead: math.stackexchange.com/questions/2827/…. $\endgroup$ Feb 16 '21 at 13:47
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Personally I am quite fond of Evan's Partial differential equations as an introductory textbook.

I would not expect to find something really "easy to read", though, simply because the subject matter tends not be all that easy.

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    $\begingroup$ Evans is a great book but if OP is having trouble with the Strauss book (Ch 1: "Where PDEs come from", Ch 2: 1D Wave eq, Ch 3: Heat equation on $(0,\infty)$, Ch 4: Introduction of separation of variables...Ch 10: generalisation to 2D) then there's going to be blood sweat and tears on reading Evans $\endgroup$ Feb 16 '21 at 12:31
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I agree with the advice to continue with the Zill book, and to fill in steps in math books such as Strauss, but if you want something really easy, I have some lecture notes on differential equations at http://bterrell.net that introduce various topics in ODE and PDE by focusing on some applications.

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For undergraduate level, the book "Partial Differential Equations An Introduction" by Walter A. Strauss is decent and is highly recommended

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