I need advice on my studies of mathematics... I'm really depressed because it's impossible for me to understand many important parts of books such as Tenenbaum & Pollard "Ordinary Differential Equations" or Kreyszig's "Differential Geometry", even after having got an A at a rigorous course in calculus (construction of the reals, limits with epsilon-delta arguments, proofs of almost all theorems presented...).
The reason is that these books on DE and DG use thinks like multiply the two sides of the equation by dx, or integrate dt, consider an infinitesimal displacement, etc, to arrive at conclusions... I really can't understand this reasonings... And I'm now looking at books on mechanics (for engineers) and it's even worse, because they talk about "virtual work", and other impossible-to-understand (for me) things...
What should I do? Relearn calculus from some textbook that teach these things or maybe search other books for learning differential equations, mechanics, and differential geometry? I'm feeling really dumb.
Thanks in advance.