Rigorous mathematical treatments of engineering topics I started out as an engineering student and got interested in mathematics. So after some point (Rigorous analysis and linear algebra, some real analysis, basic measure theory and topology etc.) I thought it would be nice if I could turn all of my engineering knowledge into mathematical knowledge. So I'm looking for books with rigorous mathematical treatments of topics such as Mechanics, Thermodynamics, Control Systems, Dynamical Systems.... 
Ideally I'm looking for books that are not just a sequence of theorems and proofs in computer-testable form, but rather ones where the theorems and definitions are motivated. Also since each of the topics I mentioned is a mathematical field in itself I would say "nothing too advanced". For example when by "dynamical systems" I don't mean a book for graduate students in ergodic theory.
Thanks

Control theory is quite rigorous, one of the more mathematical areas of engineering. Eduardo Sontag's "Mathematical Control Theory: Deterministic Finite Dimensional Systems" is a textbook written by a mathematician that covers a lot of the field. It is not too advanced or too specialized. I can't think of a better place to start. http://www.math.rutgers.edu/~sontag/mct.html
