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## Main Question or Discussion Point

I'm looking for recommendations about advanced calculus books. I'm interested in going further and deeper than nth-order linear differential equations, but overall as a Physics student I'm deeply interested in being very, very comfortable dealing with line, surface and volume integration.

Specifically, my biggest concerns at the moment are two:

1. Applying methods to solve linear and surface integrals without really understanding why they work.

2. I have the feeling that when it comes to this kind of integrals, the hardest part is parametrizing the geometrical object, so I want to be "fluent" at that.

Let me also tell you that I might be a physics student, but I don't like seeing mathematics as a mere tool. Maths without proofs or foundation is like putting an end to the hunger without eating, so I want my books to tell me why we do things this or that way, not just giving me solution recipes.

Thank you very much. :)

Specifically, my biggest concerns at the moment are two:

1. Applying methods to solve linear and surface integrals without really understanding why they work.

2. I have the feeling that when it comes to this kind of integrals, the hardest part is parametrizing the geometrical object, so I want to be "fluent" at that.

Let me also tell you that I might be a physics student, but I don't like seeing mathematics as a mere tool. Maths without proofs or foundation is like putting an end to the hunger without eating, so I want my books to tell me why we do things this or that way, not just giving me solution recipes.

Thank you very much. :)