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In your opinion, with my lack of previous education, would my determination be enough to still consider a degree in Electrical Engineering?
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It's hard to say. You are going to run into classes that are MUCH tougher than you have been exposed to thus far. You are going to need to learn calculus and perhaps linear algebra and differential equations. I think your calculus 1 class will go a long way towards determining if you will have the ability to accomplish your goals in EET. If you can do well in calc 1 and grasp the topics then you should be able to handle calc 2 and calc 3. If you can handle calc 1-3 then you should be able to get by differential equations as well as linear algebra.
In summation, calc 1 and general physics will be you tester classes. If you can perform well in those then you will most likely have the ability to make it through an EET program. Beware, though, a lot of students will get weeded out of calc 1 and general physics so you are going to have to put in a good deal of time in order to ensure that you understand the topics being discussed and to ensure that you perform well on the tests.