I've read this book. It's definitely one of the more interesting and readable maths texts out there. I wasn't exactly sure I'd use the methods. Working as a mechanical engineer I probably go straight to numerical methods, or approximate things even more crudely and approximately than a mathematician's 'rough' work. Though "replace a complicated function with a rectangle" definitely resonated. Overall the impression was that it was full of great techniques for mathematicians and scientists puzzling out every bit of meaning they can from a situation whose true features aren't yet known.
That's kind of how I do maths, too. Working out the lengths of antenna feeders, for example, where a coil of cable is about 30cm across. One turn of that is about one metre, so a coil with ten turns is about ten metres. Roughly. Close enough. I can coil it up shorter but I can't coil it up longer.
If I'm doing really precise stuff, I'm either doing it on a computer already or it's something that's just going to have to be "adjusted" into place when it's done.
In high school my maths teacher said "You'll need to learn all this, you won't always have a calculator!"
My dude, I am walking around with a supercomputer the size of half a slice of bread in my pocket, that probably has a sizeable fraction of the total computing power available in the world when you told me that.
It turns out I don't need either of these things, I just need a good sense of "yeah that feels about right".
