Block Diagram Reduction: Is it necessary to do it stepwise?

Question

Just a short question: Is there any usefulness in doing block diagram reduction piecewise?

The reason I am asking is that I find it much (!) easier to just find the final $\frac{output}{input}$ transfer function using mathematics (the brute force method), but my professor does it stepwise.

If I am to do it stepwise, I still feel like I have to do it mathematically, rendering the stepwise reduction pretty useless as far as I can tell.

I realize this seems like a banal question, but I cannot find anything answering this question is my controls book.

Answer 1

When you are solving a problem in the real world, there are 2 main important requirements

1. Get the correct answer.
2. Solve it using sound methods.

There might be a half-dozen different ways to solve a given problem, so long as you arrive at the correct answer and don't pick a method involving rain dances or Satanic rituals, you are free to pick the method that you find easiest.

However, the requirements in academia are often different. There is a good chance that your professor has a reason for using the method he does. If he asks you to solve a problem step-wise, you should do what he asks.

It's likely that, at a certain point, doing it directly rather than piecemeal becomes overly complex and involves massive equations. At this point, knowing how to do it step-wise becomes necessary, and your professor is preparing you for this. But the only way to know for sure is to ask him.

As I said, beyond this class, the only thing that will matter is getting the correct answer and being able to explain how you arrived at that answer, so if you get the same answer through both methods, both are equally valid.