It's great to hear someone with the same diploma (or at least an equivalent -- I'll have 2-3 years of EET in college) can get a good job! I'm certainly willing to work from the bottom up, but I definitely want to end up somewhere I love! I have been thinking a lot about careers and what I want to do after school and it's definitely hard to decide. I'll have to see how I feel as time goes by.
To second what everyone else has said above, Congrats! And I hope you find real satisfaction in your new job!
I'm 37, so figure about 20 years of persistent effort. The most important part of my experience was that I owned a small business as an engineering contractor. I built switch-mode power supplies, detectors, audio amplifiers, signal processors and many other "things" over the years. I also spent time as a repair technician so I can also fix nearly anything (but not everything is worth fixing).
You basically has to be
carefully discontent with your current situation and be willing to put in the work. Also, being able to ignore people that say you're wasting time is a plus.
I'm sure I've said it before, but my lack of education is not for lack of trying. I was the first in my family to go to college (and so far the only to graduate). My family was poor and there was no expectation of getting out of the ghetto. I literally made up my mind that I WILL become an engineer, however I can. I was an average student and not so good at math. It wasn't until just before college that I learned that math was the key to future success in engineering. Do I use longhand? Hell no! I use a calculator just like everyone else.
I was also a forum whore for years, contributing many thousands of posts of good data to various topics. It forced me to investigate, experiment and verify my claims. Being able to communicate effectively on a forum has done wonders in communicating with suppliers over email. I will use the phone if necessary, but I have fulfilled whole contracts using email. Writing skills are a huge requirement in today's job market.
Finally, you need to be more than just an engineer. One of the most overlooked aspects of engineering is the ability to verbally communicate concepts. For an applications engineer, being able to travel to a customer site with the sales rep and client and not stare at the floor is imperative. That's not to say you have to be gregarious, you just have to present a good front for the company. I am a dedicated yet emotionally detached employee. I care, but not too much. Besides, I'm not trying to climb the corporate ladder. I've got a family that I love and will not sacrifice any family time for the company. I can always climb that ladder after the kids are grown.