Dealing with a mental illness, how much will grad schools care about my improvement?

So I was diagnosed with PTSD from child abuse, and when I first entered college, I needed to heal on several fronts. My grades were not good the first half of my college career, and I focused on a lot more on dealing with my abuse and finding peace with it.

My second half although is a completely different story. Once I felt a lot more control with my mental illness, my academic profile changed a lot. I’m a physics major and math minor. I got on the Dean’s list several times, I started doing research, became a math tutor, and then petitioned into the honors college on a technicality(my in major GPA with physics was really high and I knew my physics) so I was granted permission into honors quantum mechanics and honors electricity and magnetism for my final year next year.

It’s just my cumulative sucks. I came into undergrad as an aerospace engineer, failed classes, got Ds etc. I actually didn’t get into the major but wanted to do space research so switched into physics. I found out I was much more of a scientist than an engineer, and with my therapy flourished in the major.

If I wrote about this in my application and explained my mental illness and my desire to improve as a person, will they take that into consideration?

Yes, but please don’t write it like that.

All you need is a brief 2-3 sentence statement that says you were dealing with an illness in the beginning of your college career, but you have since recovered from such illness. Since you recovered, your performance has improved immensely, which is reflected by [insert metric here]. An example might be something like “During my first two years of college, I was dealing with a serious illness that adversely affected my performance. However, I recovered from that illness during my sophomore year, and subsequently my performance improved by leaps and bounds. My GPA in my last 60 credits is a 3.7, and my physics major GPA is a 3.9.”

And follow with more upbeat/positive language about your research interests and why you are a good fit for the department.

The programs don’t care that you want to improve as a person; they want to know whether you will be a successful PhD student and scientist and what the probability is that you will flame out for whatever reason. You need to give them reason to believe that you will be successful and that you will not flame out.