<p>Your question probably would be better answered at physicsforums. </p>
<p>I haven’t used it so I can’t vouch for it personally, but the undergraduate course on PDEs at my school uses the book Partial Differential Equations: An Introduction by Strauss. Looking at the first few pages that Amazon lets me look at, the book doesn’t look like a technical math major book (it isn’t definition-theorem-proof the whole way through).</p>