I don't know much more about Analysis than what I've read about it on Wikipedia, although I have just begun reading Introduction to Calculus and Analysis I, by Richard Courant.
My understanding is that Analysis is mostly concerned with Calculus topics on a much more rigorous level: mainly the study of proofs for the theorems and concepts that comprise Calculus.
If that is true, how are proofs applied to real-world, practical problems? I guess I'm either confused in my understanding of what Analysis is, or don't understand how it is useful in a practical sense.
I've heard people say that "Analysis just covers virtually the same topics as Calculus, but at a more in-depth level," but what I've read about it on Wikipedia makes me skeptical about these claims. Is it true that Analysis is just a sort of more in-depth/thorough version of Calculus?