I am an aerospace/electrical engineer. When I took PDEs, I found I needed to review ODEs because you have to be able to solve ODEs in your sleep, to begin to solve PDEs. But since you are a math major...
I can understand your frustration at the way they just throw bits and pieces of physics at you while teaching you PDEs. But you will find that you really need to ignore that nagging feeling that there is something you are missing and try to understand the phenomena only in terms of the PD equations only. These equations were developed hundreds of years ago in some cases. They are based on somewhat hazy ideas like The Caloric Fluid that turned out to be right in application even though they now seem wrong in reality. Enjoy the somewhat ephemeral, soft nature of the physics concepts presented in PDE class. Ultimately, the only reality you are interested in, is the one described by the bare PDEs you work with. After you can do that, you then have the tool to learn physics.
Of course, the only thing that really cures that nagging feeling is to fail a few tests.
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I am an aerospace/electrical engineer. When I took PDEs, I found I needed to review ODEs because you have to be able to solve ODEs in your sleep, to begin to solve PDEs. But since you are a math major... I can understand your frustration at the way they just throw bits and pieces of physics at you while teaching you PDEs. But you will find that you really need to ignore that nagging feeling that there is something you are missing and try to understand the phenomena only in terms of the PD equations only. These equations were developed hundreds of years ago in some cases. They are based on somewhat hazy ideas like The Caloric Fluid that turned out to be right in application even though they now seem wrong in reality. Enjoy the somewhat ephemeral, soft nature of the physics concepts presented in PDE class. Ultimately, the only reality you are interested in, is the one described by the bare PDEs you work with. After you can do that, you then have the tool to learn physics. Of course, the only thing that really cures that nagging feeling is to fail a few tests.
That was very interesting. Not a lawyer my ass.