Complex numbers have probably their most useful application in engineering because without them we can't model damped or forced oscillations (amongst plenty of other things(. Differentiation (the process of finding derivatives) is used by statisticians to analyse things like population growth and their findings on that kind of thing are often important to the running of a country. Integration's main use is solving the differential equations that describe the material world (and also for slightly less significant but equally useful purposes such as finding centres of mass of complicated bodies).

I can't suggest a book because I don't know of one, all of that came straight from my head.