I was wondering if there is a book out there that doesn't teach you how to do calculus, but teaches you how to apply it in the physical or social sciences.
I know calculus, integration and differentiation and the applications for each, but I struggle to find a book that teaches me how to use calculus to derive my own mathematical models.
I think it will be easier to give an example:
Imagine a spinning rod with uniform mass with length, $L$. To find the kinetic energy of the rod I know that each part of the rod moves at a different speed, and therefore the entire kinetic energy of the rod is the sum of all the infinitesimals of little sections on the rod.
I am not going to solve this problem, because this isn't the question on hand, but the point is is that I am looking for a book that teaches you, and challenges you to use your already knowledge of calculus to solve problems like this?
Hope I am making myself clear, and any input would greatly be appreciated.