What are the most fundamental and important formulas to know for a career in aerospace

I can tell you from my own personal experience, and I’m sure many can corroborate, that memorizing formulæ is a waste of time.

As you progress through an education in physics, you start to develop an understanding for different aspects of the universe, and how it works. As you learn more things, you draw an increasing number of connections between these things, which leads to learning more things!

Instead of memorizing equations, it’s easier (and more useful) in the long run to understand the underlying principles.

As an example, I do not have Maxwell’s equations memorized. But because I understand the underlying principles, I can materialize them. E.g. let’s say I’m doing some problem where I need to calculate the charge density of some body, and I know the electric field E. Well, I know that charges act as a source of electric flux. So I can define some arbitrary surface which encloses my charged body, and integrate the field strength over this surface to find the enclosed charge. If I want the charge density specifically I can use the equivalent differential form, which I can find from the divergence theorem (another great example where understanding > memorizing).

At a point, this process almost becomes effectively indistinguishable from memorization. It only takes me a few seconds to reason out in my mind what the symbolic form of Gauss’s law must be — which while externally the same as having it memorized is obviously far more powerful.

Another great example is the differential EoM for a harmonic oscillator. While the SHO has an extremely simple form of d_t2 q + q = 0, I assure you that no one really memorizes this. Instead, people understand what it means for a particle to experience a harmonic potential, and how that corresponds to each of the terms above. A few seconds of thinking is all it takes to pull the EoM out of the air.

There are essentially innumerably many examples of this, and I’m a strong advocate for it. I recommend you dive into some texts and deepen your understanding in whatever areas you have an interest in; the experience is extremely fulfilling.

/r/AskPhysics Thread