First principles is what makes engineering similar to scientists, but different from other designers and technologists. We use first principles  scientific knowledge  to provide optimized solutions as explained in my book on being a global engineer.
There are 2 major parts to the use of first principles:
To provide you with insight into how this has come to be, take a look at the video below from the physics lecturer Eric Mazur. It’s not about engineers specifically, but the phenomenon is the same all over.
There are 2 major parts to the use of first principles:
 Knowing the principles and being able to see them at play in the physical world
 Choosing to use them to optimize your engineering solutions (calculating very variable values or even using mathematical modelling to optimize
To provide you with insight into how this has come to be, take a look at the video below from the physics lecturer Eric Mazur. It’s not about engineers specifically, but the phenomenon is the same all over.
As you would have seen in the video, many of us end up not grasping the fundamentals of physics, which are vital to being able to apply first principles as an engineer. The following will give you guidance on how you can correct for this.
Knowing the principles
There are many conceptual tests available that you can use to evaluate your understanding. By completing these tests you can determine the areas of comprehension that you need to work on. Here are some that I have found.
Physics
The following test (and solutions document) has been produced by Paul Hewitt and shared by The Arbor Scientific Team. Go through the test first. Record your answers. Compare them to the solutions. If you get them right, then you're doing OK. If however, you get an answer wrong, then it might be time to hit the text books or talk to colleagues to get yourself back on track.
Physics
The following test (and solutions document) has been produced by Paul Hewitt and shared by The Arbor Scientific Team. Go through the test first. Record your answers. Compare them to the solutions. If you get them right, then you're doing OK. If however, you get an answer wrong, then it might be time to hit the text books or talk to colleagues to get yourself back on track.
The practical use of first principles
First principles are almost always used in the form of mathematics. They can be used as a guideline – keeping the center of mass low to ensure stability of an item – but when you combine it with mathematics, you can predict and optimize performance – calculate the actual tipping angle of an item and know it can’t be any greater, and ensure maximum stability. Therefore, the use of first principles is very much a case of mathematical modelling.
Even though it is based on the most fundamental of sciences (and all the other sciences), mathematical modelling is actually quite an art. That means you can get advice on it, like that given in my book on global engineering, but if you really want to be skilled at it, then you need to:
Nevertheless, it is helpful to see examples and read about how others do it. Thus, here are some texts that can help you.
Even though it is based on the most fundamental of sciences (and all the other sciences), mathematical modelling is actually quite an art. That means you can get advice on it, like that given in my book on global engineering, but if you really want to be skilled at it, then you need to:
 try it,
 be prepared to make a mistake and
 try again.
Nevertheless, it is helpful to see examples and read about how others do it. Thus, here are some texts that can help you.



The first book has a very good chapter on modeling, but is more focused on mechanical related systems. The second book is more general with a focus on optimization, but that might make it harder to see the application to engineering. The third is easy to read, but more closely related to the modeling and control of dynamic systems. Choose the one that you think will help you most.