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I am wondering if there are any books providing intuitive explanations for PDEs. I have been using Evans' PDE, but it only focuses on how to solve PDEs and some other theoretical properties. I would like to find a book that discusses how to derive certain PDEs (such as the wave equation, Laplace's equation or some more advanced ones, etc.), as well as providing intuitive interpretations for each differential operator (For example: like what $\Delta$ is trying to do in the equation $u_t= \Delta u + u_x$). It doesn't need to be too mathematically rigorous.

My background is in mathematics, and I haven't studied much physics. So, books on physics are also great!

Zorualyh
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  • Partial differential equations: an introduction to theory and applications by Shearer and Levy might be good for you. – Finn Pillar Mar 28 '24 at 19:11
  • There are many good suggestions here too: https://math.stackexchange.com/questions/2827/good-1st-pde-book-for-self-study – Hans Lundmark Mar 29 '24 at 13:14

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There is an absolutely amazing and very mathematically non-rigorous book by Stanley Farlow Partial Differential Equations for Scientists and Engineers. I recommend this book to anyone who wants some intuition but is ok to skip on many mathematical steps. It could be a somewhat too extreme counterpart to Evans' book, but I would still recommend it even for mathematically mature students.

Artem
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