Physics Not Presented Rigorously Enough

[liorde]

I am a physics student, doing my graduate degree.
I am wondering if anyone else feels like me concerning the following topic:
Physics is usually presented in a very imprecise way, and it would be much easier to understand if it would be presented more precisely.

I felt this way towards all my physics courses so far, and I refer both to lecturers and to textbooks.
I wish physics would be taught in a much more rigorous way.
An example which I encountered recently is the Lagrangian formalism of the electromagnetic field. From the standard notation it is very hard to understand, for example, if the Lagrangian density is a function of the type $${ℝ^n} \to ℝ$$ or of the type $$\left\{ {{ℝ^m} \to ℝ} \right\} \to ℝ$$ Or with respect to what exactly do I differentiate in the expression $$\frac{{\partial {\cal L}\left( {\phi \;,\;{\partial ^\mu }\phi } \right)}}{{\partial \phi }}$$ etc. (I am not requesting for answers on these issues. I'm jut trying to give an example).
For me, personally, physics would be much easier to cope with if it were presented more precisely and rigorously.

Do you agree?
What do you think is the reason that physicists tend to be so fuzzy and unclear in their definitions?

 

[WannabeNewton]

Correct me if I'm wrong but your example seems to be more of an issue with computation than theory? I know what you mean though: when I first saw Lagrangian densities in the specific case of GR where you are told to vary it with respect to a 2 - tensor field I was like how the heck do I do that o.0 but then I found another book that worked through the computation and it became more clear so maybe your textbook(s) just don't have enough worked examples? Then again that seems to be the case with many grad texts. I have seen, in my opinion anyways, that when mathematicians write physics related books, the expositions and theorems / proofs tend to be much neater with no beating around the bush or hand - waving and the ideas are presented more rigorously (Arnold's classical mechanics text in particular comes to mind and especially Burgess's text on classical co-variant fields). I really don't know why; I used to think it was to put more emphasis on physical concepts but to be honest I see more math than physical concepts in many of these graduate physics texts anyways.