Studying analysis gives you more tools to model changing systems. The more tools you have, the easier it is to abstract things. That's really all applied mathem

Studying analysis gives you more tools to model changing systems. The more tools you have, the easier it is to abstract things. That's really all applied mathematics is, abstracting stuff to things you can do mathematical operations on. When counting sheep, all you're really do is abstracting the sheep as units and then performing simple arithmetic. So why should you have all these tools to abstract stuff? Because you want to do something new and innovative. If this really isn't that interesting to you then don't bother but every time I find a new way to model something and try it out (often with unsuccessful result, though) I get giddy with joy. The few times I come up with something new and people actually value what I've contributed with it feels like heaven, however small these contributions end up being.