Zill & Cullen's "Differential Equations with Boundary Value Problems" has good PDE applications (9th chapter onwards), including the heat/wave/etc. equations mentioned. It should be a good starting point to bridge where you currently are with a physical basis (they uncover what the equations physically represent with some mini-derivations). I used 4th ed.
I would be surprised if Arfken didn't hit this.
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Zill & Cullen's "Differential Equations with Boundary Value Problems" has good PDE applications (9th chapter onwards), including the heat/wave/etc. equations mentioned. It should be a good starting point to bridge where you currently are with a physical basis (they uncover what the equations physically represent with some mini-derivations). I used 4th ed. I would be surprised if Arfken didn't hit this.