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I am studying Partial DE for my Master's.

I face a lot of difficulties in understanding them. It is the first time I am studying in my academic studies.

My main goal is to understand when systems are well placed, to be able to solve Cauchy problems, IV problems, and like this. I would like the book contains examples with solutions.

I would like to ask if there is a good book for a beginner, written as simply as possible, in Partial DE. I am interested if there is such a book with examples in Mathematica that I use to understand deeper the problems I solve.

Preferred to be an e-book.

Thank you in advance!!!

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    $\begingroup$ Just to be clear, you want a book on Mathematics, with solved exercises that also contains solutions in Mathematica? So a mathematics plus coding book? $\endgroup$
    – bmf
    Commented Dec 23, 2022 at 1:04

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You seem to be confusing two things. Learning PDE's and using a CAS to obtain a solution for a PDE.

If you use Mathematica for example to obtain an answer for a PDE, you will not learn anything about how to solve a PDE. Mathematica is blackbox that takes in a PDE and returns back the solution. It does not teach you how to solve the PDE.

There are many books that are good to learn PDE from math point of view. Below is what I liked. For learning how to use Mathematica to solve PDE's, the best thing is to just look at examples of how to enter the PDE's into Mathematica.

V 13.2 has fully updated documentation page for this. Here is the link

https://reference.wolfram.com/language/tutorial/DSolveOverview.html

There is a whole page/section on PDE's

https://reference.wolfram.com/language/tutorial/DSolvePartialDifferentialEquations.html

As for books on PDE's with Mathematica code, there are many out there. One I used is

Partial Differential Equations With Mathematica by Dimitri Vvedensky
enter image description here

But if you go to Amazon book search and type "Mathematica partial" in the title search, you'll get all of them

https://www.amazon.com/s?i=stripbooks&rh=p_28%3AMathematica+partial+differential&s=relevanceexprank&Adv-Srch-Books-Submit.x=33&Adv-Srch-Books-Submit.y=11&unfiltered=1&ref=sr_adv_b

As for math books about PDE's, I liked these

Partial Differential Equations: Sources and Solutions by David Snide

https://www.amazon.com/gp/product/0486453405?tag=collectorzapp-20

enter image description here

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Richard Haberman

https://www.amazon.com/Differential-Equations-Boundary-Problems-Featured/dp/0321797051

enter image description here

For code examples how to use DSolve to solve PDE's, the best is to look at help and look at the examples. Here are some direct links

https://reference.wolfram.com/language/tutorial/DSolveWorkingWithDSolve.html

https://reference.wolfram.com/language/ref/DSolve.html

There is also a page out there written by someone with over 2,000 PDE's all typed in with answer and some even solved by hand. Partial Dfferential Equations UsingMathematica

Best way to learn how to solve pde's is not to use Mathematica or Maple first. But to learn how to solve them by hand. Use Mathematica to verify your hand solution and to help you to overcome some math problems you are having with your hand solution. As far as I know, Wolfram alpha does not show step by step solutions to PDE's. At least last time I tried it did not do that.

The above resources should keep you busy for long time.

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